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Fast Bilateral Filter Approximation Using a Signal Processing Approach in Python
"""
bilateral_approximation.py
Fast Bilateral Filter Approximation Using a Signal Processing Approach in Python
Copyright (c) 2014 Jack Doerner
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
import numpy
import math
import scipy.signal, scipy.interpolate
def bilateral_approximation(data, edge, sigmaS, sigmaR, samplingS=None, samplingR=None, edgeMin=None, edgeMax=None):
# This function implements Durand and Dorsey's Signal Processing Bilateral Filter Approximation (2006)
# It is derived from Jiawen Chen's matlab implementation
# The original papers and matlab code are available at http://people.csail.mit.edu/sparis/bf/
inputHeight = data.shape[0]
inputWidth = data.shape[1]
samplingS = sigmaS if (samplingS is None) else samplingS
samplingR = sigmaR if (samplingR is None) else samplingR
edgeMax = numpy.amax(edge) if (edgeMax is None) else edgeMax
edgeMin = numpy.amin(edge) if (edgeMin is None) else edgeMin
edgeDelta = edgeMax - edgeMin
derivedSigmaS = sigmaS / samplingS;
derivedSigmaR = sigmaR / samplingR;
paddingXY = math.floor( 2 * derivedSigmaS ) + 1
paddingZ = math.floor( 2 * derivedSigmaR ) + 1
# allocate 3D grid
downsampledWidth = math.floor( ( inputWidth - 1 ) / samplingS ) + 1 + 2 * paddingXY
downsampledHeight = math.floor( ( inputHeight - 1 ) / samplingS ) + 1 + 2 * paddingXY
downsampledDepth = math.floor( edgeDelta / samplingR ) + 1 + 2 * paddingZ
gridData = numpy.zeros( (downsampledHeight, downsampledWidth, downsampledDepth) )
gridWeights = numpy.zeros( (downsampledHeight, downsampledWidth, downsampledDepth) )
# compute downsampled indices
(jj, ii) = numpy.meshgrid( range(inputWidth), range(inputHeight) )
di = numpy.around( ii / samplingS ) + paddingXY
dj = numpy.around( jj / samplingS ) + paddingXY
dz = numpy.around( ( edge - edgeMin ) / samplingR ) + paddingZ
# perform scatter (there's probably a faster way than this)
# normally would do downsampledWeights( di, dj, dk ) = 1, but we have to
# perform a summation to do box downsampling
for k in range(dz.size):
dataZ = data.flat[k]
if (not math.isnan( dataZ )):
dik = di.flat[k]
djk = dj.flat[k]
dzk = dz.flat[k]
gridData[ dik, djk, dzk ] += dataZ
gridWeights[ dik, djk, dzk ] += 1
# make gaussian kernel
kernelWidth = 2 * derivedSigmaS + 1
kernelHeight = kernelWidth
kernelDepth = 2 * derivedSigmaR + 1
halfKernelWidth = math.floor( kernelWidth / 2 )
halfKernelHeight = math.floor( kernelHeight / 2 )
halfKernelDepth = math.floor( kernelDepth / 2 )
(gridX, gridY, gridZ) = numpy.meshgrid( range( int(kernelWidth) ), range( int(kernelHeight) ), range( int(kernelDepth) ) )
gridX -= halfKernelWidth
gridY -= halfKernelHeight
gridZ -= halfKernelDepth
gridRSquared = (( gridX * gridX + gridY * gridY ) / ( derivedSigmaS * derivedSigmaS )) + (( gridZ * gridZ ) / ( derivedSigmaR * derivedSigmaR ))
kernel = numpy.exp( -0.5 * gridRSquared )
# convolve
blurredGridData = scipy.signal.fftconvolve( gridData, kernel, mode='same' )
blurredGridWeights = scipy.signal.fftconvolve( gridWeights, kernel, mode='same' )
# divide
blurredGridWeights = numpy.where( blurredGridWeights == 0 , -2, blurredGridWeights) # avoid divide by 0, won't read there anyway
normalizedBlurredGrid = blurredGridData / blurredGridWeights;
normalizedBlurredGrid = numpy.where( blurredGridWeights < -1, 0, normalizedBlurredGrid ) # put 0s where it's undefined
# upsample
( jj, ii ) = numpy.meshgrid( range( inputWidth ), range( inputHeight ) )
# no rounding
di = ( ii / samplingS ) + paddingXY
dj = ( jj / samplingS ) + paddingXY
dz = ( edge - edgeMin ) / samplingR + paddingZ
return scipy.interpolate.interpn( (range(normalizedBlurredGrid.shape[0]),range(normalizedBlurredGrid.shape[1]),range(normalizedBlurredGrid.shape[2])), normalizedBlurredGrid, (di, dj, dz) )
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