图像仿射变换之图像倾斜 含pyhon源码

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一. 仿射变换算法原理：

仿射变换过程，(x,y)表示原图像中的坐标，(x',y')表示目标图像的坐标 ↑

 

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二. 仿射变换倾斜算法原理：

    原图像大小为h*w

    X-sharing：

倾斜之x轴逆时针旋转tx度时的图像仿射变换公式 ↑

 

    Y-sharing：

倾斜之y轴逆时针旋转ty度时的图像仿射变换公式 ↑

 

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三. 实验：python实现仿射变换 ——> 图像倾斜 ——> x轴逆时针旋转 30°，y轴逆时针旋转30°

import cv2
import numpy as np
import matplotlib.pyplot as plt

# Affine
def affine(img, dx=30, dy=30):
    # get shape
    H, W, C = img.shape

    # Affine hyper parameters
    a = 1.
    b = dx / H
    c = dy / W
    d = 1.
    tx = 0.
    ty = 0.

    # prepare temporary
    _img = np.zeros((H+2, W+2, C), dtype=np.float32)

    # insert image to center of temporary
    _img[1:H+1, 1:W+1] = img

    # prepare affine image temporary
    H_new = np.ceil(dy + H).astype(np.int)
    W_new = np.ceil(dx + W).astype(np.int)
    out = np.zeros((H_new, W_new, C), dtype=np.float32)

    # preprare assigned index
    x_new = np.tile(np.arange(W_new), (H_new, 1))
    y_new = np.arange(H_new).repeat(W_new).reshape(H_new, -1)

    # prepare inverse matrix for affine
    adbc = a * d - b * c
    x = np.round((d * x_new  - b * y_new) / adbc).astype(np.int) - tx + 1
    y = np.round((-c * x_new + a * y_new) / adbc).astype(np.int) - ty + 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)

    # assign value from original to affine image
    out[y_new, x_new] = _img[y, x]
    out = out.astype(np.uint8)

    return out

# Read image
image1 = cv2.imread("../paojie.jpg").astype(np.float32)
# Affine
out = affine(image1, dx=30, dy=30)
# Save result
cv2.imshow("result", out)
cv2.imwrite("out.jpg", out)
cv2.waitKey(0)
cv2.destroyAllWindows()

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四. 实验结果：

x轴和y轴倾斜后图像 ↑

 

原图 ↑

 

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五. 代码疑难点讲解：

    请参考：https://www.cnblogs.com/wojianxin/p/12519498.html 的第五部分内容

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六.  参考内容：

    https://www.jianshu.com/p/08611282153f

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七. 版权声明：

    未经作者允许，请勿随意转载抄袭，抄袭情节严重者，作者将考虑追究其法律责任，创作不易，感谢您的理解和配合！