Image::Leptonica::Func::bilateral
version 0.04
bilateral.c
bilateral.c Top level approximate separable grayscale or color bilateral filtering PIX *pixBilateral() PIX *pixBilateralGray() Implementation of approximate separable bilateral filter static L_BILATERAL *bilateralCreate() static void *bilateralDestroy() static PIX *bilateralApply() Slow, exact implementation of grayscale or color bilateral filtering PIX *pixBilateralExact() PIX *pixBilateralGrayExact() PIX *pixBlockBilateralExact() Kernel helper function L_KERNEL *makeRangeKernel() This includes both a slow, exact implementation of the bilateral filter algorithm (given by Sylvain Paris and Frédo Durand), and a fast, approximate and separable implementation (following Yang, Tan and Ahuja). See bilateral.h for algorithmic details. The bilateral filter has the nice property of applying a gaussian filter to smooth parts of the image that don't vary too quickly, while at the same time preserving edges. The filter is nonlinear and cannot be decomposed into two separable filters; however, there exists an approximate method that is separable. To further speed up the separable implementation, you can generate the intermediate data at reduced resolution. The full kernel is composed of two parts: a spatial gaussian filter and a nonlinear "range" filter that depends on the intensity difference between the reference pixel at the spatial kernel origin and any other pixel within the kernel support. In our implementations, the range filter is a parameterized, one-sided, 256-element, monotonically decreasing gaussian function of the absolute value of the difference between pixel values; namely, abs(I2 - I1). In general, any decreasing function can be used, and more generally, any two-dimensional kernel can be used if you wish to relax the 'abs' condition. (In that case, the range filter can be 256 x 256).
L_KERNEL * makeRangeKernel ( l_float32 range_stdev )
makeRangeKernel() Input: range_stdev (> 0) Return: kel, or null on error Notes: (1) Creates a one-sided Gaussian kernel with the given standard deviation. At grayscale difference of one stdev, the kernel falls to 0.6, and to 0.01 at three stdev. (2) A typical input number might be 20. Then pixels whose value differs by 60 from the center pixel have their weight in the convolution reduced by a factor of about 0.01.
PIX * pixBilateral ( PIX *pixs, l_float32 spatial_stdev, l_float32 range_stdev, l_int32 ncomps, l_int32 reduction )
pixBilateral() Input: pixs (8 bpp gray or 32 bpp rgb, no colormap) spatial_stdev (of gaussian kernel; in pixels, > 0.5) range_stdev (of gaussian range kernel; > 5.0; typ. 50.0) ncomps (number of intermediate sums J(k,x); in [4 ... 30]) reduction (1, 2 or 4) Return: pixd (bilateral filtered image), or null on error Notes: (1) This performs a relatively fast, separable bilateral filtering operation. The time is proportional to ncomps and varies inversely approximately as the cube of the reduction factor. See bilateral.h for algorithm details. (2) We impose minimum values for range_stdev and ncomps to avoid nasty artifacts when either are too small. We also impose a constraint on their product: ncomps * range_stdev >= 100. So for values of range_stdev >= 25, ncomps can be as small as 4. Here is a qualitative, intuitive explanation for this constraint. Call the difference in k values between the J(k) == 'delta', where 'delta' ~ 200 / ncomps Then this constraint is roughly equivalent to the condition: 'delta' < 2 * range_stdev Note that at an intensity difference of (2 * range_stdev), the range part of the kernel reduces the effect by the factor 0.14. This constraint requires that we have a sufficient number of PCBs (i.e, a small enough 'delta'), so that for any value of image intensity I, there exists a k (and a PCB, J(k), such that |I - k| < range_stdev Any fewer PCBs and we don't have enough to support this condition. (3) The upper limit of 30 on ncomps is imposed because the gain in accuracy is not worth the extra computation. (4) The size of the gaussian kernel is twice the spatial_stdev on each side of the origin. The minimum value of spatial_stdev, 0.5, is required to have a finite sized spatial kernel. In practice, a much larger value is used. (5) Computation of the intermediate images goes inversely as the cube of the reduction factor. If you can use a reduction of 2 or 4, it is well-advised. (6) The range kernel is defined over the absolute value of pixel grayscale differences, and hence must have size 256 x 1. Values in the array represent the multiplying weight depending on the absolute gray value difference between the source pixel and the neighboring pixel, and should be monotonically decreasing. (7) Interesting observation. Run this on prog/fish24.jpg, with range_stdev = 60, ncomps = 6, and spatial_dev = {10, 30, 50}. As spatial_dev gets larger, we get the counter-intuitive result that the body of the red fish becomes less blurry.
