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