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<!DOCTYPE html>
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<meta charset="UTF-8" />
<title>Filtering » Binary image filters module | DIPlib | a library for quantitative image analysis</title>
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<a href="https://diplib.org"><img src="DIPlib_logo.svg" alt="" />DIPlib</a><span class="m-breadcrumb">┃</span><a href="index.html" class="m-thin">a library for quantitative image analysis</a><span class="m-breadcrumb">┃</span><a href="https://github.com/DIPlib/diplib/releases/tag/3.6.0" class="m-thin">version 3.6.0</a> </span>
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<h1>
<span class="m-breadcrumb"><a href="filtering.html">Filtering</a> »</span>
Binary image filters <span class="m-thin">module</span> <div class="m-doc-include m-code m-thin m-text-right">#include <a href="file--diplib--binary-h.html">"diplib/binary.h"</a></div>
</h1>
<p>Processing binary images, including binary mathematical morphology.</p>
<div class="m-index m-block m-default">
<h3>Contents</h3>
<ul>
<li>
Reference
<ul>
<li><a href="#nested-classes">Classes</a></li>
<li><a href="#alias-members">Aliases</a></li>
<li><a href="#function-members">Functions</a></li>
</ul>
</li>
</ul>
</div>
<section id="nested-classes">
<h2>Classes</h2>
<dl class="m-doc">
<dt>
class <a href="dip-Interval.html" class="m-doc">dip::<wbr />Interval</a>
</dt>
<dd>Represents the shape of an interval for inf-generating and sup-generating operators. <a href="dip-Interval.html#dip-Interval">more...</a></dd>
</dl>
</section>
<section id="alias-members">
<h2>Aliases</h2>
<dl class="m-doc">
<dt>
using <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::<wbr />IntervalArray</a> = std::vector<Interval>
</dt>
<dd>An array of intervals.</dd>
</dl>
</section>
<section id="function-members">
<h2>Functions</h2>
<dl class="m-doc">
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryAreaClosing-Image-CL-Image-L-dip-uint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryAreaClosing</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> filterSize,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& s_edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Computes the area closing of a binary image, by calling <a href="binary.html#dip-BinaryAreaOpening-Image-CL-Image-L-dip-uint--dip-uint--String-CL"><code>dip::BinaryAreaOpening</code></a> on the inverse
of the input image.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryAreaOpening-Image-CL-Image-L-dip-uint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryAreaOpening</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> filterSize,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Computes the area opening of a binary image <a href="#dip-BinaryAreaOpening-Image-CL-Image-L-dip-uint--dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryClosing-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryClosing</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::SPECIAL)</span>
</dt>
<dd>Binary morphological closing operation. <a href="#dip-BinaryClosing-Image-CL-Image-L-dip-sint--dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryDilation-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryDilation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Binary morphological dilation operation. <a href="#dip-BinaryDilation-Image-CL-Image-L-dip-sint--dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryErosion-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryErosion</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::OBJECT)</span>
</dt>
<dd>Binary morphological erosion operation. <a href="#dip-BinaryErosion-Image-CL-Image-L-dip-sint--dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryOpening-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryOpening</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::SPECIAL)</span>
</dt>
<dd>Binary morphological opening operation. <a href="#dip-BinaryOpening-Image-CL-Image-L-dip-sint--dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-BinaryPropagation-Image-CL-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc">dip::<wbr />BinaryPropagation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& inSeed,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& inMask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = 1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Morphological propagation of binary objects. <a href="#dip-BinaryPropagation-Image-CL-Image-CL-Image-L-dip-sint--dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-BoundaryPixelInterval2D" class="m-doc">dip::<wbr />BoundaryPixelInterval2D</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Interval.html" class="m-doc">dip::Interval</a></span>
</dt>
<dd>Returns a 2D interval for detecting boundary pixels. <a href="#dip-BoundaryPixelInterval2D">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-BranchPixelInterval2D" class="m-doc">dip::<wbr />BranchPixelInterval2D</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns a 2D interval array for detecting branch pixels. <a href="#dip-BranchPixelInterval2D">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-ConditionalThickening2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL" class="m-doc">dip::<wbr />ConditionalThickening2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& c_in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& c_mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& endPixelCondition = S::LOSE,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Thickens the image <code>in</code> conditioned on the mask (2D only). <a href="#dip-ConditionalThickening2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-ConditionalThinning2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL" class="m-doc">dip::<wbr />ConditionalThinning2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& endPixelCondition = S::LOSE,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Thins the image <code>in</code> conditioned on the mask (2D only). <a href="#dip-ConditionalThinning2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-ConvexHullInterval2D" class="m-doc">dip::<wbr />ConvexHullInterval2D</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns a 2D interval array to thicken to a convex hull. <a href="#dip-ConvexHullInterval2D">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL" class="m-doc">dip::<wbr />CountNeighbors</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& mode = S::FOREGROUND,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Counts the number of set neighbors for each pixel in the binary image <code>in</code>. <a href="#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-EdgeObjectsRemove-Image-CL-Image-L-dip-uint-" class="m-doc">dip::<wbr />EdgeObjectsRemove</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& c_in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 1)</span>
</dt>
<dd>Remove edge objects from a binary or labeled image. <a href="#dip-EdgeObjectsRemove-Image-CL-Image-L-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-EndPixelInterval2D-dip-uint-" class="m-doc">dip::<wbr />EndPixelInterval2D</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns an interval array for detecting end pixels. Includes isolated pixels. <a href="#dip-EndPixelInterval2D-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL" class="m-doc">dip::<wbr />EuclideanSkeleton</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& endPixelCondition = S::NATURAL,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Accurate binary skeleton (2D and 3D only). <a href="#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-FillHoles-Image-CL-Image-L-dip-uint-" class="m-doc">dip::<wbr />FillHoles</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 1)</span>
</dt>
