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digit_depth/third_party/poisson.py

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+"""
+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 copy
+import math
+
+import numpy
+import scipy
+import 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 = copy.deepcopy(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 = copy.deepcopy(boundary)
+    result[1:-1, 1:-1] = img_tt
+
+    return result