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class="reference internal" href="#">Segmenting the picture of Lena in regions</a></li> </ul> </div> <div class="content"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="segmenting-the-picture-of-lena-in-regions"> <span id="example-cluster-plot-lena-segmentation-py"></span><h1>Segmenting the picture of Lena in regions<a class="headerlink" href="#segmenting-the-picture-of-lena-in-regions" title="Permalink to this headline">ΒΆ</a></h1> <p>This example uses spectral clustering on a graph created from voxel-to-voxel difference on an image to break this image into multiple partly-homogenous regions.</p> <p>This procedure (spectral clustering on an image) is an efficient approximate solution for finding normalized graph cuts.</p> <img alt="auto_examples/cluster/images/plot_lena_segmentation.png" class="align-center" src="auto_examples/cluster/images/plot_lena_segmentation.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_lena_segmentation.py"><tt class="xref download docutils literal"><span class="pre">plot_lena_segmentation.py</span></tt></a></p> <div class="highlight-python"><div class="highlight"><pre><span class="k">print</span> <span class="n">__doc__</span> <span class="c"># Author: Gael Varoquaux <gael.varoquaux@normalesup.org></span> <span class="c"># License: BSD</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">scipy</span> <span class="kn">as</span> <span class="nn">sp</span> <span class="kn">import</span> <span class="nn">pylab</span> <span class="kn">as</span> <span class="nn">pl</span> <span class="kn">from</span> <span class="nn">scikits.learn.feature_extraction</span> <span class="kn">import</span> <span class="n">image</span> <span class="kn">from</span> <span class="nn">scikits.learn.cluster</span> <span class="kn">import</span> <span class="n">spectral_clustering</span> <span class="n">lena</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">lena</span><span class="p">()</span> <span class="c"># Downsample the image by a factor of 4</span> <span class="n">lena</span> <span class="o">=</span> <span class="n">lena</span><span class="p">[::</span><span class="mi">2</span><span class="p">,</span> <span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">lena</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">,</span> <span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">lena</span><span class="p">[::</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">lena</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="n">lena</span> <span class="o">=</span> <span class="n">lena</span><span class="p">[::</span><span class="mi">2</span><span class="p">,</span> <span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">lena</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">,</span> <span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">lena</span><span class="p">[::</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="n">lena</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span> <span class="c"># Convert the image into a graph with the value of the gradient on the</span> <span class="c"># edges.</span> <span class="n">graph</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">img_to_graph</span><span class="p">(</span><span class="n">lena</span><span class="p">)</span> <span class="c"># Take a decreasing function of the gradient: an exponential</span> <span class="c"># The smaller beta is, the more independant the segmentation is of the</span> <span class="c"># actual image. For beta=1, the segmentation is close to a voronoi</span> <span class="n">beta</span> <span class="o">=</span> <span class="mi">5</span> <span class="n">eps</span> <span class="o">=</span> <span class="mf">1e-6</span> <span class="n">graph</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">beta</span><span class="o">*</span><span class="n">graph</span><span class="o">.</span><span class="n">data</span><span class="o">/</span><span class="n">lena</span><span class="o">.</span><span class="n">std</span><span class="p">())</span> <span class="o">+</span> <span class="n">eps</span> <span class="c"># Apply spectral clustering (this step goes much faster if you have pyamg</span> <span class="c"># installed)</span> <span class="n">N_REGIONS</span> <span class="o">=</span> <span class="mi">11</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">spectral_clustering</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">N_REGIONS</span><span class="p">)</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">labels</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">lena</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="c">################################################################################</span> <span class="c"># Visualize the resulting regions</span> <span class="n">pl</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span> <span class="n">pl</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">lena</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">pl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">gray</span><span class="p">)</span> <span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_REGIONS</span><span class="p">):</span> <span class="n">pl</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">labels</span> <span class="o">==</span> <span class="n">l</span><span class="p">,</span> <span class="n">contours</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="p">[</span><span class="n">pl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">spectral</span><span class="p">(</span><span class="n">l</span><span class="o">/</span><span class="nb">float</span><span class="p">(</span><span class="n">N_REGIONS</span><span class="p">)),</span> <span class="p">])</span> <span class="n">pl</span><span class="o">.</span><span class="n">xticks</span><span class="p">(())</span> <span class="n">pl</span><span class="o">.</span><span class="n">yticks</span><span class="p">(())</span> <span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </pre></div> </div> </div> </div> </div> </div> <div class="clearer"></div> </div> </div> <div class="footer"> <p style="text-align: center">This documentation is relative to scikits.learn version 0.6.0<p> © 2010, scikits.learn developers (BSD Lincense). 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