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project.py
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<time class="js-relative-date" datetime="2012-05-02T21:34:39-07:00" title="2012-05-02 21:34:39">May 02, 2012</time>
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<div class="highlight"><pre><div class='line' id='LC1'><span class="sd">"""Image projection.</span></div><div class='line' id='LC2'><br/></div><div class='line' id='LC3'><span class="sd">"""</span></div><div class='line' id='LC4'><br/></div><div class='line' id='LC5'><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span></div><div class='line' id='LC6'><span class="kn">from</span> <span class="nn">scipy.ndimage</span> <span class="kn">import</span> <span class="n">interpolation</span> <span class="k">as</span> <span class="n">ndii</span></div><div class='line' id='LC7'><span class="kn">from</span> <span class="nn">._warp</span> <span class="kn">import</span> <span class="n">_stackcopy</span></div><div class='line' id='LC8'><br/></div><div class='line' id='LC9'><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">'homography'</span><span class="p">]</span></div><div class='line' id='LC10'><br/></div><div class='line' id='LC11'><span class="n">eps</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span></div><div class='line' id='LC12'><br/></div><div class='line' id='LC13'><span class="k">def</span> <span class="nf">homography</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">H</span><span class="p">,</span> <span class="n">output_shape</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span></div><div class='line' id='LC14'> <span class="n">mode</span><span class="o">=</span><span class="s">'constant'</span><span class="p">,</span> <span class="n">cval</span><span class="o">=</span><span class="mf">0.</span><span class="p">):</span></div><div class='line' id='LC15'> <span class="sd">"""Perform a projective transformation (homography) on an image.</span></div><div class='line' id='LC16'><br/></div><div class='line' id='LC17'><span class="sd"> For each pixel, given its homogeneous coordinate :math:`\mathbf{x}</span></div><div class='line' id='LC18'><span class="sd"> = [x, y, 1]^T`, its target position is calculated by multiplying</span></div><div class='line' id='LC19'><span class="sd"> with the given matrix, :math:`H`, to give :math:`H \mathbf{x}`.</span></div><div class='line' id='LC20'><span class="sd"> E.g., to rotate by theta degrees clockwise, the matrix should be</span></div><div class='line' id='LC21'><br/></div><div class='line' id='LC22'><span class="sd"> ::</span></div><div class='line' id='LC23'><br/></div><div class='line' id='LC24'><span class="sd"> [[cos(theta) -sin(theta) 0]</span></div><div class='line' id='LC25'><span class="sd"> [sin(theta) cos(theta) 0]</span></div><div class='line' id='LC26'><span class="sd"> [0 0 1]]</span></div><div class='line' id='LC27'><br/></div><div class='line' id='LC28'><span class="sd"> or, to translate x by 10 and y by 20,</span></div><div class='line' id='LC29'><br/></div><div class='line' id='LC30'><span class="sd"> ::</span></div><div class='line' id='LC31'><br/></div><div class='line' id='LC32'><span class="sd"> [[1 0 10]</span></div><div class='line' id='LC33'><span class="sd"> [0 1 20]</span></div><div class='line' id='LC34'><span class="sd"> [0 0 1 ]].</span></div><div class='line' id='LC35'><br/></div><div class='line' id='LC36'><span class="sd"> Parameters</span></div><div class='line' id='LC37'><span class="sd"> ----------</span></div><div class='line' id='LC38'><span class="sd"> image : 2-D array</span></div><div class='line' id='LC39'><span class="sd"> Input image.</span></div><div class='line' id='LC40'><span class="sd"> H : array of shape ``(3, 3)``</span></div><div class='line' id='LC41'><span class="sd"> Transformation matrix H that defines the homography.</span></div><div class='line' id='LC42'><span class="sd"> output_shape : tuple (rows, cols)</span></div><div class='line' id='LC43'><span class="sd"> Shape of the output image generated.</span></div><div class='line' id='LC44'><span class="sd"> order : int</span></div><div class='line' id='LC45'><span class="sd"> Order of splines used in interpolation.</span></div><div class='line' id='LC46'><span class="sd"> mode : string</span></div><div class='line' id='LC47'><span class="sd"> How to handle values outside the image borders. Passed as-is</span></div><div class='line' id='LC48'><span class="sd"> to ndimage.</span></div><div class='line' id='LC49'><span class="sd"> cval : string</span></div><div class='line' id='LC50'><span class="sd"> Used in conjunction with mode 'constant', the value outside</span></div><div class='line' id='LC51'><span class="sd"> the image boundaries.