<dd>Fill holes in binary image. <a href="#dip-FillHoles-Image-CL-Image-L-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-GetBranchPixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc">dip::<wbr />GetBranchPixels</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Returns the branch pixels in the skeleton image <code>in</code>. That is, the set pixels with more than two neighbors. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-GetEndPixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc">dip::<wbr />GetEndPixels</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Returns the end pixels in the skeleton image <code>in</code>. That is, the set pixels with one neighbor. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-GetLinkPixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc">dip::<wbr />GetLinkPixels</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Returns the link pixels in the skeleton image <code>in</code>. That is, the set pixels with two neighbors. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-GetSinglePixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc">dip::<wbr />GetSinglePixels</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Returns the isolated pixels in the binary image <code>in</code>. That is, the set pixels with zero neighbors. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-HomotopicEndPixelInterval2D-dip-uint-" class="m-doc">dip::<wbr />HomotopicEndPixelInterval2D</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns an interval array for detecting end pixels. Excludes isolated pixels <a href="#dip-HomotopicEndPixelInterval2D-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-HomotopicInverseEndPixelInterval2D-dip-uint-" class="m-doc">dip::<wbr />HomotopicInverseEndPixelInterval2D</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns an interval array for detecting end background pixels. Excludes isolated pixels. <a href="#dip-HomotopicInverseEndPixelInterval2D-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-HomotopicThickeningInterval2D-dip-uint-" class="m-doc">dip::<wbr />HomotopicThickeningInterval2D</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns a 2D interval array for homotopic thickening. <a href="#dip-HomotopicThickeningInterval2D-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-HomotopicThinningInterval2D-dip-uint-" class="m-doc">dip::<wbr />HomotopicThinningInterval2D</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2) -> <a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a></span>
</dt>
<dd>Returns a 2D interval array for homotopic thinning. <a href="#dip-HomotopicThinningInterval2D-dip-uint-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-InfGenerating-Image-CL-Image-L-Interval-CL-String-CL" class="m-doc">dip::<wbr />InfGenerating</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Inf-generating operator, the dual of the hit-miss operator. <a href="#dip-InfGenerating-Image-CL-Image-L-Interval-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-IntersectionInfGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL" class="m-doc">dip::<wbr />IntersectionInfGenerating</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Intersection of inf-generating operators. <a href="#dip-IntersectionInfGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-IntersectionInfGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL" class="m-doc">dip::<wbr />IntersectionInfGenerating2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Intersection of inf-generating operators. <a href="#dip-IntersectionInfGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="dip-Interval.html#dip-Invert-IntervalArray-L" class="m-doc">dip::<wbr />Invert</a>(</span><span class="m-doc-wrap"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a>& array)</span>
</dt>
<dd>Inverts the intervals in the array, swapping foreground and background pixels. Works correctly
if intervals in the array share data. However, this function could also affect other intervals not in
the array, if data is shared.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-IsotropicClosing-Image-CL-Image-L-dfloat-" class="m-doc">dip::<wbr />IsotropicClosing</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance)</span>
</dt>
<dd>Isotropic closing of binary image. <a href="#dip-IsotropicClosing-Image-CL-Image-L-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-IsotropicDilation-Image-CL-Image-L-dfloat-" class="m-doc">dip::<wbr />IsotropicDilation</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance)</span>
</dt>
<dd>Isotropic dilation of binary image. <a href="#dip-IsotropicDilation-Image-CL-Image-L-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-IsotropicErosion-Image-CL-Image-L-dfloat-" class="m-doc">dip::<wbr />IsotropicErosion</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance)</span>
</dt>
<dd>Isotropic erosion of binary image. <a href="#dip-IsotropicErosion-Image-CL-Image-L-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-IsotropicOpening-Image-CL-Image-L-dfloat-" class="m-doc">dip::<wbr />IsotropicOpening</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance)</span>
</dt>
<dd>Isotropic opening of binary image. <a href="#dip-IsotropicOpening-Image-CL-Image-L-dfloat-">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-MajorityVote-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc">dip::<wbr />MajorityVote</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND)</span>
</dt>
<dd>Filters the binary image by setting each pixel to the phase with more pixels in the neighborhood. <a href="#dip-MajorityVote-Image-CL-Image-L-dip-uint--dip-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-SinglePixelInterval-dip-uint-" class="m-doc">dip::<wbr />SinglePixelInterval</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> nDims = 2) -> <a href="dip-Interval.html" class="m-doc">dip::Interval</a></span>
</dt>
<dd>Returns an interval for detecting single pixels. Use with <a href="binary.html#dip-SupGenerating-Image-CL-Image-L-Interval-CL-String-CL"><code>dip::SupGenerating</code></a> to detect isolated
pixels. Note that <a href="binary.html#dip-GetSinglePixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetSinglePixels</code></a> is more efficient.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-SupGenerating-Image-CL-Image-L-Interval-CL-String-CL" class="m-doc">dip::<wbr />SupGenerating</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Sup-generating operator, also known as hit-miss operator. <a href="#dip-SupGenerating-Image-CL-Image-L-Interval-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL" class="m-doc">dip::<wbr />Thickening</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Applies the thickening operator, optionally constrained by a mask, to an image. <a href="#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-Thickening2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL" class="m-doc">dip::<wbr />Thickening2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Applies the thickening operator, optionally constrained by a mask, to an image. <a href="#dip-Thickening2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL" class="m-doc">dip::<wbr />Thinning</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Applies the thinning operator, optionally constrained by a mask, to an image. <a href="#dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-Thinning2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL" class="m-doc">dip::<wbr />Thinning2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Applies the thinning operator, optionally constrained by a mask, to an image. <a href="#dip-Thinning2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-UnionSupGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL" class="m-doc">dip::<wbr />UnionSupGenerating</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Union of sup-generating operators. <a href="#dip-UnionSupGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL">more...</a></dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-UnionSupGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL" class="m-doc">dip::<wbr />UnionSupGenerating2D</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in,
<a href="dip-Image.html" class="m-doc">dip::Image</a>& out,
<a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS)</span>
</dt>
<dd>Union of sup-generating operators. <a href="#dip-UnionSupGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL">more...</a></dd>
</dl>
</section>
<section>
<h2>Function documentation</h2>
<section class="m-doc-details" id="dip-BinaryDilation-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryDilation-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryDilation</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Binary morphological dilation operation.</p>
<p>The <code>connectivity</code> parameter defines the metric, that is, the shape of
the structuring element (see <a href="concepts.html#connectivity">Connectivity</a>). Alternating connectivity
is only implemented for 2D and 3D images.</p>
<p>The <code>edgeCondition</code> parameter specifies whether pixels past the border of the image should be
treated as object (by passing <code>"object"</code>) or as background (by passing <code>"background"</code>).</p>
<p>For dilations with arbitrary structuring elements, see <a href="morphology.html#dip-Dilation-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Dilation</code></a>, for dilations with an isotropic (disk)
structuring element, see <a href="binary.html#dip-IsotropicDilation-Image-CL-Image-L-dfloat-"><code>dip::IsotropicDilation</code></a>.</p>
<aside class="m-note m-info">
<h4>Attention</h4>
<p>This algorithm exists for historical reasons. <a href="morphology.html#dip-Dilation-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Dilation</code></a> with a diamond, square or octagonal
structuring element is always faster.</p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-BinaryErosion-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryErosion-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryErosion</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::OBJECT</span>) </h3>
