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<p>Math operations for IP algorithms.  
<a href="#details">More...</a></p>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
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double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gaaa4583e6d012a8b49ad1738cec762651">lanczos</a> (double x, std::ptrdiff_t a)</td></tr>
<tr class="memdesc:gaaa4583e6d012a8b49ad1738cec762651"><td class="mdescLeft">&#160;</td><td class="mdescRight">Lanczos response at point xLanczos response is defined as: x == 0: 1 -a &lt; x &amp;&amp; x &lt; a: 0 otherwise: normalized_sinc(x) / normalized_sinc(x / a) <br /></td></tr>
<tr class="separator:gaaa4583e6d012a8b49ad1738cec762651"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga29d420198670c0445e58a0e428ef9230"><td class="memTemplParams" colspan="2">template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:ga29d420198670c0445e58a0e428ef9230"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga29d420198670c0445e58a0e428ef9230">generate_normalized_mean</a> (std::size_t side_length)</td></tr>
<tr class="memdesc:ga29d420198670c0445e58a0e428ef9230"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generate mean kernelFills supplied view with normalized mean in which all entries will be equal to.  <a href="group___image_processing_math.html#ga29d420198670c0445e58a0e428ef9230">More...</a><br /></td></tr>
<tr class="separator:ga29d420198670c0445e58a0e428ef9230"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga182587a9a3438ba3eab25a476bbad777"><td class="memTemplParams" colspan="2"><a id="ga182587a9a3438ba3eab25a476bbad777"></a>
template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:ga182587a9a3438ba3eab25a476bbad777"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga182587a9a3438ba3eab25a476bbad777">generate_unnormalized_mean</a> (std::size_t side_length)</td></tr>
<tr class="memdesc:ga182587a9a3438ba3eab25a476bbad777"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generate kernel with all 1sFills supplied view with 1s (ones) <br /></td></tr>
<tr class="separator:ga182587a9a3438ba3eab25a476bbad777"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gac1aaebf1673d8b0f087ed851b5b7a47d"><td class="memTemplParams" colspan="2"><a id="gac1aaebf1673d8b0f087ed851b5b7a47d"></a>
template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:gac1aaebf1673d8b0f087ed851b5b7a47d"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gac1aaebf1673d8b0f087ed851b5b7a47d">generate_gaussian_kernel</a> (std::size_t side_length, double sigma)</td></tr>
<tr class="memdesc:gac1aaebf1673d8b0f087ed851b5b7a47d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generate Gaussian kernelFills supplied view with values taken from Gaussian distribution. See <a href="https://en.wikipedia.org/wiki/Gaussian_blur">https://en.wikipedia.org/wiki/Gaussian_blur</a>. <br /></td></tr>
<tr class="separator:gac1aaebf1673d8b0f087ed851b5b7a47d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gaadc550b82ba9119bad0bbf4d358e0b73"><td class="memTemplParams" colspan="2"><a id="gaadc550b82ba9119bad0bbf4d358e0b73"></a>
template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:gaadc550b82ba9119bad0bbf4d358e0b73"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gaadc550b82ba9119bad0bbf4d358e0b73">generate_dx_sobel</a> (unsigned int degree=1)</td></tr>
<tr class="memdesc:gaadc550b82ba9119bad0bbf4d358e0b73"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generates Sobel operator in horizontal directionGenerates a kernel which will represent Sobel operator in horizontal direction of specified degree (no need to convolve multiple times to obtain the desired degree). <a href="https://www.researchgate.net/publication/239398674_An_Isotropic_3_3_Image_Gradient_Operator">https://www.researchgate.net/publication/239398674_An_Isotropic_3_3_Image_Gradient_Operator</a>. <br /></td></tr>
<tr class="separator:gaadc550b82ba9119bad0bbf4d358e0b73"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gae9b2680356c21a952cb0daf2a2c779f0"><td class="memTemplParams" colspan="2"><a id="gae9b2680356c21a952cb0daf2a2c779f0"></a>
template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:gae9b2680356c21a952cb0daf2a2c779f0"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gae9b2680356c21a952cb0daf2a2c779f0">generate_dx_scharr</a> (unsigned int degree=1)</td></tr>
