圖像處理入門100題（三）

本篇記錄了自己寫的GIthub上的ImageProcessing 100 Wen的問題21-30的答案，注釋里包含了一些自己的感悟。為了方便，注釋是用英文寫的。

進一步感受到了圖像處理的本質就是矩陣運算，所以線性代數的基礎一定要牢靠。此外，Python的數據包也要用的熟練和巧妙，時刻有一個“矩陣運算”意識。

問題序號題目

21	直方圖歸一化
22	直方圖操作
23	直方圖均衡化
24	伽馬校正
25	最鄰近插值
26	雙線性插值
27	雙立方插值
28	仿射變換：平移
29	仿射變換：縮放
30	仿射變換：旋轉

Python答案如下，結尾包含了問題的驗證。

import cv2.cv2 import numpy as np import matplotlib.pyplot as plt# Question 21 # Histogram Normalization # Answerdef histogram_normalization(img, a=0, b=255):c = np.min(img) # c is the min value of all pixelsd = np.max(img) # d is the max value of all pixelsout = img.copy()out = (b - a) / (d - c) * (out - c) + a# The follow three steps are very important!out[out < 0] = 0 # step 1out[out > 255] = 255 # step 2out = out.astype(np.uint8) # step 3return out# Question 22 # to make the histogram of the image more plane, mean = 128, sigma = 52 # Answerdef histogram_mean(img, m0=128, sigma0=52):m = np.mean(img) # the old mean value of imgsigma = np.std(img) # the old standard value of imgout = img.copy()out = sigma0 / sigma * (out - m) + m0# The follow three steps are very important!out[out < 0] = 0 # step 1out[out > 255] = 255 # step 2out = out.astype(np.uint8) # step 3return out# Question 23 # histogram equalization # out = Zmax / S * SUM(h), Zmax is the max value of the pixels # S is the number of pixels, h is the distribution function # Answerdef histogram_equalization(img, Zmax=255):if len(img.shape) == 3:H, W, C = img.shapeelse:img = np.expand_dims(img, axis=-1)H, W, C = img.shapeS = H * W * Csum_h = 0out = img.copy()for i in range(1, 255):sum_h = sum_h + len(img[img == i])out[img == i] = sum_h / S * Zmax # the density function of probability times the max valueout = out.astype(np.uint8)return out# Question 24 # Gamma correction # Answerdef gamma_correction(img, c=1.0, g=2.2):out = img / 255out = 1 / c * np.power(out, 1 / g)out = out * 255out = out.astype(np.uint8)return out# Question 25 # Nearest neighbor interpolation # Answerdef nearest_neighbor_interpolation(img, a=1.5):if len(img.shape) == 3:H, W, C = img.shapeelse:np.expand_dims(img, axis=-1)H, W, C = img.shapeHa = int(H * a)Wa = int(W * a)out = np.zeros((Ha, Wa, C), dtype=np.float)for y in range(Ha):for x in range(Wa):for c in range(C):out[y, x, c] = img[int(y / a), int(x / a), c]out = out.astype(np.uint8)return out# Question 26 # Bilinear Interpolation # Answerdef bilinear_interpolation(img, a=1.5):if len(img.shape) == 3:H, W, C = img.shapeelse:img = np.expand_dims(img, axis=-1)H, W, C = img.shapeaH = int(a * H)aW = int(a * W)# get the resized positions'''The follow two operations is importantthe first objective is to build a y matrix like:array([[0, 0, 0, 0, 0],[1, 1, 1, 1, 1],[2, 2, 2, 2, 2],[3, 3, 3, 3, 3],[4, 4, 4, 4, 4]])the second objective is to build a x matrix like:array([[0, 1, 2, 3, 4],[0, 1, 2, 3, 4],[0, 1, 2, 3, 4],[0, 1, 2, 3, 4],[0, 1, 2, 3, 4]])'''y = np.arange(aH).repeat(aW).reshape(aH, -1)x = np.tile(np.arange(aW), (aH, 1))# get the original positions# floaty = (y / a)x = (x / a)# intix = np.floor(x).astype(np.int)iy = np.floor(y).astype(np.int)# to avoid overflow, the original positions must <= (x_max-1, y_max-1)# to make ix where ix > W-2 change to W-2. why W-2? because numpy.arange generate (0, W-1), W-2 = W-1-1 = x_max -1ix = np.minimum(ix, W - 2)iy = np.minimum(iy, H - 2)# get distancedx = x - ixdy = y - iy# by now, dx and