<p>Binary morphological erosion operation.</p>
<p>The <code>connectivity</code> parameter defines the metric, that is, the shape of
the structuring element (see <a href="concepts.html#connectivity">Connectivity</a>). Alternating connectivity
is only implemented for 2D and 3D images.</p>
<p>The <code>edgeCondition</code> parameter specifies whether pixels past the border of the image should be
treated as object (by passing <code>"object"</code>) or as background (by passing <code>"background"</code>).</p>
<p>For erosions with arbitrary structuring elements, see <a href="morphology.html#dip-Erosion-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Erosion</code></a>, for erosions with an isotropic (disk)
structuring element, see <a href="binary.html#dip-IsotropicDilation-Image-CL-Image-L-dfloat-"><code>dip::IsotropicDilation</code></a>.</p>
<aside class="m-note m-info">
<h4>Attention</h4>
<p>This algorithm exists for historical reasons. <a href="morphology.html#dip-Erosion-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Erosion</code></a> with a diamond, square or octagonal
structuring element is always faster.</p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-BinaryClosing-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryClosing-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryClosing</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::SPECIAL</span>) </h3>
<p>Binary morphological closing operation.</p>
<p>The <code>connectivity</code> parameter defines the metric, that is, the shape of
the structuring element (see <a href="concepts.html#connectivity">Connectivity</a>). Alternating connectivity
is only implemented for 2D and 3D images.</p>
<p>The <code>edgeCondition</code> parameter specifies whether pixels past the border of the image should be
treated as object (by passing <code>"object"</code>) or as background (by passing <code>"background"</code>).
Additionally, you can set it to <code>"special"</code> for special handling:
<code>"background"</code> for the dilation, <code>"object"</code> for the erosion; this avoids the border
effect you can get in the corners of the image in some cases.</p>
<p>For closings with arbitrary structuring elements, see <a href="morphology.html#dip-Closing-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Closing</code></a>.</p>
<aside class="m-note m-info">
<h4>Attention</h4>
<p>This algorithm exists for historical reasons. <a href="morphology.html#dip-Closing-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Closing</code></a> with a diamond, square or octagonal
structuring element is always faster.</p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-BinaryOpening-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryOpening-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryOpening</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = -1, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 3, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::SPECIAL</span>) </h3>
<p>Binary morphological opening operation.</p>
<p>The <code>connectivity</code> parameter defines the metric, that is, the shape of
the structuring element (see <a href="concepts.html#connectivity">Connectivity</a>). Alternating connectivity
is only implemented for 2D and 3D images.</p>
<p>The <code>edgeCondition</code> parameter specifies whether pixels past the border of the image should be
treated as object (by passing <code>"object"</code>) or as background (by passing <code>"background"</code>).
Additionally, you can set it to <code>"special"</code> for special handling:
<code>"object"</code> for the erosion, <code>"background"</code> for the dilation; this avoids the border
effect you can get in the corners of the image in some cases.</p>
<p>For openings with arbitrary structuring elements, see <a href="morphology.html#dip-Opening-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Opening</code></a>.</p>
<aside class="m-note m-info">
<h4>Attention</h4>
<p>This algorithm exists for historical reasons. <a href="morphology.html#dip-Opening-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Opening</code></a> with a diamond, square or octagonal
structuring element is always faster.</p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-IsotropicDilation-Image-CL-Image-L-dfloat-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-IsotropicDilation-Image-CL-Image-L-dfloat-" class="m-doc-self">dip::<wbr />IsotropicDilation</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance</span>) </h3>
<p>Isotropic dilation of binary image.</p>
<p>Does a threshold of the <a href="distance.html#dip-EuclideanDistanceTransform-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanDistanceTransform</code></a> of the background of <code>in</code>.
This is much faster than applying <a href="morphology.html#dip-Dilation-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Dilation</code></a> with a disk structuring element of diameter <code>2 * distance</code>,
for larger sizes.</p>
<p>For other structuring element shapes, or for gray-scale images, use <a href="morphology.html#dip-Dilation-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Dilation</code></a>. See also <a href="binary.html#dip-BinaryDilation-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><code>dip::BinaryDilation</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-IsotropicErosion-Image-CL-Image-L-dfloat-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-IsotropicErosion-Image-CL-Image-L-dfloat-" class="m-doc-self">dip::<wbr />IsotropicErosion</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance</span>) </h3>
<p>Isotropic erosion of binary image.</p>
<p>Does a threshold of the <a href="distance.html#dip-EuclideanDistanceTransform-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanDistanceTransform</code></a> of <code>in</code>.
This is much faster than applying <a href="morphology.html#dip-Erosion-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Erosion</code></a> with a disk structuring element of diameter <code>2 * distance</code>,
for larger sizes.</p>
<p>For other structuring element shapes, or for gray-scale images, use <a href="morphology.html#dip-Erosion-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Erosion</code></a>. See also <a href="binary.html#dip-BinaryErosion-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><code>dip::BinaryErosion</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-IsotropicClosing-Image-CL-Image-L-dfloat-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-IsotropicClosing-Image-CL-Image-L-dfloat-" class="m-doc-self">dip::<wbr />IsotropicClosing</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance</span>) </h3>
<p>Isotropic closing of binary image.</p>
<p>Composition of <a href="binary.html#dip-IsotropicDilation-Image-CL-Image-L-dfloat-"><code>dip::IsotropicDilation</code></a> and <a href="binary.html#dip-IsotropicErosion-Image-CL-Image-L-dfloat-"><code>dip::IsotropicErosion</code></a>.</p>
<p>For other structuring element shapes, or for gray-scale images, use <a href="morphology.html#dip-Closing-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Closing</code></a>. See also <a href="binary.html#dip-BinaryClosing-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><code>dip::BinaryClosing</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-IsotropicOpening-Image-CL-Image-L-dfloat-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-IsotropicOpening-Image-CL-Image-L-dfloat-" class="m-doc-self">dip::<wbr />IsotropicOpening</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> distance</span>) </h3>
<p>Isotropic opening of binary image.</p>
<p>Composition of <a href="binary.html#dip-IsotropicErosion-Image-CL-Image-L-dfloat-"><code>dip::IsotropicErosion</code></a> and <a href="binary.html#dip-IsotropicDilation-Image-CL-Image-L-dfloat-"><code>dip::IsotropicDilation</code></a>.</p>
<p>For other structuring element shapes, or for gray-scale images, use <a href="morphology.html#dip-Opening-Image-CL-Image-L-StructuringElement-CL-StringArray-CL"><code>dip::Opening</code></a>. See also <a href="binary.html#dip-BinaryOpening-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><code>dip::BinaryOpening</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-BinaryPropagation-Image-CL-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryPropagation-Image-CL-Image-CL-Image-L-dip-sint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryPropagation</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& inSeed, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& inMask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-sint" class="m-doc">dip::sint</a> connectivity = 1, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Morphological propagation of binary objects.</p>
<p><code>inSeed</code> contains the seeds to propagate. To use no seeds, simply pass a raw image, i.e. <code>dip::Image()</code>.
