# Finding the Edges (Notebook) ## We let the code do the talking in this one ```python from manim import * ``` ```python import cv2 as cv from matplotlib import pyplot as plt ``` ```python import numpy as np ``` ```python config.media_width = "75%" config.verbosity = "WARNING" ``` ```python img0 = cv.imread('sobel_example.jpeg') ``` ```python def showimg(img): # cv2 images are in bgr by default and IPython assumes RGB for display img_rgb = cv.cvtColor(img, cv.COLOR_BGR2RGB) plt.imshow(img_rgb) plt.axis("off") #display(Image.fromarray(img_rgb)) def showgray(img_gray): plt.imshow(img_gray, cmap= "gray") plt.axis("off") ``` ```python showimg(img0) ``` ![image](https://live.staticflickr.com/65535/54076476894_63086b5666.jpg) ```python print(img0[0][0]) height, width, no_of_channels = img0.shape print(height, width) ``` [158 129 0] 2250 3376 ```python b, g, r = cv.split(img0) ``` ```python b ``` array([[158, 159, 159, ..., 151, 150, 149], [157, 157, 157, ..., 152, 151, 151], [156, 155, 155, ..., 154, 154, 154], ..., [ 39, 39, 40, ..., 39, 39, 39], [ 41, 42, 43, ..., 43, 42, 40], [ 41, 42, 43, ..., 43, 42, 40]], dtype=uint8) ```python g_y = np.array([ [1, 2, 1], [0, 0, 0], [-1, -2, -1] ]) g_y ``` array([[ 1, 2, 1], [ 0, 0, 0], [-1, -2, -1]]) ```python g_x = np.transpose(g_y) g_x ``` array([[ 1, 0, -1], [ 2, 0, -2], [ 1, 0, -1]]) ```python # padding n = len(g_y) pad_pixels = int((n - 1) / 2) print("pad_pixels: ") print(pad_pixels) # we have to pad the image, not the bgr vectors, so, we give 0 padding in z direction of tensor img0_padded = np.pad(img0, pad_width=((pad_pixels, pad_pixels), (pad_pixels, pad_pixels), (0, 0)), mode='constant', constant_values=0) img0_padded.shape ``` pad_pixels: 1 (2252, 3378, 3) ```python img0_padded[:3, :3] ``` array([[[ 0, 0, 0], [ 0, 0, 0], [ 0, 0, 0]], [[ 0, 0, 0], [158, 129, 0], [159, 130, 1]], [[ 0, 0, 0], [157, 128, 0], [157, 128, 0]]], dtype=uint8) [[[ 0, 0, 0], --> bgr vector at (0, 0) of a 3x3 neighbourhood
[ 0, 0, 0], --> bgr vector at (0, 1)
[ 0, 0, 0]],--> bgr vector at (0, 2)

[[ 0, 0, 0],--> bgr vector at (1, 0)
[158, 129, 0],--> bgr vector at (1, 1) --> the result in the next cell, ie, the center bgr of the neighbourhood tensor
[159, 130, 1]],--> bgr vector at (1, 2)

[[ 0, 0, 0],--> bgr vector at (2, 0)
[157, 128, 0],--> bgr vector at (2, 1)
[157, 128, 0]]]--> bgr vector at (2, 2)
```python img0_padded[0:3, 3373:3376] ``` array([[[ 0, 0, 0], [ 0, 0, 0], [ 0, 0, 0]], [[152, 118, 0], [151, 117, 0], [150, 116, 0]], [[152, 118, 0], [152, 118, 0], [151, 117, 0]]], dtype=uint8) ```python def convolve(img, kernel): n = len(kernel) pad_pixels = int((n - 1) / 2) # we have to pad the image, not the bgr vectors, so, we give 0 padding in z direction of tensor imgp = np.pad(img, pad_width=((pad_pixels, pad_pixels), (pad_pixels, pad_pixels), (0, 0)), mode='constant', constant_values=0) height = len(img) width = len(img[0]) #print("padded shape: ", imgp.shape) convoluted_result = np.zeros([height, width]) for irow in range(1, len(imgp) - 1): for icol in range(1, len(imgp[0]) - 1): # filter going row by row # the result will be a vector if its a multi channel image # itll be a number if its a grayscale / monochannel #print("starting calculation for neighbourhood centering: ", (irow, icol)) current_neighbourhood = imgp[irow-pad_pixels : irow+pad_pixels+1, icol-pad_pixels : icol+pad_pixels+1] #print("current neighbourhood is: ") #print(current_neighbourhood) current_conv_res = sum( [sum([kernel[i][j] * current_neighbourhood[i,j] for i in range(n)]) # weighted sum of the row for j in range(n)]) # loop going through all the rows , ord = 2) #print("resultant bgr after convolving: ", current_conv_res) current_conv_res_norm = np.linalg.norm(current_conv_res) convoluted_result[irow - pad_pixels][icol - pad_pixels] = current_conv_res_norm #print("result norm for current neighbourhood is: ", current_conv_res_norm) # the norm of the bgr vector found by convolving the kernel with n x n neighbourhood return convoluted_result ``` [Visualization video of convolution on