add canny edge detection algorithm and modify sobel_filter (TheAlgorithms#991)

* add gaussian filter algorithm and lena.jpg

* add img_convolve algorithm and sobel_filter

* add canny edge detection algorithm and modify sobel_filter

* format to avoid the backslashes

Author: lighttxu

digital_image_processing/edge_detection/__init__.py

@@ -0,0 +1,107 @@
+import cv2
+import numpy as np
+from digital_image_processing.filters.convolve import img_convolve
+from digital_image_processing.filters.sobel_filter import sobel_filter
+
+PI = 180
+
+
+def gen_gaussian_kernel(k_size, sigma):
+    center = k_size // 2
+    x, y = np.mgrid[0 - center:k_size - center, 0 - center:k_size - center]
+    g = 1 / (2 * np.pi * sigma) * np.exp(-(np.square(x) + np.square(y)) / (2 * np.square(sigma)))
+    return g
+
+
+def canny(image, threshold_low=15, threshold_high=30, weak=128, strong=255):
+    image_row, image_col = image.shape[0], image.shape[1]
+    # gaussian_filter
+    gaussian_out = img_convolve(image, gen_gaussian_kernel(9, sigma=1.4))
+    # get the gradient and degree by sobel_filter
+    sobel_grad, sobel_theta = sobel_filter(gaussian_out)
+    gradient_direction = np.rad2deg(sobel_theta)
+    gradient_direction += PI
+
+    dst = np.zeros((image_row, image_col))
+
+    """
+    Non-maximum suppression. If the edge strength of the current pixel is the largest compared to the other pixels 
+    in the mask with the same direction, the value will be preserved. Otherwise, the value will be suppressed. 
+    """
+    for row in range(1, image_row - 1):
+        for col in range(1, image_col - 1):
+            direction = gradient_direction[row, col]
+
+            if (
+                0 <= direction < 22.5
+                    or 15 * PI / 8 <= direction <= 2 * PI
+                    or 7 * PI / 8 <= direction <= 9 * PI / 8
+            ):
+                W = sobel_grad[row, col - 1]
+                E = sobel_grad[row, col + 1]
+                if sobel_grad[row, col] >= W and sobel_grad[row, col] >= E:
+                    dst[row, col] = sobel_grad[row, col]
+
+            elif (PI / 8 <= direction < 3 * PI / 8) or (9 * PI / 8 <= direction < 11 * PI / 8):
+                SW = sobel_grad[row + 1, col - 1]
+                NE = sobel_grad[row - 1, col + 1]
+                if sobel_grad[row, col] >= SW and sobel_grad[row, col] >= NE:
+                    dst[row, col] = sobel_grad[row, col]
+
+            elif (3 * PI / 8 <= direction < 5 * PI / 8) or (11 * PI / 8 <= direction < 13 * PI / 8):
+                N = sobel_grad[row - 1, col]
+                S = sobel_grad[row + 1, col]
+                if sobel_grad[row, col] >= N and sobel_grad[row, col] >= S:
+                    dst[row, col] = sobel_grad[row, col]
+
+            elif (5 * PI / 8 <= direction < 7 * PI / 8) or (13 * PI / 8 <= direction < 15 * PI / 8):
+                NW = sobel_grad[row - 1, col - 1]
+                SE = sobel_grad[row + 1, col + 1]
+                if sobel_grad[row, col] >= NW and sobel_grad[row, col] >= SE:
+                    dst[row, col] = sobel_grad[row, col]
+
+            """
+            High-Low threshold detection. If an edge pixel’s gradient value is higher than the high threshold
+            value, it is marked as a strong edge pixel. If an edge pixel’s gradient value is smaller than the high
+            threshold value and larger than the low threshold value, it is marked as a weak edge pixel. If an edge
+            pixel's value is smaller than the low threshold value, it will be suppressed.
+            """
+            if dst[row, col] >= threshold_high:
+                dst[row, col] = strong
+            elif dst[row, col] <= threshold_low:
+                dst[row, col] = 0
+            else:
+                dst[row, col] = weak
+
+    """
+    Edge tracking. Usually a weak edge pixel caused from true edges will be connected to a strong edge pixel while
+    noise responses are unconnected. As long as there is one strong edge pixel that is involved in its 8-connected
+    neighborhood, that weak edge point can be identified as one that should be preserved.
+    """
+    for row in range(1, image_row):
+        for col in range(1, image_col):
+            if dst[row, col] == weak:
+                if 255 in (
+                        dst[row, col + 1],
+                        dst[row, col - 1],
+                        dst[row - 1, col],
+                        dst[row + 1, col],
+                        dst[row - 1, col - 1],
+                        dst[row + 1, col - 1],
+                        dst[row - 1, col + 1],
+                        dst[row + 1, col + 1],
+                ):
+                    dst[row, col] = strong
+                else:
+                    dst[row, col] = 0
+
+    return dst
+
+
+if __name__ == '__main__':
+    # read original image in gray mode
+    lena = cv2.imread(r'../image_data/lena.jpg', 0)
+    # canny edge detection
+    canny_dst = canny(lena)
+    cv2.imshow('canny', canny_dst)
+    cv2.waitKey(0)

digital_image_processing/edge_detection/canny.py

@@ -10,11 +10,18 @@ def sobel_filter(image):
     kernel_x = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]])
     kernel_y = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]])
 
-    dst_x = img_convolve(image, kernel_x)
-    dst_y = img_convolve(image, kernel_y)
-    dst = np.sqrt((np.square(dst_x)) + (np.square(dst_y))).astype(np.uint8)
-    degree = np.arctan2(dst_y, dst_x)
-    return dst, degree
+    dst_x = np.abs(img_convolve(image, kernel_x))
+    dst_y = np.abs(img_convolve(image, kernel_y))
+    # modify the pix within [0, 255]
+    dst_x = dst_x * 255/np.max(dst_x)
+    dst_y = dst_y * 255/np.max(dst_y)
+
+    dst_xy = np.sqrt((np.square(dst_x)) + (np.square(dst_y)))
+    dst_xy = dst_xy * 255/np.max(dst_xy)
+    dst = dst_xy.astype(np.uint8)
+
+    theta = np.arctan2(dst_y, dst_x)
+    return dst, theta
 
 
 if __name__ == '__main__':
@@ -23,9 +30,9 @@ def sobel_filter(image):
     # turn image in gray scale value
     gray = cvtColor(img, COLOR_BGR2GRAY)
 
-    sobel, d = sobel_filter(gray)
+    sobel_grad, sobel_theta = sobel_filter(gray)
 
     # show result images
-    imshow('sobel filter', sobel)
-    imshow('sobel degree', d)
+    imshow('sobel filter', sobel_grad)
+    imshow('sobel theta', sobel_theta)
     waitKey(0)