<code>inMask</code> contains the mask in which propagation is allowed.</p>
<p>The <code>connectivity</code> parameter defines the metric, that is, the shape of
the structuring element (see <a href="concepts.html#connectivity">Connectivity</a>). Alternating connectivity
is only implemented for 2D and 3D images.</p>
<p>The <code>edgeCondition</code> parameter specifies whether pixels past the border of the image should be
treated as object (by passing <code>"object"</code>) or as background (by passing <code>"background"</code>).</p>
<p>The algorithm is repeated <code>iterations</code> times. Pass 0 to continue until propagation is completed. With
<code>iterations==0</code>, a faster algorithm is used.</p>
<p>See also <a href="morphology.html#dip-MorphologicalReconstruction-Image-CL-Image-CL-Image-L-dip-uint--String-CL"><code>dip::MorphologicalReconstruction</code></a>, which is less flexible but works for gray-scale images.</p>
</div></section>
<section class="m-doc-details" id="dip-EdgeObjectsRemove-Image-CL-Image-L-dip-uint-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-EdgeObjectsRemove-Image-CL-Image-L-dip-uint-" class="m-doc-self">dip::<wbr />EdgeObjectsRemove</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& c_in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 1</span>) </h3>
<p>Remove edge objects from a binary or labeled image.</p>
<p>Removes those objects from <code>in</code> that are connected to the edges of the image.</p>
<p>If the input image is binary. this function calls <a href="binary.html#dip-BinaryPropagation-Image-CL-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><code>dip::BinaryPropagation</code></a> with no seed image
and <code>edgeCondition</code> set to <code>"object"</code>. The result of the propagation is xor-ed with the input image.
In this case, the <code>connectivity</code> parameter defines the metric, that is, the shape of the structuring
element (see <a href="concepts.html#connectivity">Connectivity</a>).</p>
<p>If the input image is labeled, this function erases the labels that touch the image edge.
In this case, <code>connectivity</code> is ignored. Note that a labeled image must be of an unsigned integer type.</p>
</div></section>
<section class="m-doc-details" id="dip-FillHoles-Image-CL-Image-L-dip-uint-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-FillHoles-Image-CL-Image-L-dip-uint-" class="m-doc-self">dip::<wbr />FillHoles</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 1</span>) </h3>
<p>Fill holes in binary image.</p>
<p>Removes holes in binary objects in <code>in</code> that are not connected to the edges of the image.
This function calls <a href="binary.html#dip-BinaryPropagation-Image-CL-Image-CL-Image-L-dip-sint--dip-uint--String-CL"><code>dip::BinaryPropagation</code></a> using the inverted <code>in</code>, with no seed image, and
<code>edgeCondition</code> set to <code>"object"</code>. This finds the background connected to the edge, which is
the only background to be preserved.</p>
<p>The <code>connectivity</code> parameter defines the metric, that is, the shape of
the structuring element (see <a href="concepts.html#connectivity">Connectivity</a>).</p>
</div></section>
<section class="m-doc-details" id="dip-ConditionalThickening2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-ConditionalThickening2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL" class="m-doc-self">dip::<wbr />ConditionalThickening2D</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& c_in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& c_mask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& endPixelCondition = S::LOSE, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Thickens the image <code>in</code> conditioned on the mask (2D only).</p>
<p>A thickening is a dilation that preserves topology. If no <code>mask</code> is given (i.e. the image is raw),
it will produce an inverse skeleton of the background (given sufficient iterations).
If a <code>mask</code> is given, the dilation will not propagate outside of the set pixels in <code>mask</code>.</p>
<p>The dilation always uses the unit 4-connected neighborhood. That is, it iteratively propagates using
a connectivity of 1. The topology preserved is that of the 8-connected background. <code>iterations</code> iterations
are applied. If <code>iterations</code> is 0, the algorithm iterates until idempotency.</p>
<p><code>endPixelCondition</code> determines if background branches are kept. The string <code>"keep"</code> is equivalent to the
<code>"natural"</code> end pixel condition in <a href="binary.html#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanSkeleton</code></a>, and <code>"lose"</code> causes branches to not be kept
(meaning that only single background pixels and loops in background are kept).</p>
<p>The <code>edgeCondition</code> parameter specifies whether the border of the image should be treated as object (<code>"object"</code>)
or as background (<code>"background"</code>). Note that the algorithm doesn’t propagate into the pixels around the edge
of the image. The <code>edgeCondition</code> is used to modify the input image before the iterative process starts.</p>
</div></section>
<section class="m-doc-details" id="dip-ConditionalThinning2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-ConditionalThinning2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL" class="m-doc-self">dip::<wbr />ConditionalThinning2D</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& endPixelCondition = S::LOSE, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Thins the image <code>in</code> conditioned on the mask (2D only).</p>
<p>A thinning is an erosion that preserves topology. If no <code>mask</code> is given (i.e. the image is raw),
it will produce a skeleton of the object (given sufficient iterations).
If a <code>mask</code> is given, the erosion will not propagate outside of the set pixels in <code>mask</code>.
