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<h1>
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Get min and max distance withing a point cloud
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</h1>
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<ol class="breadcrumb">
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<time class="published" datetime="2019-12-01T19:35:00+01:00">
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01 décembre 2019
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</time>
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</li>
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<li>Python</li>
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<li>Data Wrangling</li>
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<div class='article_content'>
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<p>In this article we will see how to filter all the point whose distance to any point in an ensemble of points is greater than a specified value. For example, we have two set of points :
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* the source in orange
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* the target in blue</p>
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<p>And we want to find all the points in the target ensemble that are at most at a distance of 0.5 of any point in the source distribution.</p>
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<div class="highlight"><pre><span></span><span class="o">%</span><span class="n">matplotlib</span> <span class="n">inline</span>
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<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
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<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
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<span class="n">target</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
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<span class="n">source</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">((</span><span class="mi">100</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">source</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">source</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"orange"</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">target</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">target</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"blue"</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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</pre></div>
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<p><img alt="png" src="../images/points_too_far_away/output_1_0.png"></p>
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<p>In order to do so, we will use the <code>cdist</code> function form the <code>scipy.spatial.distance</code> package. This function computes the distance between each pair of the two collections of points. </p>
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<p>We compute the minimum distance form all the points in the target ensemble from any point in the source ensemble.</p>
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<div class="highlight"><pre><span></span><span class="n">dist</span> <span class="o">=</span> <span class="n">cdist</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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</pre></div>
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<p>Once the distance has been computed, we filter out all the points that have more distant that the threshold value.</p>
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<div class="highlight"><pre><span></span><span class="n">dist</span><span class="p">[</span><span class="n">dist</span><span class="o">></span><span class="n">thres</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
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<span class="n">dist</span><span class="p">[</span><span class="n">dist</span> <span class="o">!=</span> <span class="kc">False</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
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</pre></div>
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<p>after that, we only need to format the result array and filter out all the zero values.</p>
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<div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">target</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">,</span> <span class="n">target</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
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<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="o">~</span><span class="p">(</span><span class="n">a</span><span class="o">==</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="mi">1</span><span class="p">)]</span>
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</pre></div>
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<div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <span class="n">cdist</span>
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<span class="k">def</span> <span class="nf">filter_too_far</span><span class="p">(</span><span class="n">target</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">thres</span> <span class="o">=</span> <span class="mi">1</span><span class="p">):</span>
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<span class="sd">"""</span>
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<span class="sd"> Filters out all the points in the target array </span>
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<span class="sd"> whose distance to any point in the source array </span>
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<span class="sd"> is greater than the threshold value</span>
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<span class="sd"> This function is made for 2D points</span>
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<span class="sd"> """</span>
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<span class="n">dist</span> <span class="o">=</span> <span class="n">cdist</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<span class="n">dist</span><span class="p">[</span><span class="n">dist</span><span class="o">></span><span class="n">thres</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
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<span class="n">dist</span><span class="p">[</span><span class="n">dist</span> <span class="o">!=</span> <span class="kc">False</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
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<span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">target</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">,</span> <span class="n">target</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
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<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="o">~</span><span class="p">(</span><span class="n">a</span><span class="o">==</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="mi">1</span><span class="p">)]</span>
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</pre></div>
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<p>Here we have in green all the point in the target ensemble that are distant from any point in the source ensemble of at most 0.5 units</p>
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<div class="highlight"><pre><span></span><span class="n">filtered</span> <span class="o">=</span> <span class="n">filter_too_far</span><span class="p">(</span><span class="n">target</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">thres</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">source</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">source</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"orange"</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">target</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">target</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"blue"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span> <span class="s2">"+"</span><span class="p">)</span>
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<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">filtered</span><span class="p">[:,</span><span class="mi">0</span><span class="p">],</span> <span class="n">filtered</span><span class="p">[:,</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s2">"green"</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span> <span class="s2">"+"</span><span class="p">)</span>
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</pre></div>
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<div class="highlight"><pre><span></span><span class="err"><matplotlib.collections.PathCollection at 0x7fde375a4490></span>
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</pre></div>
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<p><img alt="png" src="../images/points_too_far_away/output_5_1.png"></p>
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<p>This function can easily be adapted to work for 3D-points</p>
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<div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <span class="n">cdist</span>
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<span class="k">def</span> <span class="nf">filter_too_far</span><span class="p">(</span><span class="n">target</span><span class="p">,</span> <span class="n">source</span><span class="p">,</span> <span class="n">thres</span> <span class="o">=</span> <span class="mi">1</span><span class="p">):</span>
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<span class="sd">"""</span>
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<span class="sd"> Filters out all the points in the target array </span>
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<span class="sd"> whose distance to any point in the source array </span>
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<span class="sd"> is greater than the threshold value</span>
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<span class="sd"> This function is made for 3D points</span>
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<span class="sd"> """</span>
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<span class="n">dist</span> <span class="o">=</span> <span class="n">cdist</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<span class="n">dist</span><span class="p">[</span><span class="n">dist</span><span class="o">></span><span class="n">thres</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
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<span class="n">dist</span><span class="p">[</span><span class="n">dist</span> <span class="o">!=</span> <span class="kc">False</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
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<span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">target</span><span class="p">[:,</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">,</span> <span class="n">target</span><span class="p">[:,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">,</span> <span class="n">target</span><span class="p">[:,</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">dist</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
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<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="o">~</span><span class="p">(</span><span class="n">a</span><span class="o">==</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="mi">1</span><span class="p">)]</span>
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</pre></div>
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<p>Note that you are not restricted to the euclidian distance, the cdist function can use the following distances:
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* braycurtis
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* canberra
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* chebyshev
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* cityblock
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* correlation
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* cosine
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* dice
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* euclidean
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* hamming
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* jaccard
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* jensenshannon
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* kulsinski
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* mahalanobis
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* matching
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* minkowski
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* rogerstanimoto
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* russellrao
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* euclidean
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* sokalmichener
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* sokalsneath
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* sqeuclidean
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* wminkowski
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* yule</p>
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<div class="highlight"><pre><span></span>
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</pre></div>
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<p>Everything on this site is avaliable on GitHub. Head on over and <a href='https://github.com/redoules/redoules.github.io/issues/new'>submit an issue.</a> You can also message me directly by <a href='mailto:guillaume.redoules@gadz.org'>email</a>.</p>
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<center>This project contains 119 pages and is available on <a href="https://github.com/redoules/redoules.github.io">GitHub</a>.
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Copyright © Guillaume Redoulès,
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