dy is a 2*2 matrix, but an image is generally 2*2*3 matrix, because there are 3 channels RGB# so we should expand dx and dy to 2*2*3# and keep the distance is the same to 3 channelsdx = np.expand_dims(dx, axis=-1)dx = np.repeat(dx, C, axis=-1) # repeat the channel dimensiondy = np.expand_dims(dy, axis=-1)dy = np.repeat(dy, C, axis=-1)# interpolationout = (1 - dx) * (1 - dy) * img[iy, ix] + dx * (1 - dy) * img[iy, ix + 1] + (1 - dx) * dy * img[iy + 1, ix] + dx * dy * \img[iy + 1, ix + 1]out = np.clip(out, 0, 255)out = out.astype(np.uint8)return out# Question 27 # bicubic interpolationdef bicubic_interpolation(img, a=1.5):if len(img.shape) == 3:H, W, C = img.shapeelse:img = np.expand_dims(img, axis=-1)H, W, C = img.shapeaH = int(a * H)aW = int(a * W)# get positions of resized imagey = np.arange(aH).repeat(aW).reshape(aH, -1)x = np.tile(np.arange(aW), (aH, 1))# get positions of original image# floaty = y / ax = x / a# intiy = np.floor(y).astype(np.int)ix = np.floor(x).astype(np.int)# to avoid overflowiy = np.minimum(iy, H - 2)ix = np.minimum(ix, W - 2)# compute distancesdx1 = np.abs(x - ix + 1)dx2 = np.abs(x - ix)dx3 = np.abs(x - ix - 1)dx4 = np.abs(x - ix - 2)dx = [dx1, dx2, dx3, dx4]dy1 = np.abs(y - iy + 1)dy2 = np.abs(y - iy)dy3 = np.abs(y - iy - 1)dy4 = np.abs(y - iy - 2)dy = [dy1, dy2, dy3, dy4]# compute weight according to distancedef h(t):m = -1t_abs = np.abs(t)w = np.zeros_like(t)condition1 = t_abs <= 1w[condition1] = ((m + 2) * np.power(t_abs, 3) - (m + 3) * np.power(t_abs, 2) + 1)[condition1]condition2 = (t_abs > 1) & (t_abs <= 2)w[condition2] = (m * np.power(t, 3) - 5 * m * np.power(t_abs, 2) + 8 * m * t_abs - 4 * m)[condition2]return wsum_h = np.zeros((aH, aW, C), dtype=np.float)out = np.zeros((aH, aW, C), dtype=np.float)for j in range(1, 5):for i in range(1, 5):# to avoid overflowindex_x = np.minimum(np.maximum(ix + i - 2, 0), W - 1)index_y = np.minimum(np.maximum(iy + j - 2, 0), H - 1)# i-1, j-1h_dx = h(dx[i - 1])h_dy = h(dy[j - 1])h_dx = np.expand_dims(h_dx, axis=-1)h_dx = np.repeat(h_dx, C, axis=-1)h_dy = np.expand_dims(h_dy, axis=-1)h_dy = np.repeat(h_dy, C, axis=-1)sum_h = sum_h + h_dx * h_dyout = out + img[index_y, index_x] * h_dx * h_dyout = out / sum_hout = np.clip(out, 0, 255)out = out.astype(np.uint8)return out# Question 28-29 # afine transformations # Answerdef afine_image(img, a, b, c, d, tx=30, ty=-30):if len(img.shape) == 3:H, W, C = img.shapeelse:img = np.expand_dims(img, axis=-1)H, W, C = img.shape# to make the place after afine blackimg_expand = np.zeros((H + 2, W + 2, C), dtype=np.float)img_expand[1:H + 1, 1:W + 1] = img# get new image shapeH_new = np.round(H * d).astype(np.int)W_new = np.round(W * a).astype(np.int)out = np.zeros((H_new + 1, W_new + 1, C), dtype=np.float)y_new = np.arange(H_new).repeat(W_new).reshape(H_new, -1)x_new = np.tile(np.arange(W_new), (H_new, 1))adbc = a * d - b * cx = np.round((d * x_new - b * y_new) / adbc - tx).astype(np.int) + 1y = np.round((-c * x_new + a * y_new) / adbc - ty).astype(np.int) + 1 # please note that img_expand[1:H+1, 1:W+1]x = np.minimum(np.maximum(x, 0), W + 1).astype(np.int)y = np.minimum(np.maximum(y, 0), H + 1).astype(np.int)out[y_new, x_new] = img_expand[y, x]out = out[:H_new, :W_new]out = out.astype(np.uint8)return out# Question 30 # rotation # Answerdef rotation_image(img, a, b, c, d, tx=30, ty=-30):if len(img.shape) == 