Note that <a href="binary.html#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanSkeleton</code></a> produces a better skeleton.</p>
<p>The erosion always uses the unit 4-connected neighborhood. That is, it iteratively propagates using
a connectivity of 1. The topology preserved is that of the 8-connected foreground. <code>iterations</code> iterations
are applied. If <code>iterations</code> is 0, the algorithm iterates until idempotency.</p>
<p><code>endPixelCondition</code> determines if background branches are kept. The string <code>"keep"</code> is equivalent to the
<code>"natural"</code> end pixel condition in <a href="binary.html#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanSkeleton</code></a>, and <code>"lose"</code> causes branches to not be kept
(meaning that only single background pixels and loops in background are kept).</p>
<p>The <code>edgeCondition</code> parameter specifies whether the border of the image should be treated as object (<code>"object"</code>)
or as background (<code>"background"</code>). Note that the algorithm doesn’t propagate into the pixels around the edge
of the image. The <code>edgeCondition</code> is used to modify the input image before the iterative process starts.</p>
</div></section>
<section class="m-doc-details" id="dip-BinaryAreaOpening-Image-CL-Image-L-dip-uint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryAreaOpening-Image-CL-Image-L-dip-uint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryAreaOpening</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> filterSize, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Computes the area opening of a binary image</p>
<p>The area opening removes all connected components that have an area smaller than the given parameter <code>filterSize</code>,
and is equivalent to the supremum of openings with all possible connected structuring elements of that area.</p>
<p><code>connectivity</code> determines what a connected component is. See <a href="concepts.html#connectivity">Connectivity</a> for information on the
connectivity parameter.</p>
<p>The <code>edgeCondition</code> parameter specifies whether pixels past the border of the image should be
treated as object (by passing <code>"object"</code>) or as background (by passing <code>"background"</code>).</p>
<p>The operation is implemented through <a href="graphs.html#dip-Label-Graph-CL"><code>dip::Label</code></a>.</p>
<aside class="m-note m-default">
<h4>See also</h4>
<p><a href="morphology.html#dip-AreaOpening-Image-CL-Image-CL-Image-L-dip-uint--dip-uint--String-CL"><code>dip::AreaOpening</code></a>, <a href="morphology.html#dip-AreaClosing-Image-CL-Image-CL-Image-L-dip-uint--dip-uint-"><code>dip::AreaClosing</code></a></p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-BinaryAreaClosing-Image-CL-Image-L-dip-uint--dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-BinaryAreaClosing-Image-CL-Image-L-dip-uint--dip-uint--String-CL" class="m-doc-self">dip::<wbr />BinaryAreaClosing</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> filterSize, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& s_edgeCondition = S::BACKGROUND</span>) </h3>
<p>Computes the area closing of a binary image, by calling <a href="binary.html#dip-BinaryAreaOpening-Image-CL-Image-L-dip-uint--dip-uint--String-CL"><code>dip::BinaryAreaOpening</code></a> on the inverse
of the input image.</p>
</div></section>
<section class="m-doc-details" id="dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL" class="m-doc-self">dip::<wbr />EuclideanSkeleton</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& endPixelCondition = S::NATURAL, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Accurate binary skeleton (2D and 3D only).</p>
<p>This algorithm computes quasi-Euclidean distances and tests Hilditch conditions to preserve topology. In 2D,
integer distances to neighbors are as follows:</p>
<table class="m-table">
<thead>
<tr>
<th>neighbors</th>
<th>distance</th>
</tr>
</thead>
<tbody>
<tr>
<td>4-connected</td>
<td>5</td>
</tr>
<tr>
<td>8-connected</td>
<td>7</td>
</tr>
<tr>
<td>knight’s move</td>
<td>11</td>
</tr>
</tbody>
</table>
<p>and in 3D as follows:</p>
<table class="m-table">
<thead>
<tr>
<th>neighbors</th>
<th>distance</th>
</tr>
</thead>
<tbody>
<tr>
<td>6-connected neighbors</td>
<td>4</td>
</tr>
<tr>
<td>18-connected neighbors</td>
<td>6</td>
</tr>
<tr>
<td>26-connected neighbors</td>
<td>7</td>
</tr>
<tr>
<td>knight’s move</td>
<td>9</td>
</tr>
<tr>
<td>(2,1,1) neighbors</td>
<td>10</td>
</tr>
<tr>
<td>(2,2,1) neighbors</td>
<td>12</td>
</tr>
</tbody>
</table>
<p>The <code>endPixelCondition</code> parameter determines what is considered an “end pixel” in the skeleton, and thus affects
how many branches are generated. It is one of the following strings:</p>
<ul>
<li><code>"loose ends away"</code>: Loose ends are eaten away (nothing is considered an end point).</li>
<li><code>"natural"</code>: “natural” end pixel condition of this algorithm.</li>
<li><code>"one neighbor"</code>: Keep endpoint if it has one neighbor.</li>
<li><code>"two neighbors"</code>: Keep endpoint if it has two neighbors.</li>
<li><code>"three neighbors"</code>: Keep endpoint if it has three neighbors.</li>
</ul>
<p>The <code>edgeCondition</code> parameter specifies whether the border of the image should be treated as object (<code>"object"</code>)
or as background (<code>"background"</code>).</p>
<aside class="m-note m-warning">
<h4>Warning</h4>
<p>Pixels in a 2-pixel border around the edge are not processed. If this is an issue, consider adding 2 pixels
on each side of your image.</p>
</aside>
<aside class="m-note m-danger">
<h4>Bug</h4>
<p>Results in 3D are not always correct: <code>"loose ends away"</code>, <code>"one neighbor"</code> and <code>"three neighbors"</code> produce the
same results, and sometimes planes in the skeleton are not thinned to a single pixel thickness.</p>
</aside>
<aside class="m-note m-default">
<h4>Literature</h4>
<ul>
<li>B.J.H. Verwer, “Improved metrics in image processing applied to the Hilditch skeleton”, 9<sup>th</sup> ICPR, 1988.</li>
</ul>
</aside>
</div></section>
<section class="m-doc-details" id="dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL" class="m-doc-self">dip::<wbr />CountNeighbors</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& mode = S::FOREGROUND, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Counts the number of set neighbors for each pixel in the binary image <code>in</code>.</p>
<p>Out will contain, for each set pixel, 1 + the number of neighbors that are also set. The neighborhood is
given by <code>connectivity</code>, see <a href="concepts.html#connectivity">Connectivity</a> for more information. If <code>mode</code> is set to <code>"all"</code>, the
count is computed for all pixels, not only the foreground ones. In this case, for the non-set pixels the
count is not increased by 1, and therefore yields simply the count of set pixels in the full neighborhood.</p>
<p><code>edgeCondition</code> determines the value of pixels outside the image domain, and can be <code>"object"</code> or <code>"background"</code>.</p>
<p>This function is typically used on the output of <a href="binary.html#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanSkeleton</code></a> to distinguish different types
of pixels.</p>
<aside class="m-note m-default">
<h4>See also</h4>