</span></div><div class='line' id='LC52'><br/></div><div class='line' id='LC53'><span class="sd"> Examples</span></div><div class='line' id='LC54'><span class="sd"> --------</span></div><div class='line' id='LC55'><span class="sd"> >>> # rotate by 90 degrees around origin and shift down by 2</span></div><div class='line' id='LC56'><span class="sd"> >>> x = np.arange(9, dtype=np.uint8).reshape((3, 3)) + 1</span></div><div class='line' id='LC57'><span class="sd"> >>> x</span></div><div class='line' id='LC58'><span class="sd"> array([[1, 2, 3],</span></div><div class='line' id='LC59'><span class="sd"> [4, 5, 6],</span></div><div class='line' id='LC60'><span class="sd"> [7, 8, 9]], dtype=uint8)</span></div><div class='line' id='LC61'><span class="sd"> >>> theta = -np.pi/2</span></div><div class='line' id='LC62'><span class="sd"> >>> M = np.array([[np.cos(theta),-np.sin(theta),0],</span></div><div class='line' id='LC63'><span class="sd"> ... [np.sin(theta), np.cos(theta),2],</span></div><div class='line' id='LC64'><span class="sd"> ... [0, 0, 1]])</span></div><div class='line' id='LC65'><span class="sd"> >>> x90 = homography(x, M, order=1)</span></div><div class='line' id='LC66'><span class="sd"> >>> x90</span></div><div class='line' id='LC67'><span class="sd"> array([[3, 6, 9],</span></div><div class='line' id='LC68'><span class="sd"> [2, 5, 8],</span></div><div class='line' id='LC69'><span class="sd"> [1, 4, 7]], dtype=uint8)</span></div><div class='line' id='LC70'><span class="sd"> >>> # translate right by 2 and down by 1</span></div><div class='line' id='LC71'><span class="sd"> >>> y = np.zeros((5,5), dtype=np.uint8)</span></div><div class='line' id='LC72'><span class="sd"> >>> y[1, 1] = 255</span></div><div class='line' id='LC73'><span class="sd"> >>> y</span></div><div class='line' id='LC74'><span class="sd"> array([[ 0, 0, 0, 0, 0],</span></div><div class='line' id='LC75'><span class="sd"> [ 0, 255, 0, 0, 0],</span></div><div class='line' id='LC76'><span class="sd"> [ 0, 0, 0, 0, 0],</span></div><div class='line' id='LC77'><span class="sd"> [ 0, 0, 0, 0, 0],</span></div><div class='line' id='LC78'><span class="sd"> [ 0, 0, 0, 0, 0]], dtype=uint8)</span></div><div class='line' id='LC79'><span class="sd"> >>> M = np.array([[ 1., 0., 2.],</span></div><div class='line' id='LC80'><span class="sd"> ... [ 0., 1., 1.],</span></div><div class='line' id='LC81'><span class="sd"> ... [ 0., 0., 1.]])</span></div><div class='line' id='LC82'><span class="sd"> >>> y21 = homography(y, M, order=1)</span></div><div class='line' id='LC83'><span class="sd"> >>> y21</span></div><div class='line' id='LC84'><span class="sd"> array([[ 0, 0, 0, 0, 0],</span></div><div class='line' id='LC85'><span class="sd"> [ 0, 0, 0, 0, 0],</span></div><div class='line' id='LC86'><span class="sd"> [ 0, 0, 0, 255, 0],</span></div><div class='line' id='LC87'><span class="sd"> [ 0, 0, 0, 0, 0],</span></div><div class='line' id='LC88'><span class="sd"> [ 0, 0, 0, 0, 0]], dtype=uint8)</span></div><div class='line' id='LC89'><span class="sd"> </span></div><div class='line' id='LC90'><span class="sd"> """</span></div><div class='line' id='LC91'> <span class="k">if</span> <span class="n">image</span><span class="o">.</span><span class="n">ndim</span> <span class="o"><</span> <span class="mi">2</span><span class="p">:</span></div><div class='line' id='LC92'> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"Input must have more than 1 dimension."</span><span class="p">)</span></div><div class='line' id='LC93'><br/></div><div class='line' id='LC94'> <span class="n">image</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">atleast_3d</span><span class="p">(</span><span class="n">image</span><span class="p">)</span></div><div class='line' id='LC95'> <span class="n">ishape</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">image</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span></div><div class='line' id='LC96'> <span class="n">bands</span> <span class="o">=</span> <span class="n">ishape</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span></div><div class='line' id='LC97'><br/></div><div class='line' id='LC98'> <span class="k">if</span> <span class="n">output_shape</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span></div><div class='line' id='LC99'> <span class="n">output_shape</span> <span class="o">=</span> <span class="n">ishape</span></div><div class='line' id='LC100'><br/></div><div class='line' id='LC101'> <span class="n">coords</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="n">output_shape</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span></div><div class='line' id='LC102'><br/></div><div class='line' id='LC103'> <span class="c"># TODO: Refactor this method to use transform.warp instead.</span></div><div class='line' id='LC104'><br/></div><div class='line' id='LC105'> <span class="c"># Construct transformed coordinates</span></div><div class='line' id='LC106'> <span class="n">rows</span><span class="p">,</span> <span class="n">cols</span> <span class="o">=</span> <span class="n">output_shape</span><span class="p">[:</span><span class="mi">2</span><span class="p">]</span></div><div class='line' id='LC107'> <span class="n">rows</span><span class="p">,</span> <span class="n">cols</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[:</span><span class="n">rows</span><span class="p">,</span> <span class="p">:</span><span class="n">cols</span><span class="p">]</span></div><div class='line' id='LC108'> <span class="n">tf_coords</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">cols</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span></div><div class='line' id='LC109'> <span class="n">dtype</span><span class="o">=</span><span class="p">[(</span><span class="s">'cols'</span><span class="p">,</span> <span class="nb">float</span><span class="p">),</span></div><div class='line' id='LC110'> <span class="p">(</span><span class="s">'rows'</span><span class="p">,</span> <span class="nb">float</span><span class="p">),</span></div><div class='line' id='LC111'> <span class="p">(</span><span class="s">'z'</span><span class="p">,</span> <span class="nb">float</span><span class="p">)])</span></div><div class='line' id='LC112'> <span class="n">tf_coords</span><span class="p">[</span><span class="s">'cols'</span><span class="p">],</span> <span class="n">tf_coords</span><span class="p">[</span><span class="s">'rows'</span><span class="p">]</span> <span class="o">=</span> <span class="n">cols</span><span class="p">,</span> <span class="n">rows</span></div><div class='line' id='LC113'> <span class="n">tf_coords</span><span class="p">[</span><span class="s">'z'</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span></div><div class='line' id='LC114'> <span class="n">tf_coords</span> <span class="o">=</span> <span class="n">tf_coords</span><span class="o">.