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import numpy as np
import cv2
from scipy import sparse
from scipy.sparse.linalg import spsolve
def regionfill(I, mask, factor=1.0): # I -> flow, mask -> flow mask
if np.count_nonzero(mask) == 0:
return I.copy() # All of the regions in mask has been filled
resize_mask = cv2.resize(
mask.astype(float), (0, 0), fx=factor, fy=factor) > 0
resize_I = cv2.resize(I.astype(float), (0, 0), fx=factor, fy=factor)
maskPerimeter = findBoundaryPixels(resize_mask) # boundary pixels in the resized mask
regionfillLaplace(resize_I, resize_mask, maskPerimeter)
resize_I = cv2.resize(resize_I, (I.shape[1], I.shape[0]))
resize_I[mask == 0] = I[mask == 0]
return resize_I
def findBoundaryPixels(mask):
kernel = cv2.getStructuringElement(cv2.MORPH_CROSS, (3, 3))
maskDilated = cv2.dilate(mask.astype(float), kernel)
return (maskDilated > 0) & (mask == 0)
def regionfillLaplace(I, mask, maskPerimeter):
height, width = I.shape
rightSide = formRightSide(I, maskPerimeter)
# Location of mask pixels
maskIdx = np.where(mask)
# Only keep values for pixels that are in the mask
rightSide = rightSide[maskIdx]
# Number the mask pixels in a grid matrix
grid = -np.ones((height, width))
grid[maskIdx] = range(0, maskIdx[0].size)
# Pad with zeros to avoid "index out of bounds" errors in the for loop
grid = padMatrix(grid)
gridIdx = np.where(grid >= 0)
# Form the connectivity matrix D=sparse(i,j,s)
# Connect each mask pixel to itself
i = np.arange(0, maskIdx[0].size)
j = np.arange(0, maskIdx[0].size)
# The coefficient is the number of neighbors over which we average
numNeighbors = computeNumberOfNeighbors(height, width)
s = numNeighbors[maskIdx]
# Now connect the N,E,S,W neighbors if they exist
for direction in ((-1, 0), (0, 1), (1, 0), (0, -1)):
# Possible neighbors in the current direction
neighbors = grid[gridIdx[0] + direction[0], gridIdx[1] + direction[1]]
# ConDnect mask points to neighbors with -1's
index = (neighbors >= 0)
i = np.concatenate((i, grid[gridIdx[0][index], gridIdx[1][index]]))
j = np.concatenate((j, neighbors[index]))
s = np.concatenate((s, -np.ones(np.count_nonzero(index))))
D = sparse.coo_matrix((s, (i.astype(int), j.astype(int)))).tocsr()
sol = spsolve(D, rightSide)
I[maskIdx] = sol
return I
def formRightSide(I, maskPerimeter):
height, width = I.shape
perimeterValues = np.zeros((height, width))
assert perimeterValues.shape == I.shape, 'P shape: {}, I shape: {}'.format(perimeterValues.shape, I.shape)
perimeterValues[maskPerimeter] = I[maskPerimeter]
rightSide = np.zeros((height, width))
rightSide[1:height - 1, 1:width - 1] = (
perimeterValues[0:height - 2, 1:width - 1] +
perimeterValues[2:height, 1:width - 1] +
perimeterValues[1:height - 1, 0:width - 2] +
perimeterValues[1:height - 1, 2:width])
rightSide[1:height - 1, 0] = (
perimeterValues[0:height - 2, 0] + perimeterValues[2:height, 0] +
perimeterValues[1:height - 1, 1])
rightSide[1:height - 1, width - 1] = (
perimeterValues[0:height - 2, width - 1] +
perimeterValues[2:height, width - 1] +
perimeterValues[1:height - 1, width - 2])
rightSide[0, 1:width - 1] = (
perimeterValues[1, 1:width - 1] + perimeterValues[0, 0:width - 2] +
perimeterValues[0, 2:width])
rightSide[height - 1, 1:width - 1] = (
perimeterValues[height - 2, 1:width - 1] +
perimeterValues[height - 1, 0:width - 2] +
perimeterValues[height - 1, 2:width])
rightSide[0, 0] = perimeterValues[0, 1] + perimeterValues[1, 0]
rightSide[0, width - 1] = (
perimeterValues[0, width - 2] + perimeterValues[1, width - 1])
rightSide[height - 1, 0] = (
perimeterValues[height - 2, 0] + perimeterValues[height - 1, 1])
rightSide[height - 1, width - 1] = (perimeterValues[height - 2, width - 1] +
perimeterValues[height - 1, width - 2])
return rightSide
def computeNumberOfNeighbors(height, width):
# Initialize
numNeighbors = np.zeros((height, width))
# Interior pixels have 4 neighbors
numNeighbors[1:height - 1, 1:width - 1] = 4
# Border pixels have 3 neighbors
numNeighbors[1:height - 1, (0, width - 1)] = 3
numNeighbors[(0, height - 1), 1:width - 1] = 3
# Corner pixels have 2 neighbors
numNeighbors[(0, 0, height - 1, height - 1), (0, width - 1, 0,
width - 1)] = 2
return numNeighbors
def padMatrix(grid):
height, width = grid.shape
gridPadded = -np.ones((height + 2, width + 2))
gridPadded[1:height + 1, 1:width + 1] = grid
gridPadded = gridPadded.astype(grid.dtype)
return gridPadded
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