<p><a href="binary.html#dip-GetSinglePixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetSinglePixels</code></a>, <a href="binary.html#dip-GetEndPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetEndPixels</code></a>, <a href="binary.html#dip-GetLinkPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetLinkPixels</code></a>, <a href="binary.html#dip-GetBranchPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetBranchPixels</code></a></p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-MajorityVote-Image-CL-Image-L-dip-uint--dip-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-MajorityVote-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc-self">dip::<wbr />MajorityVote</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Filters the binary image by setting each pixel to the phase with more pixels in the neighborhood.</p>
<p>The majority vote filter is the binary equivalent to the median filter. If in the neighborhood of a pixel there
are more foreground than background pixels, the pixel will be set to foreground. Otherwise it will be set to
background. The pixel itself is part of the neighborhood, and therefore the neighborhood always has an odd number
of pixels.</p>
<p>Note that this is equivalent to (but more efficient than):</p>
<div class="m-code"><pre><span></span><span class="n">dip</span><span class="o">::</span><span class="n">uint</span><span class="w"> </span><span class="n">neighborhoodSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">NeighborList</span><span class="p">(</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="s">"connected"</span><span class="p">,</span><span class="w"> </span><span class="n">connectivity</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="n">in</span><span class="p">.</span><span class="n">Dimensionality</span><span class="p">()</span><span class="w"> </span><span class="p">).</span><span class="n">Size</span><span class="p">();</span>
<span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">CountNeighbors</span><span class="p">(</span><span class="w"> </span><span class="n">in</span><span class="p">,</span><span class="w"> </span><span class="n">connectivity</span><span class="p">,</span><span class="w"> </span><span class="s">"all"</span><span class="p">,</span><span class="w"> </span><span class="n">edgeCondition</span><span class="w"> </span><span class="p">)</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">neighborhoodSize</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
</pre></div>
<p>with <code>neighborhoodSize</code> the number of pixels in the neighborhood given by <code>connectivity</code>.</p>
<p><code>edgeCondition</code> determines the value of pixels outside the image domain, and can be <code>"object"</code> or <code>"background"</code>.</p>
<aside class="m-note m-default">
<h4>See also</h4>
<p><a href="nonlinear.html#dip-MedianFilter-Image-CL-Image-L-Kernel-CL-StringArray-CL"><code>dip::MedianFilter</code></a>, <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a></p>
</aside>
</div></section>
<section class="m-doc-details" id="dip-GetSinglePixels-Image-CL-Image-L-dip-uint--dip-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-GetSinglePixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc-self">dip::<wbr />GetSinglePixels</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Returns the isolated pixels in the binary image <code>in</code>. That is, the set pixels with zero neighbors. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-GetEndPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-GetEndPixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc-self">dip::<wbr />GetEndPixels</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Returns the end pixels in the skeleton image <code>in</code>. That is, the set pixels with one neighbor. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-GetLinkPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-GetLinkPixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc-self">dip::<wbr />GetLinkPixels</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Returns the link pixels in the skeleton image <code>in</code>. That is, the set pixels with two neighbors. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-GetBranchPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-GetBranchPixels-Image-CL-Image-L-dip-uint--dip-String-CL" class="m-doc-self">dip::<wbr />GetBranchPixels</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& edgeCondition = S::BACKGROUND</span>) </h3>
<p>Returns the branch pixels in the skeleton image <code>in</code>. That is, the set pixels with more than two neighbors. See <a href="binary.html#dip-CountNeighbors-Image-CL-Image-L-dip-uint--dip-String-CL-dip-String-CL"><code>dip::CountNeighbors</code></a>.</p>
</div></section>
<section class="m-doc-details" id="dip-SupGenerating-Image-CL-Image-L-Interval-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-SupGenerating-Image-CL-Image-L-Interval-CL-String-CL" class="m-doc-self">dip::<wbr />SupGenerating</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Sup-generating operator, also known as hit-miss operator.</p>
<p>The sup-generating operator is a relaxed template matching, where <code>interval</code> is the template.
<code>interval</code> contains some pixels that must be foreground, and some that must be background, but
also allows “don’t care” pixels, which will be ignored in the matching.</p>
<p>This operator is equal to the infimum of an erosion and an anti-erosion:</p>
<div class="m-code"><pre><span></span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Infimum</span><span class="p">(</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Erosion</span><span class="p">(</span><span class="w"> </span><span class="n">in</span><span class="p">,</span><span class="w"> </span><span class="n">hit</span><span class="w"> </span><span class="p">),</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Erosion</span><span class="p">(</span><span class="w"> </span><span class="o">~</span><span class="n">in</span><span class="p">,</span><span class="w"> </span><span class="n">miss</span><span class="w"> </span><span class="p">));</span>
</pre></div>
<p>where <code>hit</code> and <code>miss</code> are the two binary structuring elements in <code>interval</code>.</p>
<p>This function is specifically for binary images. Use <a href="morphology.html#dip-HitAndMiss-Image-CL-Image-L-StructuringElement-CL-StructuringElement-CL-String-CL-StringArray-CL"><code>dip::HitAndMiss</code></a> for a more general operator.</p>
</div></section>
<section class="m-doc-details" id="dip-InfGenerating-Image-CL-Image-L-Interval-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-InfGenerating-Image-CL-Image-L-Interval-CL-String-CL" class="m-doc-self">dip::<wbr />InfGenerating</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Inf-generating operator, the dual of the hit-miss operator.</p>
<p>This operator is equal to the supremum of a dilation and an anti-dilation:</p>
<div class="m-code"><pre><span></span><span class="n">out</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Supremum</span><span class="p">(</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Dilation</span><span class="p">(</span><span class="w"> </span><span class="n">in</span><span class="p">,</span><span class="w"> </span><span class="n">hit</span><span class="w"> </span><span class="p">),</span><span class="w"> </span><span class="n">dip</span><span class="o">::</span><span class="n">Dilation</span><span class="p">(</span><span class="w"> </span><span class="o">~</span><span class="n">in</span><span class="p">,</span><span class="w"> </span><span class="n">miss</span><span class="w"> </span><span class="p">));</span>
</pre></div>
<p>where <code>hit</code> and <code>miss</code> are the two binary structuring elements in <code>interval</code>.</p>
