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<h1 class="mt-5 fs-4">Connected Components Labeling</h1>
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<p class="lead">Connected-component labeling (alternatively connected-component analysis, blob extraction, region labeling, blob discovery, or region extraction) uniquely labels connected components in an image. The labeling process scans the image, pixel-by-pixel from top-left to bottom-right, in order to identify connected pixel regions, i.e. regions of adjacent pixels which share the same set of intensity values. For example, let's find the objects in this image:</p>
<ul>
<a href="../images/objects.gif"><img src="../images/objects.gif" width="256" height="171" class="image-slices" alt="purse" /></a>
</ul>
<p>To identify the objects in this image, use this command:</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary cli"><samp>magick objects.gif -connected-components 4 -auto-level -depth 8 objects.png</samp></pre>
<p>The detected objects are uniquely labeled. Use auto leveling to visualize the detected objects:</p>
<ul>
<a href="../images/objects.png"><img src="../images/objects.png" width="256" height="171" class="image-slices" alt="Objects" /></a>
</ul>
<p>Object statistics is useful to review. To display them, use this command:</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary cli"><samp>magick objects.gif -define connected-components:verbose=true -connected-components 4 objects.png</samp></pre>
<p>Five objects were detected in the source image with these statistics:</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary"><samp>Objects (id: bounding-box centroid area mean-color):
0: 256x171+0+0 119.2,80.8 33117 srgb(0,0,0)
2: 120x135+104+18 159.5,106.5 8690 srgb(255,255,255)
3: 50x36+129+44 154.2,63.4 1529 srgb(0,0,0)
4: 21x23+0+45 8.8,55.9 409 srgb(255,255,255)
1: 4x10+252+0 253.9,4.1 31 srgb(255,255,255)
</samp></pre>
<p>Add <samp>-define connected-components:exclude-header=true</samp> to show the objects without the header-line. Add <samp>-define connected-components:exclude-ids=true</samp>. Use <samp>-define connected-components:sort=<var>area | width | height | x | y</var></samp> to sort the verbose connected components objects. By default, the objects are listed in decreasing area. Add <samp>-define connected-components:sort-order=<var>increasing | decreasing</var> to specify the sort order.</samp></p>
<p>Use <samp>-connected-components 8</samp> to visit 8 neighbors rather than 4. By default, neighbor colors must be exact to be part of a unique object. Use the <a href="command-line-options.html#fuzz">-fuzz</a> option to include pixels as part of an object that are <var>close</var> in color.</p>
<p>You might want to eliminate small objects by merging them with their larger neighbors. If so, use this command:</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary cli"><samp>magick objects.gif -define connected-components:area-threshold=410 -connected-components 4 \
-auto-level objects.jpg</samp></pre>
<p>Here are the expected results. Notice, how the small objects are now merged with the background.</p>
<ul>
<a href="../images/objects.jpg"><img src="../images/objects.jpg" width="256" height="171" class="image-slices" alt="Objects" /></a>
</ul>
<p>Notice how two of the objects were merged leaving three remaining objects:</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary"><samp>Objects (id: bounding-box centroid area mean-color):
0: 256x171+0+0 118.0,80.4 33557 srgb(0,0,0)
2: 120x135+104+18 159.5,106.5 8690 srgb(255,255,255)
3: 50x36+129+44 154.2,63.4 1529 srgb(0,0,0)</samp></pre>
<p>By default, the labeled image is grayscale. You can instead replace the object color in the labeled image with the mean-color from the source image. Simply add this setting, <samp>-define connected-components:mean-color=true</samp>, to your command line.</p>
<p>Thresholds can optionally include ranges, e.g. <samp>-define connected-components:area-threshold=410-1600</samp>. To keep the background object, identify it with <samp>-define connected-components:background-id=<var>object-id</var></samp>. The default background object is the object with the largest area.</p>
<p>In addition to area, there is support for these thresholding metrics:</p>
<ul>
<li>connected-components:angle-threshold (from equivalent ellipse)</li>
<li>connected-components:circularity-threshold (4*pi*area/perimeter^2)</li>
<li>connected-components:diameter-threshold (sqrt(4*area/pi))</li>
<li>connected-components:eccentricity-threshold (from equivalent ellipse)</li>
<li>connected-components:major-axis-threshold (diameter from equivalent ellipse)</li>
<li>connected-components:minor-axis-threshold (diameter from equivalent ellipse)</li>
<li>connected-components:perimeter-threshold</li>
</ul>
<p>You may want to remove certain objects. Use <samp>-define connected-components:remove-ids=<em>list-of-ids</em></samp> (e.g. -define connected-components:remove-ids=2,4-5). Or use <samp>-define connected-components:keep-ids=<em>list-of-ids</em></samp> to keep these objects and merge all others. For convenience, you can keep the top objects with this option: <samp>-define connected-components:keep-top=<em>number-of-objects</em></samp>. Rather than object ids, you can instead remove or keep objects identified by there color, e.g. <samp>-define connected-components:keep-colors=<em>red;green;blue</em></samp>.</p>
<p>Objects in your image may look homogeneous but have slightly different color values. By default, only pixels that match exactly are considered as part of a particular object. For slight variations of color in an object, use <samp>-fuzz</samp>. For example,</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary cli"><samp>magick star-map.png -fuzz 5% -define connected-components:verbose=true \
-define connected-components:mean-color=true -connected-components 4 stars.gif</samp></pre>
<h4>Connected Components</h4>
<p>The algorithm walks through the pixels of a component, in the usual row-column order, looking for a component above or to the left. For the component at top-left, there are no components above or to the left to merge into. As a result, there are special cases where you need to rotate, repeat the connected components, then rotate back. For example</p>
<pre class="p-3 mb-2 text-body-secondary bg-body-tertiary"><samp> magick \
objects.gif \
-define connected-components:verbose=true \
-define connected-components:area-threshold=6000 \
-virtual-pixel None \
-connected-components 4 -rotate 180 \
-connected-components 4 -rotate -180 \
objects.png
</samp></pre>
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