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<h3><a href="../index.html"><img alt="Boost GIL" src="../_static/gil.png" border="0"></a></h3>
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<a href="#func-members">Functions</a> </div>
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<div class="headertitle"><div class="title">ImageProcessingMath</div></div>
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<div class="contents">
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<p>Math operations for IP algorithms.
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<a href="#details">More...</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:gae9f1ef23591e1b4a5d974090b3aef0c7" id="r_gae9f1ef23591e1b4a5d974090b3aef0c7"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gae9f1ef23591e1b4a5d974090b3aef0c7">lanczos</a> (double x, std::ptrdiff_t a)</td></tr>
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<tr class="memdesc:gae9f1ef23591e1b4a5d974090b3aef0c7"><td class="mdescLeft"> </td><td class="mdescRight">Lanczos response at point x. <br /></td></tr>
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<tr class="separator:gae9f1ef23591e1b4a5d974090b3aef0c7"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaec666d97dfea82bd6fa608bca92a6fd1" id="r_gaec666d97dfea82bd6fa608bca92a6fd1"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:gaec666d97dfea82bd6fa608bca92a6fd1"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gaec666d97dfea82bd6fa608bca92a6fd1">generate_normalized_mean</a> (std::size_t side_length) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:gaec666d97dfea82bd6fa608bca92a6fd1"><td class="mdescLeft"> </td><td class="mdescRight">Generate mean kernel. <br /></td></tr>
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<tr class="separator:gaec666d97dfea82bd6fa608bca92a6fd1"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga75f408389d62130314890c81f7894ed2" id="r_ga75f408389d62130314890c81f7894ed2"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:ga75f408389d62130314890c81f7894ed2"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga75f408389d62130314890c81f7894ed2">generate_unnormalized_mean</a> (std::size_t side_length) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:ga75f408389d62130314890c81f7894ed2"><td class="mdescLeft"> </td><td class="mdescRight">Generate kernel with all 1s. <br /></td></tr>
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<tr class="separator:ga75f408389d62130314890c81f7894ed2"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga26eea098b8eb037c207240828fb0fdf1" id="r_ga26eea098b8eb037c207240828fb0fdf1"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:ga26eea098b8eb037c207240828fb0fdf1"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga26eea098b8eb037c207240828fb0fdf1">generate_gaussian_kernel</a> (std::size_t side_length, double sigma) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:ga26eea098b8eb037c207240828fb0fdf1"><td class="mdescLeft"> </td><td class="mdescRight">Generate Gaussian kernel. <br /></td></tr>
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<tr class="separator:ga26eea098b8eb037c207240828fb0fdf1"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaabc9c7cd5876b5a7ddf1ee568d3b8553" id="r_gaabc9c7cd5876b5a7ddf1ee568d3b8553"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:gaabc9c7cd5876b5a7ddf1ee568d3b8553"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#gaabc9c7cd5876b5a7ddf1ee568d3b8553">generate_dx_sobel</a> (unsigned int degree=1) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:gaabc9c7cd5876b5a7ddf1ee568d3b8553"><td class="mdescLeft"> </td><td class="mdescRight">Generates Sobel operator in horizontal direction. <br /></td></tr>
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<tr class="separator:gaabc9c7cd5876b5a7ddf1ee568d3b8553"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga4cc5c53a7cbddd81c47e9d80424886fd" id="r_ga4cc5c53a7cbddd81c47e9d80424886fd"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:ga4cc5c53a7cbddd81c47e9d80424886fd"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga4cc5c53a7cbddd81c47e9d80424886fd">generate_dx_scharr</a> (unsigned int degree=1) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:ga4cc5c53a7cbddd81c47e9d80424886fd"><td class="mdescLeft"> </td><td class="mdescRight">Generate Scharr operator in horizontal direction. <br /></td></tr>
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<tr class="separator:ga4cc5c53a7cbddd81c47e9d80424886fd"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga9617799d5b34ecf368c9611c2c471017" id="r_ga9617799d5b34ecf368c9611c2c471017"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:ga9617799d5b34ecf368c9611c2c471017"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga9617799d5b34ecf368c9611c2c471017">generate_dy_sobel</a> (unsigned int degree=1) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:ga9617799d5b34ecf368c9611c2c471017"><td class="mdescLeft"> </td><td class="mdescRight">Generates Sobel operator in vertical direction. <br /></td></tr>
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<tr class="separator:ga9617799d5b34ecf368c9611c2c471017"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga3f798e12d2f00de60fb8d0be35cd99b0" id="r_ga3f798e12d2f00de60fb8d0be35cd99b0"><td class="memTemplParams" colspan="2">template<typename T = float, typename Allocator = std::allocator<T>> </td></tr>
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<tr class="memitem:ga3f798e12d2f00de60fb8d0be35cd99b0"><td class="memTemplItemLeft" align="right" valign="top">auto </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga3f798e12d2f00de60fb8d0be35cd99b0">generate_dy_scharr</a> (unsigned int degree=1) -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a>< T, Allocator ></td></tr>
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<tr class="memdesc:ga3f798e12d2f00de60fb8d0be35cd99b0"><td class="mdescLeft"> </td><td class="mdescRight">Generate Scharr operator in vertical direction. <br /></td></tr>
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<tr class="separator:ga3f798e12d2f00de60fb8d0be35cd99b0"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga426f799ec568d39aad3d6fbc8745606a" id="r_ga426f799ec568d39aad3d6fbc8745606a"><td class="memTemplParams" colspan="2">template<typename GradientView , typename OutputView > </td></tr>
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<tr class="memitem:ga426f799ec568d39aad3d6fbc8745606a"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group___image_processing_math.html#ga426f799ec568d39aad3d6fbc8745606a">compute_hessian_entries</a> (GradientView dx, GradientView dy, OutputView ddxx, OutputView dxdy, OutputView ddyy)</td></tr>
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<tr class="memdesc:ga426f799ec568d39aad3d6fbc8745606a"><td class="mdescLeft"> </td><td class="mdescRight">Compute xy gradient, and second order x and y gradients. <br /></td></tr>
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<tr class="separator:ga426f799ec568d39aad3d6fbc8745606a"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<p>Math operations for IP algorithms. </p>
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<p>This is mostly handful of mathemtical operations that are required by other image processing algorithms</p>
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<p>Normalized cardinal sine</p>
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<p>normalized_sinc(x) = sin(pi * x) / (pi * x) </p>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="ga426f799ec568d39aad3d6fbc8745606a" name="ga426f799ec568d39aad3d6fbc8745606a"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga426f799ec568d39aad3d6fbc8745606a">◆ </a></span>compute_hessian_entries()</h2>