<p>This function is specifically for binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-UnionSupGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-UnionSupGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL" class="m-doc-self">dip::<wbr />UnionSupGenerating</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Union of sup-generating operators.</p>
<p>Applies the sup-generating operator with each of the intervals in <code>intervals</code>, and takes the union
of the results.</p>
<p>This function is specifically for binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-UnionSupGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-UnionSupGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL" class="m-doc-self">dip::<wbr />UnionSupGenerating2D</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Union of sup-generating operators.</p>
<p>Applies the sup-generating operator with all the rotated versions of <code>interval</code>, and takes the union
of the results. See <a href="dip-Interval.html#dip-Interval-GenerateRotatedVersions-dip-uint--String-CL-C"><code>dip::Interval::GenerateRotatedVersions</code></a> for the definition of <code>rotationAngle</code>
and <code>rotationDirection</code>.</p>
<p>This function is specifically for 2D binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-IntersectionInfGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-IntersectionInfGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL" class="m-doc-self">dip::<wbr />IntersectionInfGenerating</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Intersection of inf-generating operators.</p>
<p>Applies the inf-generating operator with each of the intervals in <code>intervals</code>, and takes the intersection
of the results.</p>
<p>This function is specifically for binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-IntersectionInfGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-IntersectionInfGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL" class="m-doc-self">dip::<wbr />IntersectionInfGenerating2D</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Intersection of inf-generating operators.</p>
<p>Applies the inf-generating operator with all the rotated versions of <code>interval</code>, and takes the intersection
of the results. See <a href="dip-Interval.html#dip-Interval-GenerateRotatedVersions-dip-uint--String-CL-C"><code>dip::Interval::GenerateRotatedVersions</code></a> for the definition of <code>rotationAngle</code>
and <code>rotationDirection</code>.</p>
<p>This function is specifically for 2D binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL" class="m-doc-self">dip::<wbr />Thickening</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Applies the thickening operator, optionally constrained by a mask, to an image.</p>
<p>Thickening is defined as <code>in + SupGenerating(in)</code>. The constrained operation is defined as
<code>in + (SupGenerating(in) & mask)</code>.</p>
<p>The operation is applied with each of the intervals in <code>intervals</code>, and repeated <code>iterations</code>
times. If <code>iterations</code> is 0, the operation is repeated until convergence.</p>
<p>A thickening with the right set of intervals leads to a background skeleton, also called skiz.
See <a href="binary.html#dip-HomotopicThickeningInterval2D-dip-uint-"><code>dip::HomotopicThickeningInterval2D</code></a>.
The intervals returned by <a href="binary.html#dip-HomotopicInverseEndPixelInterval2D-dip-uint-"><code>dip::HomotopicInverseEndPixelInterval2D</code></a> prune the skiz to single
points and circles.</p>
<p>This function is specifically for binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-Thickening2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-Thickening2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL" class="m-doc-self">dip::<wbr />Thickening2D</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Applies the thickening operator, optionally constrained by a mask, to an image.</p>
<p>The operation is applied with with all the rotated versions of <code>interval</code>, and repeated <code>iterations</code>
times. See <a href="binary.html#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thickening</code></a> for a description of the operation.
See <a href="dip-Interval.html#dip-Interval-GenerateRotatedVersions-dip-uint--String-CL-C"><code>dip::Interval::GenerateRotatedVersions</code></a> for the definition of <code>rotationAngle</code> and <code>rotationDirection</code>.</p>
<p>This function is specifically for 2D binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL" class="m-doc-self">dip::<wbr />Thinning</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> const& intervals, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Applies the thinning operator, optionally constrained by a mask, to an image.</p>
<p>Thinning is defined as <code>in - SupGenerating(in)</code>. The constrained operation is defined as
<code>in - (SupGenerating(in) & mask)</code>.</p>
<p>The operation is applied with each of the intervals in <code>intervals</code>, and repeated <code>iterations</code>
times. If <code>iterations</code> is 0, the operation is repeated until convergence.</p>
<p>A thinning with the right set of intervals leads to a skeleton. See <a href="binary.html#dip-HomotopicThinningInterval2D-dip-uint-"><code>dip::HomotopicThinningInterval2D</code></a>.
The intervals returned by <a href="binary.html#dip-HomotopicEndPixelInterval2D-dip-uint-"><code>dip::HomotopicEndPixelInterval2D</code></a> prune the skeleton to single points and
circles.</p>
<p>This function is specifically for binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-Thinning2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-Thinning2D-Image-CL-Image-CL-Image-L-Interval-CL-dip-uint--dip-uint--String-CL-String-CL" class="m-doc-self">dip::<wbr />Thinning2D</a></span>(
<span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& in, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& mask, </span><span class="m-doc-arg"><a href="dip-Image.html" class="m-doc">dip::Image</a>& out, </span><span class="m-doc-arg"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> const& interval, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> iterations = 0, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rotationAngle = 45, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& rotationDirection = S::INTERLEAVED_CLOCKWISE, </span><span class="m-doc-arg"><a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& boundaryCondition = S::ADD_ZEROS</span>) </h3>
<p>Applies the thinning operator, optionally constrained by a mask, to an image.</p>
<p>The operation is applied with with all the rotated versions of <code>interval</code>, and repeated <code>iterations</code>
times. See <a href="binary.html#dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thinning</code></a> for a description of the operation.
See <a href="dip-Interval.html#dip-Interval-GenerateRotatedVersions-dip-uint--String-CL-C"><code>dip::Interval::GenerateRotatedVersions</code></a> for the definition of <code>rotationAngle</code> and <code>rotationDirection</code>.</p>
<p>This function is specifically for 2D binary images.</p>
</div></section>
<section class="m-doc-details" id="dip-HomotopicThinningInterval2D-dip-uint-"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-HomotopicThinningInterval2D-dip-uint-" class="m-doc-self">dip::<wbr />HomotopicThinningInterval2D</a></span>(
<span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2</span>) </h3>
<p>Returns a 2D interval array for homotopic thinning.</p>
<p>Use with <a href="binary.html#dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thinning</code></a> to shrink objects without changing the Euler number.