<tr class="memdesc:gae9b2680356c21a952cb0daf2a2c779f0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generate Scharr operator in horizontal directionGenerates a kernel which will represent Scharr operator in horizontal direction of specified degree (no need to convolve multiple times to obtain the desired degree). <a href="https://www.researchgate.net/profile/Hanno_Scharr/publication/220955743_Optimal_Filters_for_Extended_Optical_Flow/links/004635151972eda98f000000/Optimal-Filters-for-Extended-Optical-Flow.pdf">https://www.researchgate.net/profile/Hanno_Scharr/publication/220955743_Optimal_Filters_for_Extended_Optical_Flow/links/004635151972eda98f000000/Optimal-Filters-for-Extended-Optical-Flow.pdf</a>. <br /></td></tr>
<tr class="separator:gae9b2680356c21a952cb0daf2a2c779f0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga726dd0714f3e65ea9bab6b9201c16c96"><td class="memTemplParams" colspan="2"><a id="ga726dd0714f3e65ea9bab6b9201c16c96"></a>
template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:ga726dd0714f3e65ea9bab6b9201c16c96"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga726dd0714f3e65ea9bab6b9201c16c96">generate_dy_sobel</a> (unsigned int degree=1)</td></tr>
<tr class="memdesc:ga726dd0714f3e65ea9bab6b9201c16c96"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generates Sobel operator in vertical directionGenerates a kernel which will represent Sobel operator in vertical direction of specified degree (no need to convolve multiple times to obtain the desired degree). <a href="https://www.researchgate.net/publication/239398674_An_Isotropic_3_3_Image_Gradient_Operator">https://www.researchgate.net/publication/239398674_An_Isotropic_3_3_Image_Gradient_Operator</a>. <br /></td></tr>
<tr class="separator:ga726dd0714f3e65ea9bab6b9201c16c96"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gad626d5b1cbd1e81ffbf638c2ec1e030c"><td class="memTemplParams" colspan="2"><a id="gad626d5b1cbd1e81ffbf638c2ec1e030c"></a>
template&lt;typename T  = float, typename Allocator  = std::allocator&lt;T&gt;&gt; </td></tr>
<tr class="memitem:gad626d5b1cbd1e81ffbf638c2ec1e030c"><td class="memTemplItemLeft" align="right" valign="top">detail::kernel_2d&lt; T, Allocator &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gad626d5b1cbd1e81ffbf638c2ec1e030c">generate_dy_scharr</a> (unsigned int degree=1)</td></tr>
<tr class="memdesc:gad626d5b1cbd1e81ffbf638c2ec1e030c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generate Scharr operator in vertical directionGenerates a kernel which will represent Scharr operator in vertical direction of specified degree (no need to convolve multiple times to obtain the desired degree). <a href="https://www.researchgate.net/profile/Hanno_Scharr/publication/220955743_Optimal_Filters_for_Extended_Optical_Flow/links/004635151972eda98f000000/Optimal-Filters-for-Extended-Optical-Flow.pdf">https://www.researchgate.net/profile/Hanno_Scharr/publication/220955743_Optimal_Filters_for_Extended_Optical_Flow/links/004635151972eda98f000000/Optimal-Filters-for-Extended-Optical-Flow.pdf</a>. <br /></td></tr>
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<tr class="memitem:ga5b662d207dd54aba778c0f8c3697c025"><td class="memTemplParams" colspan="2"><a id="ga5b662d207dd54aba778c0f8c3697c025"></a>
template&lt;typename GradientView , typename OutputView &gt; </td></tr>
<tr class="memitem:ga5b662d207dd54aba778c0f8c3697c025"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga5b662d207dd54aba778c0f8c3697c025">compute_hessian_entries</a> (GradientView dx, GradientView dy, OutputView ddxx, OutputView dxdy, OutputView ddyy)</td></tr>
<tr class="memdesc:ga5b662d207dd54aba778c0f8c3697c025"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute xy gradient, and second order x and y gradientsHessian matrix is defined as a matrix of partial derivates for 2d case, it is [[ddxx, dxdy], [dxdy, ddyy]. d stands for derivative, and x or y stand for direction. For example, dx stands for derivative (gradient) in horizontal direction, and ddxx means second order derivative in horizon direction <a href="https://en.wikipedia.org/wiki/Hessian_matrix">https://en.wikipedia.org/wiki/Hessian_matrix</a>. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<p>Math operations for IP algorithms. </p>
<p>This is mostly handful of mathemtical operations that are required by other image processing algorithms</p>
<p>Normalized cardinal sine</p>
<p>normalized_sinc(x) = sin(pi * x) / (pi * x) </p>
<h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ga29d420198670c0445e58a0e428ef9230">&#9670;&nbsp;</a></span>generate_normalized_mean()</h2>

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<p>Generate mean kernelFills supplied view with normalized mean in which all entries will be equal to. </p>
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