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# Minimal makefile for Sphinx documentation
#
# You can set these variables from the command line.
SPHINXOPTS =
SPHINXBUILD = sphinx-build
SPHINXPROJ = Navigation_Toolbox
SOURCEDIR = source
BUILDDIR = build
# Put it first so that "make" without argument is like "make help".
help:
@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
.PHONY: help Makefile
# Catch-all target: route all unknown targets to Sphinx using the new
# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS).
%: Makefile
@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<title>Overview: module code &#8212; Navigation Toolbox a0 documentation</title>
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<h1>All modules for which code is available</h1>
<ul><li><a href="processing.html">processing</a></li>
</ul>
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<h3>Related Topics</h3>
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<h1>Source code for processing</h1><div class="highlight"><pre>
<span></span><span class="sd">&quot;&quot;&quot;</span>
<span class="sd">The scene processing part of the toolbox defines methodes</span>
<span class="sd">to transform an image into a place code in the sense</span>
<span class="sd">of Basten and Mallot (2010).</span>
<span class="sd">The scene is either</span>
<span class="sd">* a 4d numpy array, used when the image is a equirectangular \</span>
<span class="sd">projection, i.e. a panoramic image.</span>
<span class="sd">* a 3d numpy array, used when the viewing direction can not \</span>
<span class="sd">be mapped/projected on a regular image (e.g. insect eye).</span>
<span class="sd">We thus define the following for a scene:</span>
<span class="sd">image based scene (IBS)</span>
<span class="sd"> A classical image. Each pixel is viewed in a direction</span>
<span class="sd"> (elevation,azimuth) in a regular manner.</span>
<span class="sd"> In that case the scene is a 4d numpy array</span>
<span class="sd"> [elevation-index,azimuth-index,channel-index,1].</span>
<span class="sd">Omatidium based scene (OBS)</span>
<span class="sd"> In an ommatidia based scene, the viewing direction</span>
<span class="sd"> do not need to be regularally spaced.</span>
<span class="sd"> In that case the scene is a 3d numpy array</span>
<span class="sd"> [ommatidia-index, channel-index,1].</span>
<span class="sd">By extension a place-code is either image based or ommatidium based.</span>
<span class="sd">The number of dimension of an ib-place-code is always 4, and of an</span>
<span class="sd">ob-place-code always 3.</span>
<span class="sd">image based place-code (IBPC)</span>
<span class="sd"> A place code derived from IBS. Each pixel is viewed in a direction</span>
<span class="sd"> (elevation,azimuth) in a regular manner.</span>
<span class="sd"> In that case the scene is a 4d numpy array</span>
<span class="sd"> [elevation-index,azimuth-index,channel-index,component-index].</span>
<span class="sd">Omatidium based place-code (OBPC)</span>
<span class="sd"> A place code derived from OBS, the viewing direction</span>
<span class="sd"> do not need to be regularally spaced.</span>
<span class="sd"> In that case the scene is a 3d numpy array</span>
<span class="sd"> [ommatidia-index, channel-index,component-index].</span>
<span class="sd">Abusing the terminology of a place-code, a scene can be a place-code.</span>
<span class="sd">Therefore ibs and obs have 4 and 3 dimension, respectively.</span>
<span class="sd">.. todo:</span>
<span class="sd"> * implement optic flow vector</span>
<span class="sd">&quot;&quot;&quot;</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="kn">from</span> <span class="nn">scipy.ndimage</span> <span class="k">import</span> <span class="n">maximum_filter</span><span class="p">,</span> <span class="n">minimum_filter</span>
<span class="kn">import</span> <span class="nn">processing.constants</span> <span class="k">as</span> <span class="nn">prc</span>
<span class="kn">import</span> <span class="nn">processing.tools</span> <span class="k">as</span> <span class="nn">prt</span>
<div class="viewcode-block" id="scene"><a class="viewcode-back" href="../processing.html#processing.scene">[docs]</a><span class="k">def</span> <span class="nf">scene</span><span class="p">(</span><span class="n">database</span><span class="p">,</span> <span class="n">posorient</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">rowid</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot; Return a scene at a position orientation or given rowid</span>
<span class="sd"> in a given database.</span>
<span class="sd"> :param database: a DataBaseLoad class \</span>
<span class="sd"> :param posorient: a pandas Series with index: \</span>
<span class="sd">[&#39;x&#39;,&#39;y&#39;,&#39;z&#39;,&#39;alpha_0,&#39;alpha_1,&#39;alpha_2&#39;] (default None, i.e. not used)</span>
<span class="sd"> :param rowid: a row identification integer for directly reading \</span>
<span class="sd">in the database (default None, i.e. not used).</span>
<span class="sd"> :returns: a scene [elevation, azimuth, channel, 1] or \</span>
<span class="sd">[ommatidia,channel,1].</span>