Note that <a href="binary.html#dip-ConditionalThinning2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL"><code>dip::ConditionalThinning2D</code></a> is more efficient, though the two functions do not produce exactly
the same output. To create a skeleton, use <a href="binary.html#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanSkeleton</code></a>.</p>
<p><code>connectivity</code> can be 1 to produce 4-connected skeletons, or 2 for 8-connected skeletons.</p>
</div></section>
<section class="m-doc-details" id="dip-HomotopicThickeningInterval2D-dip-uint-"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-HomotopicThickeningInterval2D-dip-uint-" class="m-doc-self">dip::<wbr />HomotopicThickeningInterval2D</a></span>(
<span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2</span>) </h3>
<p>Returns a 2D interval array for homotopic thickening.</p>
<p>Use with <a href="binary.html#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thickening</code></a> to grow objects without merging them.
This produces a background skeleton (also known as skiz).
Note that <a href="binary.html#dip-ConditionalThickening2D-Image-CL-Image-CL-Image-L-dip-uint--String-CL-String-CL"><code>dip::ConditionalThickening2D</code></a> is more efficient, though the two options do not produce exactly
the same output. To create a background skeleton, use <a href="binary.html#dip-EuclideanSkeleton-Image-CL-Image-L-String-CL-String-CL"><code>dip::EuclideanSkeleton</code></a> on the inverted image.</p>
<p><code>connectivity</code> can be 1 to produce 4-connected skeletons, or 2 for 8-connected skeletons.</p>
</div></section>
<section class="m-doc-details" id="dip-EndPixelInterval2D-dip-uint-"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-EndPixelInterval2D-dip-uint-" class="m-doc-self">dip::<wbr />EndPixelInterval2D</a></span>(
<span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2</span>) </h3>
<p>Returns an interval array for detecting end pixels. Includes isolated pixels.</p>
<p>Use with <a href="binary.html#dip-UnionSupGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL"><code>dip::UnionSupGenerating</code></a> to detect skeleton end pixels. Note that <a href="binary.html#dip-GetEndPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetEndPixels</code></a>
is more efficient.</p>
<p><code>connectivity</code> can be 1 to work with 4-connected skeletons, or 2 for 8-connected skeletons.</p>
</div></section>
<section class="m-doc-details" id="dip-HomotopicEndPixelInterval2D-dip-uint-"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-HomotopicEndPixelInterval2D-dip-uint-" class="m-doc-self">dip::<wbr />HomotopicEndPixelInterval2D</a></span>(
<span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2</span>) </h3>
<p>Returns an interval array for detecting end pixels. Excludes isolated pixels</p>
<p>Use with <a href="binary.html#dip-Thinning-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thinning</code></a> to prune end points from the skeleton.</p>
<p><code>connectivity</code> can be 1 to prune 4-connected skeletons, or 2 for 8-connected skeletons.</p>
</div></section>
<section class="m-doc-details" id="dip-HomotopicInverseEndPixelInterval2D-dip-uint-"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-HomotopicInverseEndPixelInterval2D-dip-uint-" class="m-doc-self">dip::<wbr />HomotopicInverseEndPixelInterval2D</a></span>(
<span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 2</span>) </h3>
<p>Returns an interval array for detecting end background pixels. Excludes isolated pixels.</p>
<p>Use with <a href="binary.html#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thickening</code></a> to prune end points from the background skeleton.</p>
<p><code>connectivity</code> can be 1 to prune 4-connected skeletons, or 2 for 8-connected skeletons.</p>
</div></section>
<section class="m-doc-details" id="dip-SinglePixelInterval-dip-uint-"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> </span>
<span class="m-doc-name"><a href="#dip-SinglePixelInterval-dip-uint-" class="m-doc-self">dip::<wbr />SinglePixelInterval</a></span>(
<span class="m-doc-arg"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> nDims = 2</span>) </h3>
<p>Returns an interval for detecting single pixels. Use with <a href="binary.html#dip-SupGenerating-Image-CL-Image-L-Interval-CL-String-CL"><code>dip::SupGenerating</code></a> to detect isolated
pixels. Note that <a href="binary.html#dip-GetSinglePixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetSinglePixels</code></a> is more efficient.</p>
</div></section>
<section class="m-doc-details" id="dip-BranchPixelInterval2D"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-BranchPixelInterval2D" class="m-doc-self">dip::<wbr />BranchPixelInterval2D</a></span>(
) </h3>
<p>Returns a 2D interval array for detecting branch pixels.</p>
<p>Use with <a href="binary.html#dip-UnionSupGenerating-Image-CL-Image-L-IntervalArray-CL-String-CL"><code>dip::UnionSupGenerating</code></a> to detect skeleton branch pixels. Note that <a href="binary.html#dip-GetBranchPixels-Image-CL-Image-L-dip-uint--dip-String-CL"><code>dip::GetBranchPixels</code></a>
is more efficient.</p>
</div></section>
<section class="m-doc-details" id="dip-BoundaryPixelInterval2D"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html" class="m-doc">dip::Interval</a> </span>
<span class="m-doc-name"><a href="#dip-BoundaryPixelInterval2D" class="m-doc-self">dip::<wbr />BoundaryPixelInterval2D</a></span>(
) </h3>
<p>Returns a 2D interval for detecting boundary pixels.</p>
<p>Use with <a href="binary.html#dip-UnionSupGenerating2D-Image-CL-Image-L-Interval-CL-dip-uint--String-CL-String-CL"><code>dip::UnionSupGenerating2D</code></a> to detect object boundary pixels. Set <code>rotationAngle</code> to 45 to detect pixels
8-connected to the background, and to 90 to detect pixels 4-connected to the background. Note that the
difference between the input image and the eroded image accomplishes the same thing.</p>
</div></section>
<section class="m-doc-details" id="dip-ConvexHullInterval2D"><div>
<h3>
<span class="m-doc-return"><a href="dip-Interval.html#dip-IntervalArray" class="m-doc">dip::IntervalArray</a> </span>
<span class="m-doc-name"><a href="#dip-ConvexHullInterval2D" class="m-doc-self">dip::<wbr />ConvexHullInterval2D</a></span>(
) </h3>
<p>Returns a 2D interval array to thicken to a convex hull.</p>
<p>Use with <a href="binary.html#dip-Thickening-Image-CL-Image-CL-Image-L-IntervalArray-CL-dip-uint--String-CL"><code>dip::Thickening</code></a> to grow concave sections of objects until the objects are all convex.
This leads to octagonal shapes.</p>
</div></section>
</section>
</div>
</div>
</div>
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