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<section id="histogram-equalization">
<span id="he"></span><h1>Histogram Equalization<a class="headerlink" href="#histogram-equalization" title="Link to this heading"></a></h1>
<section id="description">
<h2>Description<a class="headerlink" href="#description" title="Link to this heading"></a></h2>
<p>Histogram equalization also known as histogram flattening, is a non-linear image enhancement
algorithm that follows the idea that not only should an image cover the entire grayscale space
but also be uniformly distributed over that range.</p>
<p>An ideal image would be the one having a flat histogram.</p>
<p>Although care should be taken before applying a non-linear transformation on the image
histogram, there are good mathematical reasons why a flat histogram is the desired goal.</p>
<p>A simple scenario would be an image with pixels concentrated in an interval, in which case
histogram equalization transforms pixels to achieve a flat histogram image. Thus enhancing
the image contrast.</p>
<figure class="align-center" id="id1">
<a class="reference internal image-reference" href="image_processing/contrast_enhancement/he_chart.png"><img alt="Could not load image." src="image_processing/contrast_enhancement/he_chart.png" style="width: 200px; height: 100px;" /></a>
<figcaption>
<p><span class="caption-text">Pixels concentrated in an interval spread out.</span><a class="headerlink" href="#id1" title="Link to this image"></a></p>
</figcaption>
</figure>
</section>
<section id="algorithm">
<h2>Algorithm<a class="headerlink" href="#algorithm" title="Link to this heading"></a></h2>
<ol class="arabic simple">
<li><p>First calculate the histogram corresponding to input image.</p></li>
<li><p>If it is a multi channeled image (e.g. RGB), convert it to a independent color space
(like YCbCr, HSV etc.).</p></li>
<li><p>Then calculate the cumulative histogram over the input image.</p></li>
<li><p>Normalize the histogram to bring bin values between 0-1. For multi-channeled images
normalize each channel independently (by the number of pixels in image).</p></li>
<li><p>If the histogram of image is H(p<sub>x</sub>) p<sub>x</sub> in [0, 255], then apply
the transformation p<sub>x’</sub> = H(p<sub>x</sub>), p<sub>x’</sub> is pixel in output
image.</p></li>
</ol>
<p><strong>Explanation</strong></p>
<p>Since we will be transforming the image to match a flat histogram, we match
the cumulative histogram of the image to the cumulative histogram of a flat histogram.</p>
<p>Cumulative histogram of flat image is H(p<sub>x’</sub>) = p<sub>x’</sub> .</p>
<p>Hence,</p>
<blockquote>
<div><p>=&gt; H(p<sub>x’</sub>) = H(p<sub>x</sub>)</p>
<p>=&gt; p<sub>x’</sub> = H(p<sub>x</sub>)</p>
</div></blockquote>
</section>
<section id="results">
<h2>Results<a class="headerlink" href="#results" title="Link to this heading"></a></h2>
<p>The algorithm is applied on a few standard images. One of the transformations in shown below:</p>
<p><strong>Grayscale Image</strong></p>
<figure class="align-center">
<a class="reference internal image-reference" href="https://github.com/boost-gil/test-images/blob/master/jpeg/suite/barbara.jpg"><img alt="Could not load image." src="https://github.com/boost-gil/test-images/blob/master/jpeg/suite/barbara.jpg" style="width: 512px; height: 256px;" /></a>
</figure>
<p><strong>RGB</strong></p>
<figure class="align-center">
<a class="reference internal image-reference" href="https://github.com/boost-gil/test-images/blob/master/jpeg/suite/church.jpg"><img alt="Could not load image." src="https://github.com/boost-gil/test-images/blob/master/jpeg/suite/church.jpg" style="width: 900px; height: 300px;" /></a>
</figure>
</section>
<section id="demo">
<h2>Demo<a class="headerlink" href="#demo" title="Link to this heading"></a></h2>
<p>Usage Syntax:</p>
<blockquote>
<div><div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span><span class="n">gray8_image_t</span><span class="w"> </span><span class="n">inp_img</span><span class="p">;</span>
<span class="n">read_image</span><span class="p">(</span><span class="s">&quot;your_image.png&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">inp_img</span><span class="p">,</span><span class="w"> </span><span class="n">png_tag</span><span class="p">{});</span>
<span class="n">gray8_image_t</span><span class="w"> </span><span class="nf">dst_img</span><span class="p">(</span><span class="n">inp_img</span><span class="p">.</span><span class="n">dimensions</span><span class="p">());</span>
<span class="n">histogram_equalization</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">inp_img</span><span class="p">),</span><span class="w"> </span><span class="n">view</span><span class="p">(</span><span class="n">dst_img</span><span class="p">));</span>
<span class="c1">// To specify mask over input image</span>
<span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">mask</span><span class="p">(</span><span class="n">inp_img</span><span class="p">.</span><span class="n">height</span><span class="p">(),</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="p">(</span><span class="n">inp_img</span><span class="p">.</span><span class="n">width</span><span class="p">(),</span><span class="w"> </span><span class="nb">true</span><span class="p">));</span>
<span class="n">histogram_equalization</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">inp_img</span><span class="p">),</span><span class="w"> </span><span class="n">view</span><span class="p">(</span><span class="n">dst_img</span><span class="p">),</span><span class="w"> </span><span class="nb">true</span><span class="p">,</span><span class="w"> </span><span class="n">mask</span><span class="p">);</span>
</pre></div>
</div>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>Convert an RGB image to a channel independent color space
before trying the histogram equalization algorithm.</p>
</div>
</div></blockquote>
</section>
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