<span class="sd"> :rtype: np.ndarray</span>
<span class="sd"> .. literalinclude:: example/processing/scene.py</span>
<span class="sd"> :lines: 13-14</span>
<span class="sd"> .. plot:: example/processing/scene.py</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">posorient</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">posorient</span><span class="p">,</span> <span class="n">pd</span><span class="o">.</span><span class="n">Series</span><span class="p">),</span>\
<span class="s1">&#39;posorient should be a pandas Series&#39;</span>
<span class="n">scene</span> <span class="o">=</span> <span class="n">database</span><span class="o">.</span><span class="n">read_image</span><span class="p">(</span><span class="n">posorient</span><span class="o">=</span><span class="n">posorient</span><span class="p">,</span>
<span class="n">rowid</span><span class="o">=</span><span class="n">rowid</span><span class="p">)</span>
<span class="n">scene</span> <span class="o">=</span> <span class="n">scene</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
<span class="k">return</span> <span class="n">scene</span></div>
<div class="viewcode-block" id="skyline"><a class="viewcode-back" href="../processing.html#processing.skyline">[docs]</a><span class="k">def</span> <span class="nf">skyline</span><span class="p">(</span><span class="n">scene</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the average along the elevation of a scene</span>
<span class="sd"> :param scene: the scenery at a given location (a 4d numpy array)</span>
<span class="sd"> :returns: the skyline [1,azimuth,channel,1]</span>
<span class="sd"> :rtype: np.ndarray</span>
<span class="sd"> .. literalinclude:: example/processing/skyline.py</span>
<span class="sd"> :lines: 12-14</span>
<span class="sd"> .. plot:: example/processing/skyline.py</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_ibpc</span><span class="p">(</span><span class="n">scene</span><span class="p">),</span>\
<span class="s1">&#39;scene should be image based to compute a skyline&#39;</span>
<span class="n">skyline</span> <span class="o">=</span> <span class="n">scene</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="n">prc</span><span class="o">.</span><span class="n">__ibpc_indeces__</span><span class="p">[</span><span class="s1">&#39;elevation&#39;</span><span class="p">])</span>
<span class="k">return</span> <span class="n">skyline</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:]</span></div>
<div class="viewcode-block" id="michelson_contrast"><a class="viewcode-back" href="../processing.html#processing.michelson_contrast">[docs]</a><span class="k">def</span> <span class="nf">michelson_contrast</span><span class="p">(</span><span class="n">scene</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the michelson constrast</span>
<span class="sd"> .. math::</span>
<span class="sd"> \\frac{I_\\text{max}-I_\\text{min}}{I_\\text{max}+I_\\text{min}}</span>
<span class="sd"> with :math:`I_\\text{max}` and :math:`I_\\text{min}` representing the \</span>
<span class="sd">highest and lowest luminance in an image region around each pixel.</span>
<span class="sd"> :param scene: an image based scene</span>
<span class="sd"> :param size: the size of the region to calculate the maximum \</span>
<span class="sd">and minimum of the local image intensity</span>
<span class="sd"> :returns: the michelson-contrast</span>
<span class="sd"> :rtype: np.ndarray</span>
<span class="sd"> .. literalinclude:: example/processing/michelson_contrast.py</span>
<span class="sd"> :lines: 12-14</span>
<span class="sd"> .. plot:: example/processing/michelson_contrast.py</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_ibpc</span><span class="p">(</span><span class="n">scene</span><span class="p">),</span> \
<span class="s1">&#39;scene should be image based to compute the michelson constrast&#39;</span>
<span class="n">contrast</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">scene</span><span class="p">)</span>
<span class="k">for</span> <span class="n">channel</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">scene</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">prc</span><span class="o">.</span><span class="n">__ibpc_indeces__</span><span class="p">[</span><span class="s1">&#39;channel&#39;</span><span class="p">]]):</span>
<span class="n">i_max</span> <span class="o">=</span> <span class="n">maximum_filter</span><span class="p">(</span><span class="n">scene</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">channel</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;wrap&#39;</span><span class="p">)</span>
<span class="n">i_min</span> <span class="o">=</span> <span class="n">minimum_filter</span><span class="p">(</span><span class="n">scene</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">channel</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="n">size</span><span class="o">=</span><span class="n">size</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;wrap&#39;</span><span class="p">)</span>