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template<typename GradientView , typename OutputView > </div>
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<td class="memname">void compute_hessian_entries </td>
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<td>(</td>
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<td class="paramtype">GradientView </td>
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<td class="paramname"><em>dx</em>, </td>
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<td class="paramtype">GradientView </td>
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<td class="paramname"><em>dy</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">OutputView </td>
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<td class="paramname"><em>ddxx</em>, </td>
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<td class="paramname"><em>dxdy</em>, </td>
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<td class="paramtype">OutputView </td>
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<td class="paramname"><em>ddyy</em> </td>
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<td>)</td>
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<p>Compute xy gradient, and second order x and y gradients. </p>
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<p>Hessian 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> </p>
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<a id="ga4cc5c53a7cbddd81c47e9d80424886fd" name="ga4cc5c53a7cbddd81c47e9d80424886fd"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga4cc5c53a7cbddd81c47e9d80424886fd">◆ </a></span>generate_dx_scharr()</h2>
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template<typename T = float, typename Allocator = std::allocator<T>> </div>
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<td class="memname">auto generate_dx_scharr </td>
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<td>(</td>
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<td class="paramtype">unsigned int </td>
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<td class="paramname"><em>degree</em> = <code>1</code></td><td>)</td>
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<td> -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a><T, Allocator>
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<p>Generate Scharr operator in horizontal direction. </p>
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<p>Generates 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> </p>
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<a id="gaabc9c7cd5876b5a7ddf1ee568d3b8553" name="gaabc9c7cd5876b5a7ddf1ee568d3b8553"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gaabc9c7cd5876b5a7ddf1ee568d3b8553">◆ </a></span>generate_dx_sobel()</h2>
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template<typename T = float, typename Allocator = std::allocator<T>> </div>
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<td class="memname">auto generate_dx_sobel </td>
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<td>(</td>
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<td class="paramtype">unsigned int </td>
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<td class="paramname"><em>degree</em> = <code>1</code></td><td>)</td>
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<td> -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a><T, Allocator>
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<p>Generates Sobel operator in horizontal direction. </p>
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<p>Generates 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> </p>
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<a id="ga3f798e12d2f00de60fb8d0be35cd99b0" name="ga3f798e12d2f00de60fb8d0be35cd99b0"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga3f798e12d2f00de60fb8d0be35cd99b0">◆ </a></span>generate_dy_scharr()</h2>
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template<typename T = float, typename Allocator = std::allocator<T>> </div>
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<td class="memname">auto generate_dy_scharr </td>
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<td>(</td>
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<td class="paramtype">unsigned int </td>
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<td class="paramname"><em>degree</em> = <code>1</code></td><td>)</td>
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<td> -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a><T, Allocator>
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<p>Generate Scharr operator in vertical direction. </p>
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<p>Generates 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> </p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga9617799d5b34ecf368c9611c2c471017">◆ </a></span>generate_dy_sobel()</h2>
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template<typename T = float, typename Allocator = std::allocator<T>> </div>
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<td class="memname">auto generate_dy_sobel </td>
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<td>(</td>
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<td class="paramtype">unsigned int </td>
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<td class="paramname"><em>degree</em> = <code>1</code></td><td>)</td>
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<td> -> <a class="el" href="classboost_1_1gil_1_1detail_1_1kernel__2d.html">detail::kernel_2d</a><T, Allocator>
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<p>Generates Sobel operator in vertical direction. </p>
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<p>Generates 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> </p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga26eea098b8eb037c207240828fb0fdf1">◆ </a></span>generate_gaussian_kernel()</h2>
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template<typename T = float, typename Allocator = std::allocator<T>> </div>
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<td class="memname">auto generate_gaussian_kernel </td>
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<td>(</td>
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<p>Generate Gaussian kernel. </p>
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<p>Fills 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> </p>
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<h2 class="memtitle"><span class="permalink"><a href="#gaec666d97dfea82bd6fa608bca92a6fd1">◆ </a></span>generate_normalized_mean()</h2>
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<p>Generate mean kernel. </p>
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<p>Fills supplied view with normalized mean in which all entries will be equal to </p><div class="fragment"><div class="line">1 / (dst.size()) </div>
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<h2 class="memtitle"><span class="permalink"><a href="#ga75f408389d62130314890c81f7894ed2">◆ </a></span>generate_unnormalized_mean()</h2>
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<p>Generate kernel with all 1s. </p>
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<p>Fills supplied view with 1s (ones) </p>
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<h2 class="memtitle"><span class="permalink"><a href="#gae9f1ef23591e1b4a5d974090b3aef0c7">◆ </a></span>lanczos()</h2>
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<p>Lanczos response at point x. </p>
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<p>Lanczos response is defined as: x == 0: 1 -a < x && x < a: 0 otherwise: normalized_sinc(x) / normalized_sinc(x / a) </p>
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