图像几何变换代码.zip

import cv2 import numpy as np from matplotlib import pyplot as plt import math import numba as nb @nb.jit() def nearest(img, x, y): if x < 0 or y < 0: return 0 new_x = round(x) new_y = round(y) sp = img.shape if new_x < 0 or new_y < 0 or new_x > sp[1] or new_y > sp[0]: return 0 return img[new_y, new_x] @nb.jit() def bilinear(img, x, y): x1 = math.floor(x) x2 = math.ceil(x) y1 = math.floor(y) y2 = math.ceil(y) sp = img.shape if x1 < 0 or x2 < 0 or y1 < 0 or y2 < 0 or x1 > sp[1] or x2 > sp[1] or y1 > sp[0] or y2 > sp[0]: return 0 wx1 = x - math.floor(x) wx2 = math.ceil(x) - x wy1 = y - math.floor(y) wy2 = math.ceil(y) - y if wx1 == wx2: if x1 == 0: wx2 = 1 x2 += 1 else: wx1 = 1 x1 -= 1 if wy1 == wy2: if y1 == 0: wy2 = 1 y2 += 1 else: wy1 = 1 y1 -= 1 w = np.array([wx2 * wy1, wx1 * wy1, wx2 * wy2, wx1 * wy2]) v = np.array([img[y2, x1], img[y2, x2], img[y1, x1], img[y1, x2]]) return (w * v).sum() / w.sum() @nb.jit() def translation(img, tx, ty): sp = img.shape new_img = np.zeros((sp[0] + ty, sp[1] + tx), dtype=img.dtype) new_sp = new_img.shape T = np.array([[1, 0, tx], [0, 1, ty], [0, 0, 1]], dtype=np.float64) T_inv = np.linalg.inv(T) for i in range(new_sp[1]): for j in range(new_sp[0]): tmp = np.dot(T_inv, np.array([[i], [j], [1]], dtype=np.float64)) new_img[j][i] = nearest(img, tmp[0, 0], tmp[1, 0]) return new_img @nb.jit() def scale(img, cx, cy): sp = img.shape new_img = np.zeros((int(sp[0] * cy), int(sp[1] * cx)), dtype=img.dtype) new_sp = new_img.shape T = np.zeros((3, 3), dtype=np.float64) T[0, 0] = cx T[1, 1] = cy T[2, 2] = 1 T_inv = np.linalg.inv(T) for i in range(new_sp[1]): for j in range(new_sp[0]): tmp = np.dot(T_inv, np.array([[i], [j], [1]], dtype=np.float64)) new_img[j][i] = bilinear(img, tmp[0, 0], tmp[1, 0]) return new_img @nb.jit() def rotate(img, theta): cos_theta = math.cos(theta) sin_theta = math.sin(theta) sp = img.shape shift = int(math.sqrt(sp[0] ** 2 + sp[1] ** 2)) new_img = np.zeros( (int(math.sqrt(sp[0] ** 2 + sp[1] ** 2)) * 2 + 1, int(math.sqrt(sp[0] ** 2 + sp[1] ** 2)) * 2 + 1), dtype=img.dtype) new_sp = new_img.shape T = np.zeros((3, 3), dtype=np.float64) T[0, 0] = cos_theta T[0, 1] = -sin_theta T[1, 0] = sin_theta T[1, 1] = cos_theta T[2, 2] = 1 T_inv = np.linalg.inv(T) for i in range(new_sp[1]): for j in range(new_sp[0]): tmp = np.dot(T_inv, np.array([[i - shift], [j - shift], [1]], dtype=np.float64)) new_img[j][i] = bilinear(img, tmp[0, 0], tmp[1, 0]) return new_img def euclidean(img, theta, tx, ty): return translation(rotate(img, theta), tx, ty) def similarity(img, theta, tx, ty, cx, cy): return translation(rotate(scale(img, cx, cy), theta), tx, ty) @nb.jit() def affine(img, a11, a12, a21, a22, tx, ty): sp = img.shape corner = [[0, 0], [sp[1], 0], [0, sp[0]], [sp[1], sp[0]]] T = np.zeros((3, 3), dtype=np.float64) T[0, 0] = a11 T[0, 1] = a12 T[1, 0] = a21 T[1, 1] = a22 T[0, 2] = tx T[1, 2] = ty T[2, 2] = 1 new_corner = [np.dot(T, np.array([[c[0]], [c[1]], [1]], dtype=np.float64)) for c in corner] shift_x = min([int(c[0][0]) for c in new_corner]) shift_y = min([int(c[1][0]) for c in new_corner]) if shift_x > 0: shift_x = 0 if shift_y > 0: shift_y = 0 new_img = np.zeros((max([int(c[1][0]) for c in new_corner]) - shift_y, max([int(c[0][0]) for c in new_corner]) - shift_x), dtype=img.dtype) new_sp = new_img.shape T_inv = np.linalg.inv(T) for i in range(new_sp[1]): for j in range(new_sp[0]): tmp = np.dot(T_inv, np.array([[i + shift_x], [j + shift_y], [1]], dtype=np.float64)) new_img[j][i] = bilinear(img, tmp[0, 0], tmp[1, 0]) return new_img @nb.jit() def projective(img, h11, h12, h13, h21, h22, h23, h31, h32): sp = img.shape corner = [[0, 0], [sp[1], 0], [0, sp[0]], [sp[1], sp[0]]] T = np.zeros((3, 3), dtype=np.float64) T[0, 0] = h11 T[0, 1] = h12 T[0, 2] = h13 T[1, 0] = h21 T[1, 1] = h22 T[1, 2] = h23 T[2, 0] = h31 T[2, 1] = h32 T[2, 2] = 1 new_corner = [np.dot(T, np.array([[c[0]], [c[1]], [1]], dtype=np.float64)) for c in corner] shift_x = min([int(c[0][0] / c[2][0]) for c in new_corner]) shift_y = min([int(c[1][0] / c[2][0]) for c in new_corner]) if shift_x > 0: shift_x = 0 if shift_y > 0: shift_y = 0 new_img = np.zeros((max([int(c[1][0] / c[2][0]) for c in new_corner]) - shift_y, max([int(c[0][0] / c[2][0]) for c in new_corner]) - shift_x), dtype=img.dtype) new_sp = new_img.shape T_inv = np.linalg.inv(T) for i in range(new_sp[1]): for j in range(new_sp[0]): tmp = np.dot(T_inv, np.array([[i + shift_x], [j + shift_y], [1]], dtype=np.float64)) new_img[j][i] = bilinear(img, tmp[0, 0] / tmp[2, 0], tmp[1, 0] / tmp[2, 0]) return new_img if __name__ == '__main__': img = cv2.imread('lena.tif', cv2.IMREAD_GRAYSCALE) plt.rcParams['figure.figsize'] = (7, 4) plt.rcParams['figure.dpi'] = 200 plt.subplot(2, 4, 1) plt.title('origin') plt.imshow(img, cmap='gray') tx = 50 ty = 200 new_img = translation(img, tx, ty) plt.subplot(2, 4, 2) plt.title('translation') plt.imshow(new_img, cmap='gray') cx = 0.5 cy = 2 new_img = scale(img, cx, cy) plt.subplot(2, 4, 3) plt.title('scale') plt.imshow(new_img, cmap='gray') theta = 0.3 new_img = rotate(img, theta) plt.subplot(2, 4, 4) plt.title('rotate') plt.imshow(new_img, cmap='gray') theta = 0.3 tx = 200 ty = 100 new_img = euclidean(img, theta, tx, ty) plt.subplot(2, 4, 5) plt.title('euclidean') plt.imshow(new_img, cmap='gray') theta = 0.3 tx = 200 ty = 100 cx = 2 cy = 0.5 new_img = similarity(img, theta, tx, ty, cx, cy) plt.subplot(2, 4, 6) plt.title('similarity') plt.imshow(new_img, cmap='gray') tx = 100 ty = 200 a11 = 1 a12 = 0 a21 = 2 a22 = 1 new_img = affine(img, a11, a12, a21, a22, tx, ty) plt.subplot(2, 4, 7) plt.title('affine') plt.imshow(new_img, cmap='gray') h11 = 0.97 h12 = -0.14 h13 = 167 h21 = 0.02 h22 = 1.02 h23 = 116 h31 = 0.0005 h32 = 0.0005 new_img = projective(img, h11, h12, h13, h21, h22, h23, h31, h32) plt.subplot(2, 4, 8) plt.title('projective') plt.imshow(new_img, cmap='gray') plt.show()