<span class="n">contrast</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">channel</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">i_max</span> <span class="o">-</span> <span class="n">i_min</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">i_max</span> <span class="o">+</span> <span class="n">i_min</span><span class="p">)</span>
<span class="k">return</span> <span class="n">contrast</span></div>
<div class="viewcode-block" id="contrast_weighted_nearness"><a class="viewcode-back" href="../processing.html#processing.contrast_weighted_nearness">[docs]</a><span class="k">def</span> <span class="nf">contrast_weighted_nearness</span><span class="p">(</span><span class="n">scene</span><span class="p">,</span> <span class="n">contrast_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">distance_channel</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the michelson contrast wheighted nearness</span>
<span class="sd"> :param scene: an image based scene</span>
<span class="sd"> :param contrast_size: the size of the region to calculate the maximum \</span>
<span class="sd">and minimum of the local image intensity in the michelson-contrast.</span>
<span class="sd"> :param distance_channel: the index of the distance-channel.</span>
<span class="sd"> .. literalinclude:: example/processing/contrast_weighted_nearness.py</span>
<span class="sd"> :lines: 12-14</span>
<span class="sd"> .. plot:: example/processing/contrast_weighted_nearness.py</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">assert</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_ibpc</span><span class="p">(</span><span class="n">scene</span><span class="p">),</span> \
<span class="s1">&#39;scene should be image based to compute the contrast weighted nearness&#39;</span>
<span class="n">contrast</span> <span class="o">=</span> <span class="n">michelson_contrast</span><span class="p">(</span><span class="n">scene</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">contrast_size</span><span class="p">)</span>
<span class="n">distance</span> <span class="o">=</span> <span class="n">scene</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">distance_channel</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">distance</span> <span class="o">=</span> <span class="n">distance</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
<span class="n">distance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">distance</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">scene</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="mi">1</span><span class="p">))</span>
<span class="k">return</span> <span class="n">contrast</span> <span class="o">/</span> <span class="n">distance</span></div>
<div class="viewcode-block" id="pcv"><a class="viewcode-back" href="../processing.html#processing.pcv">[docs]</a><span class="k">def</span> <span class="nf">pcv</span><span class="p">(</span><span class="n">place_code</span><span class="p">,</span> <span class="n">viewing_directions</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Place code vectors</span>
<span class="sd"> :param place_code: the place code at a given location (e.g. an ibs scene)</span>
<span class="sd"> :param viewing_directions: viewing direction of each pixel</span>
<span class="sd"> :returns: the place code vectors in cartesian coordinates</span>
<span class="sd"> :rtype: (np.ndarray)</span>
<span class="sd"> .. literalinclude:: example/processing/pcv.py</span>
<span class="sd"> :lines: 12-14</span>
<span class="sd"> .. plot:: example/processing/pcv.py</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_ibpc</span><span class="p">(</span><span class="n">place_code</span><span class="p">):</span>
<span class="n">component_dim</span> <span class="o">=</span> <span class="n">prc</span><span class="o">.</span><span class="n">__ibpc_indeces__</span><span class="p">[</span><span class="s1">&#39;component&#39;</span><span class="p">]</span>
<span class="n">channel_dim</span> <span class="o">=</span> <span class="n">prc</span><span class="o">.</span><span class="n">__ibpc_indeces__</span><span class="p">[</span><span class="s1">&#39;channel&#39;</span><span class="p">]</span>
<span class="k">elif</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_obpc</span><span class="p">(</span><span class="n">place_code</span><span class="p">):</span>
<span class="n">component_dim</span> <span class="o">=</span> <span class="n">prc</span><span class="o">.</span><span class="n">__obpc_indeces__</span><span class="p">[</span><span class="s1">&#39;component&#39;</span><span class="p">]</span>
<span class="n">channel_dim</span> <span class="o">=</span> <span class="n">prc</span><span class="o">.</span><span class="n">__obpc_indeces__</span><span class="p">[</span><span class="s1">&#39;channel&#39;</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;place code should be either an ibpc or obpc&#39;</span><span class="p">)</span>
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">viewing_directions</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">),</span> \
<span class="s1">&#39;viewing_directions should be a numpy array&#39;</span>
<span class="k">assert</span> <span class="n">place_code</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">component_dim</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> \
