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Last active March 26, 2024 03:09
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Fast Poisson Reconstruction in Python
"""
poisson_reconstruct.py
Fast Poisson Reconstruction 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 math
import numpy
import scipy, scipy.fftpack
def poisson_reconstruct(grady, gradx, boundarysrc):
# Thanks to Dr. Ramesh Raskar for providing the original matlab code from which this is derived
# Dr. Raskar's version is available here: http://web.media.mit.edu/~raskar/photo/code.pdf
# Laplacian
gyy = grady[1:,:-1] - grady[:-1,:-1]
gxx = gradx[:-1,1:] - gradx[:-1,:-1]
f = numpy.zeros(boundarysrc.shape)
f[:-1,1:] += gxx
f[1:,:-1] += gyy
# Boundary image
boundary = boundarysrc.copy()
boundary[1:-1,1:-1] = 0;
# Subtract boundary contribution
f_bp = -4*boundary[1:-1,1:-1] + boundary[1:-1,2:] + boundary[1:-1,0:-2] + boundary[2:,1:-1] + boundary[0:-2,1:-1]
f = f[1:-1,1:-1] - f_bp
# Discrete Sine Transform
tt = scipy.fftpack.dst(f, norm='ortho')
fsin = scipy.fftpack.dst(tt.T, norm='ortho').T
# Eigenvalues
(x,y) = numpy.meshgrid(range(1,f.shape[1]+1), range(1,f.shape[0]+1), copy=True)
denom = (2*numpy.cos(math.pi*x/(f.shape[1]+2))-2) + (2*numpy.cos(math.pi*y/(f.shape[0]+2)) - 2)
f = fsin/denom
# Inverse Discrete Sine Transform
tt = scipy.fftpack.idst(f, norm='ortho')
img_tt = scipy.fftpack.idst(tt.T, norm='ortho').T
# New center + old boundary
result = boundary
result[1:-1,1:-1] = img_tt
return result
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