PIX * pixBilateralExact ( PIX *pixs, L_KERNEL *spatial_kel, L_KERNEL *range_kel )
pixBilateralExact() Input: pixs (8 bpp gray or 32 bpp rgb) spatial_kel (gaussian kernel) range_kel (<optional> 256 x 1, monotonically decreasing) Return: pixd (8 bpp bilateral filtered image) Notes: (1) The spatial_kel is a conventional smoothing kernel, typically a 2-d Gaussian kernel or other block kernel. It can be either normalized or not, but must be everywhere positive. (2) The range_kel is defined over the absolute value of pixel grayscale differences, and hence must have size 256 x 1. Values in the array represent the multiplying weight for each gray value difference between the target pixel and center of the kernel, and should be monotonically decreasing. (3) If range_kel == NULL, a constant weight is applied regardless of the range value difference. This degenerates to a regular pixConvolve() with a normalized kernel.
PIX * pixBilateralGray ( PIX *pixs, l_float32 spatial_stdev, l_float32 range_stdev, l_int32 ncomps, l_int32 reduction )
pixBilateralGray() Input: pixs (8 bpp gray) spatial_stdev (of gaussian kernel; in pixels, > 0.5) range_stdev (of gaussian range kernel; > 5.0; typ. 50.0) ncomps (number of intermediate sums J(k,x); in [4 ... 30]) reduction (1, 2 or 4) Return: pixd (8 bpp bilateral filtered image), or null on error Notes: (1) See pixBilateral() for constraints on the input parameters. (2) See pixBilateral() for algorithm details.
PIX * pixBilateralGrayExact ( PIX *pixs, L_KERNEL *spatial_kel, L_KERNEL *range_kel )
pixBilateralGrayExact() Input: pixs (8 bpp gray) spatial_kel (gaussian kernel) range_kel (<optional> 256 x 1, monotonically decreasing) Return: pixd (8 bpp bilateral filtered image) Notes: (1) See pixBilateralExact().
PIX* pixBlockBilateralExact ( PIX *pixs, l_float32 spatial_stdev, l_float32 range_stdev )
pixBlockBilateralExact() Input: pixs (8 bpp gray or 32 bpp rgb) spatial_stdev (> 0.0) range_stdev (> 0.0) Return: pixd (8 bpp or 32 bpp bilateral filtered image) Notes: (1) See pixBilateralExact(). This provides an interface using the standard deviations of the spatial and range filters. (2) The convolution window halfwidth is 2 * spatial_stdev, and the square filter size is 4 * spatial_stdev + 1. The kernel captures 95% of total energy. This is compensated by normalization. (3) The range_stdev is analogous to spatial_halfwidth in the grayscale domain [0...255], and determines how much damping of the smoothing operation is applied across edges. The larger this value is, the smaller the damping. The smaller the value, the more edge details are preserved. These approximations are useful for deciding the appropriate cutoff. kernel[1 * stdev] ~= 0.6 * kernel[0] kernel[2 * stdev] ~= 0.14 * kernel[0] kernel[3 * stdev] ~= 0.01 * kernel[0] If range_stdev is infinite there is no damping, and this becomes a conventional gaussian smoothing. This value does not affect the run time. (4) If range_stdev is negative or zero, the range kernel is ignored and this degenerates to a straight gaussian convolution. (5) This is very slow for large spatial filters. The time on a 3GHz pentium is roughly T = 1.2 * 10^-8 * (A * sh^2) sec where A = # of pixels, sh = spatial halfwidth of filter.
Zakariyya Mughal <zmughal@cpan.org>
This software is copyright (c) 2014 by Zakariyya Mughal.
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