convolve and sobel (TheAlgorithms#971)

* add gaussian filter algorithm and lena.jpg

* add img_convolve algorithm and sobel_filter

digital_image_processing/filters/convolve.py

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+# @Author  : lightXu
+# @File    : convolve.py
+# @Time    : 2019/7/8 0008 下午 16:13
+from cv2 import imread, cvtColor, COLOR_BGR2GRAY, imshow, waitKey
+from numpy import array, zeros, ravel, pad, dot, uint8
+
+
+def im2col(image, block_size):
+    rows, cols = image.shape
+    dst_height = cols - block_size[1] + 1
+    dst_width = rows - block_size[0] + 1
+    image_array = zeros((dst_height * dst_width, block_size[1] * block_size[0]))
+    row = 0
+    for i in range(0, dst_height):
+        for j in range(0, dst_width):
+            window = ravel(image[i:i + block_size[0], j:j + block_size[1]])
+            image_array[row, :] = window
+            row += 1
+
+    return image_array
+
+
+def img_convolve(image, filter_kernel):
+    height, width = image.shape[0], image.shape[1]
+    k_size = filter_kernel.shape[0]
+    pad_size = k_size//2
+    # Pads image with the edge values of array.
+    image_tmp = pad(image, pad_size, mode='edge')
+
+    # im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
+    image_array = im2col(image_tmp, (k_size, k_size))
+
+    #  turn the kernel into shape(k*k, 1)
+    kernel_array = ravel(filter_kernel)
+    # reshape and get the dst image
+    dst = dot(image_array, kernel_array).reshape(height, width)
+    return dst
+
+
+if __name__ == '__main__':
+    # read original image
+    img = imread(r'../image_data/lena.jpg')
+    # turn image in gray scale value
+    gray = cvtColor(img, COLOR_BGR2GRAY)
+    # Laplace operator
+    Laplace_kernel = array([[0, 1, 0], [1, -4, 1], [0, 1, 0]])
+    out = img_convolve(gray, Laplace_kernel).astype(uint8)
+    imshow('Laplacian', out)
+    waitKey(0)

digital_image_processing/filters/sobel_filter.py

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+# @Author  : lightXu
+# @File    : sobel_filter.py
+# @Time    : 2019/7/8 0008 下午 16:26
+import numpy as np
+from cv2 import imread, cvtColor, COLOR_BGR2GRAY, imshow, waitKey
+from digital_image_processing.filters.convolve import img_convolve
+
+
+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
+
+
+if __name__ == '__main__':
+    # read original image
+    img = imread('../image_data/lena.jpg')
+    # turn image in gray scale value
+    gray = cvtColor(img, COLOR_BGR2GRAY)
+
+    sobel, d = sobel_filter(gray)
+
+    # show result images
+    imshow('sobel filter', sobel)
+    imshow('sobel degree', d)
+    waitKey(0)