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import numpy as np
from scipy import signal
from PIL import Image, ImageFilter
GRADIENT_THRESHOLD = 50
CURVATURE_THRESHOLD = 10e3
def resize(image, size):
im = Image.fromarray(image)
im_new = im.resize(size=size, resample=Image.BILINEAR)
return np.array(im_new)
def erode(image):
im = Image.fromarray(image)
im_new = im.filter(ImageFilter.MinFilter(3))
return np.array(im_new)
def local_maxima(image):
kernel = np.array([
[-1, 0, -1],
[0, 1, 0],
[-1, 0, -1]
])
kernel = kernel - kernel.mean()
maxima = signal.convolve2d(image, kernel, boundary='symm', mode='same')
return maxima - image
def gradient_x(image):
kernel = np.array([
[1, 0, -1],
[2, 0, -2],
[1, 0, -1]
])
grad_x = signal.convolve2d(image, kernel, boundary='symm', mode='same')
return grad_x
def gradient_y(image):
kernel = np.array([
[1, 2, 1],
[0, 0, 0],
[-1, -2, -1]
])
grad_y = signal.convolve2d(image, kernel, boundary='symm', mode='same')
return grad_y
def gradient(image):
grad_x = gradient_x(image)
grad_y = gradient_y(image)
return np.sqrt(grad_x**2 + grad_y**2)
def curvature(image):
return gradient(gradient(image))
def scharr(image):
kernel = np.array([
[ -3-3j, 0-10j, +3 -3j],
[-10+0j, 0+ 0j, +10 +0j],
[ -3+3j, 0+10j, +3 +3j]
]) # Gx + j*Gy
grad = signal.convolve2d(image, kernel, boundary='symm', mode='same')
return np.absolute(grad), np.angle(grad)
def scharr_curvature(image):
kernel = np.array([
[ -3-3j, 0-10j, +3 -3j],
[-10+0j, 0+ 0j, +10 +0j],
[ -3+3j, 0+10j, +3 +3j]
]) # Gx + j*Gy
grad = signal.convolve2d(image, kernel, boundary='symm', mode='same')
curvature = signal.convolve2d(grad, kernel, boundary='symm', mode='same')
return np.absolute(curvature)
def ridges(elevation):
candidate_ridges = []
total_gradient = gradient(elevation)
curvature = resize(scharr_curvature(resize(elevation, size=(64, 64))), size=(256, 256))
for size in [(256, 256), (128, 128), (64, 64)]:
elevation_reduced = resize(elevation, size=size)
grad_x = gradient_x(elevation_reduced)
curv_x = gradient_x(grad_x > 0)
grad_y = gradient_y(elevation_reduced)
curv_y = gradient_y(grad_y > 0)
curv_xy = (curv_x<0) + (curv_y<0)
original_size = resize(curv_xy.astype(np.int8), (256, 256))
candidate_ridges.append(original_size)
candidate_ridges = np.stack(candidate_ridges + [curvature > CURVATURE_THRESHOLD], axis=2)
return np.all(candidate_ridges, axis=2)