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- Copyright (C) 2001 Leptonica. All rights reserved.
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*====================================================================*/
#ifndef LEPTONICA_BILATERAL_H
#define LEPTONICA_BILATERAL_H
/*!
* \file bilateral.h
*
* <pre>
* Contains the following struct
* struct L_Bilateral
*
*
* For a tutorial introduction to bilateral filters, which apply a
* gaussian blur to smooth parts of the image while preserving edges, see
* http://people.csail.mit.edu/sparis/bf_course/slides/03_definition_bf.pdf
*
* We give an implementation of a bilateral filtering algorithm given in:
* "Real-Time O(1) Bilateral Filtering," by Yang, Tan and Ahuja, CVPR 2009
* which is at:
* http://vision.ai.uiuc.edu/~qyang6/publications/cvpr-09-qingxiong-yang.pdf
* This is based on an earlier algorithm by Sylvain Paris and Frédo Durand:
* http://people.csail.mit.edu/sparis/publi/2006/eccv/
* Paris_06_Fast_Approximation.pdf
*
* The kernel of the filter is a product of a spatial gaussian and a
* monotonically decreasing function of the difference in intensity
* between the source pixel and the neighboring pixel. The intensity
* part of the filter gives higher influence for pixels with intensities
* that are near to the source pixel, and the spatial part of the
* filter gives higher weight to pixels that are near the source pixel.
* This combination smooths in relatively uniform regions, while
* maintaining edges.
*
* The advantage of the appoach of Yang et al is that it is separable,
* so the computation time is linear in the gaussian filter size.
* Furthermore, it is possible to do much of the computation as a reduced
* scale, which gives a good approximation to the full resolution version
* but greatly speeds it up.
*
* The bilateral filtered value at x is:
*
* sum[y in N(x)]: spatial(|y - x|) * range(|I(x) - I(y)|) * I(y)
* I'(x) = --------------------------------------------------------------
* sum[y in N(x)]: spatial(|y - x|) * range(|I(x) - I(y)|)
*
* where I() is the input image, I'() is the filtered image, N(x) is the
* set of pixels around x in the filter support, and spatial() and range()
* are gaussian functions:
* spatial(x) = exp(-x^2 / (2 * s_s^2))
* range(x) = exp(-x^2 / (2 * s_r^2))
* and s_s and s_r and the standard deviations of the two gaussians.
*
* Yang et al use a separable approximation to this, by defining a set
* of related but separable functions J(k,x), that we call Principal
* Bilateral Components (PBC):
*
* sum[y in N(x)]: spatial(|y - x|) * range(|k - I(y)|) * I(y)
* J(k,x) = -----------------------------------------------------------
* sum[y in N(x)]: spatial(|y - x|) * range(|k - I(y)|)
*
* which are computed quickly for a set of n values k[p], p = 0 ... n-1.
* Then each output pixel is found using a linear interpolation:
*
* I'(x) = (1 - q) * J(k[p],x) + q * J(k[p+1],x)
*
* where J(k[p],x) and J(k[p+1],x) are PBC for which
* k[p] <= I(x) and k[p+1] >= I(x), and
* q = (I(x) - k[p]) / (k[p+1] - k[p]).
*
* We can also subsample I(x), create subsampled versions of J(k,x),
* which are then interpolated between for I'(x).
*
* We generate 'pixsc', by optionally downscaling the input image
* (using area mapping by the factor 'reduction'), and then adding
* a mirrored border to avoid boundary cases. This is then used
* to compute 'ncomps' PBCs.
*
* The 'spatial_stdev' is also downscaled by 'reduction'. The size
* of the 'spatial' array is 4 * (reduced 'spatial_stdev') + 1.
* The size of the 'range' array is 256.
* </pre>
*/
/*------------------------------------------------------------------------*
* Bilateral filter *
*------------------------------------------------------------------------*/
/*! Bilateral filter */
struct L_Bilateral
{
struct Pix *pixs; /*!< clone of source pix */
struct Pix *pixsc; /*!< downscaled pix with mirrored border */
l_int32 reduction; /*!< 1, 2 or 4x for intermediates */
l_float32 spatial_stdev; /*!< stdev of spatial gaussian */
l_float32 range_stdev; /*!< stdev of range gaussian */
l_float32 *spatial; /*!< 1D gaussian spatial kernel */
l_float32 *range; /*!< one-sided gaussian range kernel */
l_int32 minval; /*!< min value in 8 bpp pix */
l_int32 maxval; /*!< max value in 8 bpp pix */
l_int32 ncomps; /*!< number of intermediate results */
l_int32 *nc; /*!< set of k values (size ncomps) */
l_int32 *kindex; /*!< mapping from intensity to lower k */
l_float32 *kfract; /*!< mapping from intensity to fract k */
struct Pixa *pixac; /*!< intermediate result images (PBC) */
l_uint32 ***lineset; /*!< lineptrs for pixac */
};
typedef struct L_Bilateral L_BILATERAL;
#endif /* LEPTONICA_BILATERAL_H */
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