数字图像处理100问—30 仿射变换（ Afine Transformations ）——旋转

提示：内容整理自：https://github.com/gzr2017/ImageProcessing100Wen
CV小白从0开始学数字图像处理

30 仿射变换（ Afine Transformations ）——旋转

1. 使用仿射变换，逆时针旋转30度。
2. 使用仿射变换，逆时针旋转30度并且能让全部图像显现（也就是说，单纯地做仿射变换会让图片边缘丢失，这一步中要让图像的边缘不丢失，需要耗费一些工夫）。

使用下面的式子进行逆时针方向旋转A度的仿射变换：

  x'       cosA -sinA tx    x
[ y' ] = [ sinA  cosA ty ][ y ]
  1         0     0    1    1

代码如下：

1.引入库

CV2计算机视觉库

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

2.读入数据

img = cv2.imread("imori.jpg").astype(np.float)
H, W, C = img.shape

3.旋转

A = 30.
theta = - np.pi * A / 180.

a = np.cos(theta)
b = -np.sin(theta)
c = np.sin(theta)
d = np.cos(theta)
tx = 0
ty = 0

img = np.zeros((H+2, W+2, C), dtype=np.float32)
img[1:H+1, 1:W+1] = _img

H_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.float32)

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

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

dcx = (x.max() + x.min()) // 2 - W // 2
dcy = (y.max() + y.min()) // 2 - H // 2

x -= dcx
y -= dcy

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[y, x]
out = out.astype(np.uint8)

4.保存结果

cv2.imshow("result", out)
cv2.waitKey(0)
cv2.imwrite("out.jpg", out)

5.结果