YouTube](https://youtu.be/3Tf6UZ7zp54) ```python try: convoluted_result_y = np.load('./car_image_gy_convolv.npy') except: convoluted_result_y = convolve(img0, g_y) ``` ```python convoluted_result_y ``` array([[607.69811584, 810.26415446, 811.04500492, ..., 768.30332552, 765.49722403, 573.07067627], [350.72638908, 341.55673028, 335.97767783, ..., 268.22565127, 272.47018185, 270.36271932], [354.27249399, 349.32363218, 347.20887085, ..., 269.3139432 , 272.47018185, 270.36271932], ..., [ 6.92820323, 12.12435565, 13.85640646, ..., 25.98076211, 19.05255888, 8.66025404], [ 12.12435565, 19.05255888, 19.05255888, ..., 24.24871131, 19.05255888, 8.66025404], [191.11514854, 259.38388539, 264.52032058, ..., 265.8025583 , 258.92663053, 188.61071019]]) ```python showgray(convoluted_result_y) ``` ![Result in Y](https://live.staticflickr.com/65535/54076477149_5bdc414a82.jpg) ```python try: convoluted_result_x = np.load('./car_image_gx_convolv.npy') except: convoluted_result_x = convolve(img0, g_x) ``` ```python convoluted_result_x ``` array([[607.69811584, 810.26415446, 811.04500492, ..., 768.30332552, 765.49722403, 573.07067627], [350.72638908, 341.55673028, 335.97767783, ..., 268.22565127, 272.47018185, 270.36271932], [354.27249399, 349.32363218, 347.20887085, ..., 269.3139432 , 272.47018185, 270.36271932], ..., [ 6.92820323, 12.12435565, 13.85640646, ..., 25.98076211, 19.05255888, 8.66025404], [ 12.12435565, 19.05255888, 19.05255888, ..., 24.24871131, 19.05255888, 8.66025404], [191.11514854, 259.38388539, 264.52032058, ..., 265.8025583 , 258.92663053, 188.61071019]]) ```python showgray(convoluted_result_x) ``` ![Result in X](https://live.staticflickr.com/65535/54076409673_b7a4c134a4.jpg) ```python gradient_magnitude = np.sqrt(convoluted_result_x**2 + convoluted_result_y**2) gradient_magnitude_clipped = np.clip(gradient_magnitude, 0, 255).astype(np.uint8) ``` ```python gradient_magnitude_clipped ``` array([[255, 255, 255, ..., 255, 255, 255], [255, 255, 255, ..., 255, 255, 255], [255, 255, 255, ..., 255, 255, 255], ..., [ 9, 17, 19, ..., 36, 26, 12], [ 17, 26, 26, ..., 34, 26, 12], [255, 255, 255, ..., 255, 255, 255]], dtype=uint8) ```python showgray(gradient_magnitude_clipped) ``` ![Vector Sum Result](https://live.staticflickr.com/65535/54076410303_58064d9938.jpg) ```python #np.save('car_image_gx_convolv.npy', convoluted_result) ``` ```python #np.save('car_image_gy_convolv.npy', convoluted_result) ``` ```python test_img = np.load('./test_image_bitmap_downward_arrow.npy') ``` ```python test_img ``` array([[0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 1., 1., 1., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 1., 1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]) ```python # coloring the image colored_res = np.zeros((16, 16, 3)) for i in range(len(test_img)): for j in range(len(test_img[0])): # a bgr vector being added on each point # this makes the arrow green, with incrementally getting lighter on each row # and a gradient of decreasing blue-ness on each column colored_res[i][j] = [((j+1)/len(test_img)) * test_img[i][j], ((i+1)/len(test_img)) * test_img[i][j], 0] ``` ```python colored_res.shape ``` (16, 16, 3) ```python rgb_format_res = colored_res[..., ::-1] plt.imshow(rgb_format_res) ``` ![Down Arrow Image](https://live.staticflickr.com/65535/54076410423_79fb0ab8e2_w.jpg) ```python sobel_filtered = convolve(rgb_format_res, g_y) ``` ```python showgray(sobel_filtered) ``` ![Result in Y](https://live.staticflickr.com/65535/54076153466_5c4edd8100_w.jpg) ```python sobel_filtered_x = convolve(rgb_format_res, g_x) ``` ```python showgray(sobel_filtered_x) ``` ![Result in X](https://live.staticflickr.com/65535/54076410973_0f2c7bfca2_w.jpg) ```python gradient_magnitude = np.sqrt(sobel_filtered**2 + sobel_filtered_y**2) gradient_magnitude = np.clip(gradient_magnitude, 0, 255).astype(np.uint8) gradient_magnitude ``` array([[0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8) ```python showgray(gradient_magnitude) ``` ![Vector Result](https://live.staticflickr.com/65535/54076153646_0d44da7572_w.jpg)