3:H, W, C = img.shapeelse:img = np.expand_dims(img, axis=-1)H, W, C = img.shape# to make the place after afine blackimg_expand = np.zeros((H + 2, W + 2, C), dtype=np.float)img_expand[1:H + 1, 1:W + 1] = img# get new image shapeH_new = np.round(H).astype(np.int)W_new = np.round(W).astype(np.int)out = np.zeros((H_new, W_new, C), dtype=np.float)y_new = np.arange(H_new).repeat(W_new).reshape(H_new, -1)x_new = np.tile(np.arange(W_new), (H_new, 1))adbc = a * d - b * cx = np.round((d * x_new - b * y_new) / adbc - tx).astype(np.int) + 1y = np.round((-c * x_new + a * y_new) / adbc - ty).astype(np.int) + 1 # please note that img_expand[1:H+1, 1:W+1]dcx = (x.max() + x.min()) // 2 - W // 2dcy = (y.max() + y.min()) // 2 - H // 2x -= dcxy -= dcyx = np.clip(x, 0, W + 1)y = np.clip(y, 0, H + 1)out[y_new, x_new] = img_expand[y, x]out = out.astype(np.uint8)return out# Test# Answer 21 # img = cv2.imread("imori_dark.jpg").astype(np.float) # img21 = histogram_normalization(img) # # plt.hist(img21.ravel(), bins=255, range=(0, 255)) # plt.show() # # cv2.imshow("histogram normalization", np.hstack((img.astype(np.uint8), img21))) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 22 # img = cv2.imread("imori_dark.jpg").astype(np.float) # img22 = histogram_mean(img) # # plt.hist(img22.ravel(), bins=255, range=(0, 255)) # plt.show() # # cv2.imshow("histogram normalization", np.hstack((img.astype(np.uint8), img22))) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 23 # img = cv2.imread("imori.jpg").astype(np.float) # img23 = histogram_equalization(img) # # plt.hist(img23.ravel(), bins=255, range=(0, 255)) # plt.show() # # cv2.imshow("histogram equalization", np.hstack((img.astype(np.uint8), img23))) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 24 # img = cv2.imread("imori_gamma.jpg").astype(np.float) # img24 = gamma_correction(img) # # cv2.imshow("gamma correction", np.hstack((img.astype(np.uint8), img24))) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 25 # img = cv2.imread("imori.jpg").astype(np.float) # img25 = nearest_neighbor_interpolation(img) # # cv2.imshow("gamma correction", img25) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 26 # img = cv2.imread("imori.jpg").astype(np.float) # img26 = bilinear_interpolation(img) # # cv2.imshow("bilinear interpolation", img26) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 27 # img = cv2.imread("imori.jpg").astype(np.float) # img27 = bicubic_interpolation(img) # # cv2.imshow("bicubic interpolation", img27) # cv2.waitKey(0) # cv2.destroyAllWindows()# img = cv2.imread("imori.jpg").astype(np.float) # img28 = afine_image(img, a=1, b=0, c=0, d=1, tx=30, ty=-30) # # cv2.imshow("afine interpolation", img28) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 29 # img = cv2.imread("imori.jpg").astype(np.float) # img29 = afine_image(img, a=1.3, b=0, c=0, d=0.8, tx=30, ty=-30) # # cv2.imshow("afine interpolation", img29) # cv2.waitKey(0) # cv2.destroyAllWindows()# Answer 30 # img = cv2.imread("imori.jpg").astype(np.float) # img30 = rotation_image(img, a=np.cos(-np.pi / 6.), b=-np.sin(-np.pi / 6.), c=np.sin(-np.pi / 6.), d=np.cos(-np.pi / 6.), # tx=0, ty=0) # # cv2.imshow("rotation interpolation", img30) # cv2.waitKey(0) # cv2.destroyAllWindows()

用到的圖片
imori.jpg

imori_gamma.jpg

imori_dark.jpg

總結

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