@@ -77,3 +77,55 @@ Apart from fields inspired to KeyPoint class, KeyLines stores information about
/* constructor */
KeyLine(){}
};
Lines extraction methodology
----------------------------
The lines extraction methodology described in the following is mainly based on [LBD]_.
The extraction starts with a Gaussian pyramid generated from an original image, downsampled and blurred N-1 times, to obtain N layers (one for each octave), with layer 0 corresponding to input image. Then, from each layer (octave) in the pyramid, lines are extracted using LSD algorithm.
Differently from EDLine lines extractor used in original article, LSD furnishes information only about lines extremes; thus, additional information regarding slope and equation of line are computed via analytic methods. The number of pixels is obtained using `LineIterator <http://docs.opencv.org/modules/core/doc/drawing_functions.html#lineiterator>`_. Later on, all extracted lines are arranged in buckets: two lines fall in the same bucket if they represent the same line in different octave (they have the same direction and belong to same region of original image). The set of buckets becomes the input for descriptors computation.
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 [LBD]_. 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 :math:`\{B_1, B_2, ..., B_m\}`, whose length equals the one of line.
If we indicate with :math:`\bf{d}_L` the direction of line, the orthogonal and clockwise direction to line :math:`\bf{d}_{\perp}` can be determined; these two directions, are used to construct a reference frame centered in the middle point of line. The gradients of pixels :math:`\bf{g'}` inside LSR can be projected to the newly determined frame, obtaining their local equivalent :math:`\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`.
Later on, a Gaussian function is applied to all LSR's pixels along :math:`\bf{d}_\perp` direction; first, we assign a global weighting coefficient :math:`f_g(i) = (1/\sqrt{2\pi}\sigma_g)e^{-d^2_i/2\sigma^2_g}` to *i*-th row in LSR, where :math:`d_i` is the distance of *i*-th row from the center row in LSR, :math:`\sigma_g = 0.5(m \cdot w - 1)` and :math:`w` is the width of bands (the same for every band). Secondly, considering a band :math:`B_j` and its neighbor bands :math:`B_{j-1}, B_{j+1}`, we assign a local weighting :math:`F_l(k) = (1/\sqrt{2\pi}\sigma_l)e^{-d'^2_k/2\sigma_l^2}`, where :math:`d'_k` is the distance of *k*-th row from the center row in :math:`B_j` and :math:`\sigma_l = w`. 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 :math:`B_j` 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
.. math::
LBD = (BD_1^T, BD_2^T, ... , BD^T_m)^T.
To compute a band descriptor :math:`B_j`, each *k*-th row in it is considered and the gradients in such row are accumulated:
.. [LBD] Zhang, Lilian, and Reinhard Koch. *An efficient and robust line segment matching approach based on LBD descriptor and pairwise geometric consistency*, Journal of Visual Communication and Image Representation 24.7 (2013): 794-805.
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 spite of points; a new class is defined ad hoc to summarize a line's properties, for reuse and plotting purposes.
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.
A class to represent a line: KeyLine
...
...
@@ -77,3 +77,49 @@ Apart from fields inspired to KeyPoint class, KeyLines stores information about
/* constructor */
KeyLine(){}
};
Lines extraction methodology
----------------------------
The lines extraction methodology described in the following is mainly based on [LBD]_.
The extraction starts with a Gaussian pyramid generated from an original image, downsampled and blurred N-1 times, to obtain N layers (one for each octave), with layer 0 corresponding to input image. Then, from each layer (octave) in the pyramid, lines are extracted using LSD algorithm.
Differently from EDLine lines extractor used in original article, LSD furnishes information only about lines extremes; thus, additional information regarding slope and equation of line are computed via analytic methods. The number of pixels is obtained using `LineIterator <http://docs.opencv.org/modules/core/doc/drawing_functions.html#lineiterator>`_. Later on, all extracted lines are arranged in buckets: two lines fall in the same bucket if they represent the same line in different octave (they have the same direction and belong to same region of original image). The set of buckets becomes the input for descriptors computation.
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 [LBD]_. 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 :math:`\{B_1, B_2, ..., B_m\}`, whose length equals the one of line.
If we indicate with :math:`\bf{d}_L` the direction of line, the orthogonal and clockwise direction to line :math:`\bf{d}_{\perp}` can be determined; these two directions, are used to construct a reference frame centered in the middle point of line. The gradients of pixels :math:`\bf{g'}` inside LSR can be projected to the newly determined frame, obtaining their local equivalent :math:`\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`.
Later on, a Gaussian function is applied to all LSR's pixels along :math:`\bf{d}_\perp` direction; first, we assign a global weighting coefficient :math:`f_g(i) = (1/\sqrt{2\pi}\sigma_g)e^{-d^2_i/2\sigma^2_g}` to *i*-th row in LSR, where :math:`d_i` is the distance of *i*-th row from the center row in LSR, :math:`\sigma_g = 0.5(m \cdot w - 1)` and :math:`w` is the width of bands (the same for every band). Secondly, considering a band :math:`B_j` and its neighbor bands :math:`B_{j-1}, B_{j+1}`, we assign a local weighting :math:`F_l(k) = (1/\sqrt{2\pi}\sigma_l)e^{-d'^2_k/2\sigma_l^2}`, where :math:`d'_k` is the distance of *k*-th row from the center row in :math:`B_j` and :math:`\sigma_l = w`. 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 :math:`B_j` 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
.. math::
LBD = (BD_1^T, BD_2^T, ... , BD^T_m)^T.
To compute a band descriptor :math:`B_j`, each *k*-th row in it is considered and the gradients in such row are accumulated:
