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+/*M///////////////////////////////////////////////////////////////////////////////////////
+ //
+ //  IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
+ //
+ //  By downloading, copying, installing or using the software you agree to this license.
+ //  If you do not agree to this license, do not download, install,
+ //  copy or use the software.
+ //
+ //
+ //                           License Agreement
+ //                For Open Source Computer Vision Library
+ //
+ // Copyright (C) 2013, OpenCV Foundation, all rights reserved.
+ // Third party copyrights are property of their respective owners.
+ //
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+ // are permitted provided that the following conditions are met:
+ //
+ //   * Redistribution's of source code must retain the above copyright notice,
+ //     this list of conditions and the following disclaimer.
+ //
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+ //     this list of conditions and the following disclaimer in the documentation
+ //     and/or other materials provided with the distribution.
+ //
+ //   * The name of the copyright holders may not be used to endorse or promote products
+ //     derived from this software without specific prior written permission.
+ //
+ // This software is provided by the copyright holders and contributors "as is" and
+ // any express or implied warranties, including, but not limited to, the implied
+ // warranties of merchantability and fitness for a particular purpose are disclaimed.
+ // In no event shall the Intel Corporation or contributors be liable for any direct,
+ // indirect, incidental, special, exemplary, or consequential damages
+ // (including, but not limited to, procurement of substitute goods or services;
+ // loss of use, data, or profits; or business interruption) however caused
+ // and on any theory of liability, whether in contract, strict liability,
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+ //
+ //M*/
+
+#ifndef __OPENCV_LINE_DESCRIPTOR_HPP__
+#define __OPENCV_LINE_DESCRIPTOR_HPP__
+
+#include "opencv2/line_descriptor/descriptor.hpp"
+
+/** @defgroup line_descriptor Binary descriptors for lines extracted from an image
+
+Introduction
+------------
+
+One of the most challenging activities in computer vision is the extraction of useful information
+from a given image. Such information, usually comes in the form of points that preserve some kind of
+property (for instance, they are scale-invariant) and are actually representative of input image.
+
+The goal of this module is seeking a new kind of representative information inside an image and
+providing the functionalities for its extraction and representation. In particular, differently from
+previous methods for detection of relevant elements inside an image, lines are extracted in place of
+points; a new class is defined ad hoc to summarize a line's properties, for reuse and plotting
+purposes.
+
+Computation of binary descriptors
+---------------------------------
+
+To obtatin a binary descriptor representing a certain line detected from a certain octave of an
+image, we first compute a non-binary descriptor as described in @cite LBD . Such algorithm works on
+lines extracted using EDLine detector, as explained in @cite EDL . Given a line, we consider a
+rectangular region centered at it and called *line support region (LSR)*. Such region is divided
+into a set of bands \f$\{B_1, B_2, ..., B_m\}\f$, whose length equals the one of line.
+
+If we indicate with \f$\bf{d}_L\f$ the direction of line, the orthogonal and clockwise direction to line
+\f$\bf{d}_{\perp}\f$ can be determined; these two directions, are used to construct a reference frame
+centered in the middle point of line. The gradients of pixels \f$\bf{g'}\f$ inside LSR can be projected
+to the newly determined frame, obtaining their local equivalent
+\f$\bf{g'} = (\bf{g}^T \cdot \bf{d}_{\perp}, \bf{g}^T \cdot \bf{d}_L)^T \triangleq (\bf{g'}_{d_{\perp}}, \bf{g'}_{d_L})^T\f$.
+
+Later on, a Gaussian function is applied to all LSR's pixels along \f$\bf{d}_\perp\f$ direction; first,
+we assign a global weighting coefficient \f$f_g(i) = (1/\sqrt{2\pi}\sigma_g)e^{-d^2_i/2\sigma^2_g}\f$ to
+*i*-th row in LSR, where \f$d_i\f$ is the distance of *i*-th row from the center row in LSR,
+\f$\sigma_g = 0.5(m \cdot w - 1)\f$ and \f$w\f$ is the width of bands (the same for every band). Secondly,
+considering a band \f$B_j\f$ and its neighbor bands \f$B_{j-1}, B_{j+1}\f$, we assign a local weighting
+\f$F_l(k) = (1/\sqrt{2\pi}\sigma_l)e^{-d'^2_k/2\sigma_l^2}\f$, where \f$d'_k\f$ is the distance of *k*-th
+row from the center row in \f$B_j\f$ and \f$\sigma_l = w\f$. Using the global and local weights, we obtain,
+at the same time, the reduction of role played by gradients far from line and of boundary effect,
+respectively.
+
+Each band \f$B_j\f$ in LSR has an associated *band descriptor(BD)* which is computed considering
+previous and next band (top and bottom bands are ignored when computing descriptor for first and
+last band). Once each band has been assignen its BD, the LBD descriptor of line is simply given by
+
+\f[LBD = (BD_1^T, BD_2^T, ... , BD^T_m)^T.\f]
+
+To compute a band descriptor \f$B_j\f$, each *k*-th row in it is considered and the gradients in such
+row are accumulated:
+
+\f[\begin{matrix} \bf{V1}^k_j = \lambda \sum\limits_{\bf{g}'_{d_\perp}>0}\bf{g}'_{d_\perp}, &  \bf{V2}^k_j = \lambda \sum\limits_{\bf{g}'_{d_\perp}<0} -\bf{g}'_{d_\perp}, \\ \bf{V3}^k_j = \lambda \sum\limits_{\bf{g}'_{d_L}>0}\bf{g}'_{d_L}, & \bf{V4}^k_j = \lambda \sum\limits_{\bf{g}'_{d_L}<0} -\bf{g}'_{d_L}\end{matrix}.\f]
+
+with \f$\lambda = f_g(k)f_l(k)\f$.
+
+By stacking previous results, we obtain the *band description matrix (BDM)*
+
+\f[BDM_j = \left(\begin{matrix} \bf{V1}_j^1 & \bf{V1}_j^2 & \ldots & \bf{V1}_j^n \\ \bf{V2}_j^1 & \bf{V2}_j^2 & \ldots & \bf{V2}_j^n \\ \bf{V3}_j^1 & \bf{V3}_j^2 & \ldots & \bf{V3}_j^n \\ \bf{V4}_j^1 & \bf{V4}_j^2 & \ldots & \bf{V4}_j^n \end{matrix} \right) \in \mathbb{R}^{4\times n},\f]
+
+with \f$n\f$ the number of rows in band \f$B_j\f$:
+
+\f[n = \begin{cases} 2w, & j = 1||m; \\ 3w, & \mbox{else}. \end{cases}\f]
+
+Each \f$BD_j\f$ can be obtained using the standard deviation vector \f$S_j\f$ and mean vector \f$M_j\f$ of
+\f$BDM_J\f$. Thus, finally:
+
+\f[LBD = (M_1^T, S_1^T, M_2^T, S_2^T, \ldots, M_m^T, S_m^T)^T \in \mathbb{R}^{8m}\f]
+
+Once the LBD has been obtained, it must be converted into a binary form. For such purpose, we
+consider 32 possible pairs of BD inside it; each couple of BD is compared bit by bit and comparison
+generates an 8 bit string. Concatenating 32 comparison strings, we get the 256-bit final binary
+representation of a single LBD.
+*/
+
+#endif