<span class="s1">&#39;the last dimension (</span><span class="si">{}</span><span class="s1">) of the place-code should be 1&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
<span class="n">place_code</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">component_dim</span><span class="p">])</span>
<span class="n">elevation</span> <span class="o">=</span> <span class="n">viewing_directions</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">prc</span><span class="o">.</span><span class="n">__spherical_indeces__</span><span class="p">[</span><span class="s1">&#39;elevation&#39;</span><span class="p">]]</span>
<span class="n">azimuth</span> <span class="o">=</span> <span class="n">viewing_directions</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">prc</span><span class="o">.</span><span class="n">__spherical_indeces__</span><span class="p">[</span><span class="s1">&#39;azimuth&#39;</span><span class="p">]]</span>
<span class="n">unscaled_lv</span> <span class="o">=</span> <span class="n">prt</span><span class="o">.</span><span class="n">spherical_to_cartesian</span><span class="p">(</span><span class="n">elevation</span><span class="p">,</span> <span class="n">azimuth</span><span class="p">,</span> <span class="n">radius</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="n">scaled_lv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">place_code</span><span class="p">)</span>
<span class="c1"># (3,) -&gt; (1,1,3) or (1,1,1,3) see numpy.tile</span>
<span class="n">scaled_lv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">scaled_lv</span><span class="p">,</span> <span class="p">(</span><span class="n">unscaled_lv</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],))</span>
<span class="k">for</span> <span class="n">channel_index</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">scaled_lv</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">channel_dim</span><span class="p">]):</span>
<span class="n">radius</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">place_code</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">channel_index</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span> <span class="p">(</span><span class="n">scaled_lv</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],))</span>
<span class="n">scaled_lv</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">channel_index</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">unscaled_lv</span> <span class="o">*</span> <span class="n">radius</span>
<span class="k">return</span> <span class="n">scaled_lv</span></div>
<div class="viewcode-block" id="apcv"><a class="viewcode-back" href="../processing.html#processing.apcv">[docs]</a><span class="k">def</span> <span class="nf">apcv</span><span class="p">(</span><span class="n">place_code</span><span class="p">,</span> <span class="n">viewing_directions</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Calculate the average scene vector</span>
<span class="sd"> :param place_code: the place code at a given location (e.g. an ibs scene)</span>
<span class="sd"> :param viewing_directions: viewing direction of each pixel</span>
<span class="sd"> :returns: the average place-code vector</span>
<span class="sd"> :rtype: (np.ndarray)</span>
<span class="sd"> .. literalinclude:: example/processing/apcv.py</span>
<span class="sd"> :lines: 12-14</span>
<span class="sd"> .. plot:: example/processing/apcv.py</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="n">scaled_lv</span> <span class="o">=</span> <span class="n">pcv</span><span class="p">(</span><span class="n">place_code</span><span class="p">,</span> <span class="n">viewing_directions</span><span class="p">)</span>
<span class="k">if</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_ibpc</span><span class="p">(</span><span class="n">place_code</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">scaled_lv</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="o">...</span><span class="p">]</span>
<span class="k">elif</span> <span class="n">prt</span><span class="o">.</span><span class="n">is_obpc</span><span class="p">(</span><span class="n">place_code</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">scaled_lv</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="o">...</span><span class="p">]</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;place code is neither an ibpc nor obpc&#39;</span><span class="p">)</span></div>
<div class="viewcode-block" id="optic_flow"><a class="viewcode-back" href="../processing.html#processing.optic_flow">[docs]</a><span class="k">def</span> <span class="nf">optic_flow</span><span class="p">(</span><span class="n">place_code</span><span class="p">,</span> <span class="n">viewing_directions</span><span class="p">,</span> <span class="n">velocity</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;NOT IMPLEMENTED&quot;&quot;&quot;</span>
<span class="k">raise</span> <span class="ne">NameError</span><span class="p">(</span><span class="s1">&#39;Not Implemented&#39;</span><span class="p">)</span></div>
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