</span><span class="n">view</span><span class="p">((</span><span class="nb">float</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span></div><div class='line' id='LC115'><br/></div><div class='line' id='LC116'> <span class="n">tf_coords</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">tf_coords</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">H</span><span class="p">)</span><span class="o">.</span><span class="n">transpose</span><span class="p">())</span></div><div class='line' id='LC117'> <span class="n">tf_coords</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">absolute</span><span class="p">(</span><span class="n">tf_coords</span><span class="p">)</span> <span class="o"><</span> <span class="n">eps</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.</span></div><div class='line' id='LC118'><br/></div><div class='line' id='LC119'> <span class="c"># normalize coordinates</span></div><div class='line' id='LC120'> <span class="n">tf_coords</span><span class="p">[</span><span class="o">...</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">tf_coords</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span></div><div class='line' id='LC121'><br/></div><div class='line' id='LC122'> <span class="c"># y-coordinate mapping</span></div><div class='line' id='LC123'> <span class="n">_stackcopy</span><span class="p">(</span><span class="n">coords</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">tf_coords</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span></div><div class='line' id='LC124'><br/></div><div class='line' id='LC125'> <span class="c"># x-coordinate mapping</span></div><div class='line' id='LC126'> <span class="n">_stackcopy</span><span class="p">(</span><span class="n">coords</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="o">...</span><span class="p">],</span> <span class="n">tf_coords</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="mi">0</span><span class="p">])</span></div><div class='line' id='LC127'><br/></div><div class='line' id='LC128'> <span class="c"># colour-coordinate mapping</span></div><div class='line' id='LC129'> <span class="n">coords</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="o">...</span><span class="p">]</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">bands</span><span class="p">)</span></div><div class='line' id='LC130'><br/></div><div class='line' id='LC131'> <span class="c"># Prefilter not necessary for order 1 interpolation</span></div><div class='line' id='LC132'> <span class="n">prefilter</span> <span class="o">=</span> <span class="n">order</span> <span class="o">></span> <span class="mi">1</span></div><div class='line' id='LC133'> <span class="n">mapped</span> <span class="o">=</span> <span class="n">ndii</span><span class="o">.</span><span class="n">map_coordinates</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">coords</span><span class="p">,</span> <span class="n">prefilter</span><span class="o">=</span><span class="n">prefilter</span><span class="p">,</span></div><div class='line' id='LC134'> <span class="n">mode</span><span class="o">=</span><span class="n">mode</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="n">order</span><span class="p">,</span> <span class="n">cval</span><span class="o">=</span><span class="n">cval</span><span class="p">)</span></div><div class='line' id='LC135'><br/></div><div class='line' id='LC136'> <span class="k">return</span> <span class="n">mapped</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span></div></pre></div>
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<h3>Format Text</h3>
<p>Headers</p>
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# This is an <h1> tag
## This is an <h2> tag
###### This is an <h6> tag</pre>
<p>Text styles</p>
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*This text will be italic*
_This will also be italic_
**This text will be bold**
__This will also be bold__
*You **can** combine them*
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<p>Unordered</p>
<pre>
* Item 1
* Item 2
* Item 2a
* Item 2b</pre>
<p>Ordered</p>
<pre>
1. Item 1
2. Item 2
3. Item 3
* Item 3a
* Item 3b</pre>
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Format: 
</pre>
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http://github.com - automatic!
[GitHub](http://github.com)</pre>
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As Kanye West said:
> We're living the future so
> the present is our past.
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```javascript
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
```</pre>
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Here is a Python code example
without syntax highlighting:
def foo:
if not bar:
return true</pre>
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<pre>
I think you should use an
`<addr>` element here instead.</pre>
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