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import numpy as np
import cv2
def smooth(image, sigma = 1.4, length = 5):
""" Smooth the image
Compute a gaussian filter with sigma = sigma and kernal_length = length.
Each element in the kernal can be computed as below:
G[i, j] = (1/(2*pi*sigma**2))*exp(-((i-k-1)**2 + (j-k-1)**2)/2*sigma**2)
Then, use the gaussian filter to smooth the input image.
Args:
image: array of grey image
sigma: the sigma of gaussian filter, default to be 1.4
length: the kernal length, default to be 5
Returns:
the smoothed image
"""
k = length // 2
gaussian = np.zeros([length, length])
for i in range(length):
for j in range(length):
gaussian[i, j] = np.exp(-((i-k) ** 2 + (j-k) ** 2) / (2 * sigma ** 2))
gaussian /= 2 * np.pi * sigma ** 2
gaussian = gaussian / np.sum(gaussian)
W, H = image.shape
new_image = np.zeros([W - k * 2, H - k * 2])
for i in range(W - 2 * k):
for j in range(H - 2 * k):
new_image[i, j] = np.sum(image[i:i+length, j:j+length] * gaussian)
new_image = np.uint8(new_image)
return new_image
def get_gradient_and_direction(image):
""" Compute gradients and its direction
Use Sobel filter to compute gradients and direction.
-1 0 1 -1 -2 -1
Gx = -2 0 2 Gy = 0 0 0
-1 0 1 1 2 1
Args:
image: array of grey image
Returns:
gradients: the gradients of each pixel
direction: the direction of the gradients of each pixel
"""
Gx = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]])
Gy = np.array([[-1, -2, -1], [0, 0, 0], [1, 2, 1]])
W, H = image.shape
gradients = np.zeros([W - 2, H - 2])
direction = np.zeros([W - 2, H - 2])
for i in range(W - 2):
for j in range(H - 2):
dx = np.sum(image[i:i+3, j:j+3] * Gx)
dy = np.sum(image[i:i+3, j:j+3] * Gy)
gradients[i, j] = np.sqrt(dx ** 2 + dy ** 2)
if dx == 0:
direction[i, j] = np.pi / 2
else:
direction[i, j] = np.arctan(dy / dx)
gradients = np.uint8(gradients)
return gradients, direction
def NMS(gradients, direction):
""" Non-maxima suppression
Args:
gradients: the gradients of each pixel
direction: the direction of the gradients of each pixel
Returns:
the output image
"""
W, H = gradients.shape
nms = np.copy(gradients[1:-1, 1:-1])
for i in range(1, W - 1):
for j in range(1, H - 1):
theta = direction[i, j]
weight = np.tan(theta)
if theta > np.pi / 4:
d1 = [0, 1]
d2 = [1, 1]
weight = 1 / weight
elif theta >= 0:
d1 = [1, 0]
d2 = [1, 1]
elif theta >= - np.pi / 4:
d1 = [1, 0]
d2 = [1, -1]
weight *= -1
else:
d1 = [0, -1]
d2 = [1, -1]
weight = -1 / weight
g1 = gradients[i + d1[0], j + d1[1]]
g2 = gradients[i + d2[0], j + d2[1]]
g3 = gradients[i - d1[0], j - d1[1]]
g4 = gradients[i - d2[0], j - d2[1]]
grade_count1 = g1 * weight + g2 * (1 - weight)
grade_count2 = g3 * weight + g4 * (1 - weight)
if grade_count1 > gradients[i, j] or grade_count2 > gradients[i, j]:
nms[i - 1, j - 1] = 0
return nms
def double_threshold(nms, threshold1, threshold2):
""" Double Threshold
Use two thresholds to compute the edge.
Args:
nms: the input image
threshold1: the low threshold
threshold2: the high threshold
Returns:
The binary image.
"""
visited = np.zeros_like(nms)
output_image = nms.copy()
W, H = output_image.shape
def dfs(i, j):
if i >= W or i < 0 or j >= H or j < 0 or visited[i, j] == 1:
return
visited[i, j] = 1
if output_image[i, j] > threshold1:
output_image[i, j] = 255
dfs(i-1, j-1)
dfs(i-1, j)
dfs(i-1, j+1)
dfs(i, j-1)
dfs(i, j+1)
dfs(i+1, j-1)
dfs(i+1, j)
dfs(i+1, j+1)
else:
output_image[i, j] = 0
for w in range(W):
for h in range(H):
if visited[w, h] == 1:
continue
if output_image[w, h] >= threshold2:
dfs(w, h)
elif output_image[w, h] <= threshold1:
output_image[w, h] = 0
visited[w, h] = 1
for w in range(W):
for h in range(H):
if visited[w, h] == 0:
output_image[w, h] = 0
return output_image
if __name__ == "__main__":
smoothed_image = smooth(image)
gradients, direction = get_gradient_and_direction(smoothed_image)
nms = NMS(gradients, direction)
output_image = double_threshold(nms, 40, 100)
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