Opencv 仿射变换倾斜

怎么做到仿射变换（Afine Transformations）——倾斜？

1. 使用仿射变换，输出（1）那样的x轴倾斜30度的图像（t_x=30），这种变换被称为X-sharing。
2. 使用仿射变换，输出（2）那样的y轴倾斜30度的图像（t_y=30），这种变换被称为Y-sharing。
3. 使用仿射变换，输出（3）那样的x轴、y轴都倾斜30度的图像(t_x = 30，t_y = 30)。

原图像的大小为h\ w，使用下面各式进行仿射变换：

• X-sharing
  a=\frac{t_x}{h}\
  \left[
  \begin{matrix}
  x’\\
  y’\\
  1
  \end{matrix}
  \right]=\left[
  \begin{matrix}
  1&a&t_x\\
  0&1&t_y\\
  0&0&1
  \end{matrix}
  \right]\
  \left[
  \begin{matrix}
  x\\
  y\\
  1
  \end{matrix}
  \right]

• Y-sharing
  a=\frac{t_y}{w}\
  \left[
  \begin{matrix}
  x’\\
  y’\\
  1
  \end{matrix}
  \right]=\left[
  \begin{matrix}
  1&0&t_x\\
  a&1&t_y\\
  0&0&1
  \end{matrix}
  \right]\
  \left[
  \begin{matrix}
  x\\
  y\\
  1
  \end{matrix}
  \right]

python实现：

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
img = cv2.imread("imori.jpg").astype(np.float32)

# Affine
out = affine(img, dx=30, dy=30)

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

c++实现：

#include <opencv2/core.hpp>
#include <opencv2/highgui.hpp>
#include <iostream>
#include <math.h>

// affine
cv::Mat affine(cv::Mat img, double a, double b, double c, double d, double tx, double ty, double theta, double dx, double dy){
  // get height and width
  int width = img.cols;
  int height = img.rows;
  int channel = img.channels();

  // get detriment
  double det = a * d - b * c;

  if (dx != 0){
    b = dx / height;
  }
  if (dy != 0){
    c = dy / width;
  }

  if (theta != 0){
    // Affine parameters
    double rad = theta / 180. * M_PI;
    a = std::cos(rad);
    b = - std::sin(rad);
    c = std::sin(rad);
    d = std::cos(rad);
    tx = 0;
    ty = 0;

    double det = a * d - b * c;

    // center transition
    double cx = width / 2.;
    double cy = height / 2.;
    double new_cx = (d * cx - b * cy) / det;
    double new_cy = (- c * cx + a * cy) / det;
    tx = new_cx - cx;
    ty = new_cy - cy;
  }

  // Resize width and height
  int resized_width = (int)(width * a + dx);
  int resized_height = (int)(height * d + dy);

  if (theta != 0) {
    resized_width = (int)(width + dx);
    resized_height = (int)(height + dy);
  }

  // other parameters
  int x_before, y_before;

  // output
  cv::Mat out = cv::Mat::zeros(resized_height, resized_width, CV_8UC3);

  // Affine transformation
  for (int y = 0; y < resized_height; y++){    
    for (int x = 0; x < resized_width; x++){

      // get original position x
      x_before = (int)((d * x - b * y) / det - tx);

      if ((x_before < 0) || (x_before >= width)){
        continue;
      }

      // get original position y
      y_before = (int)((-c * x + a * y) / det - ty);

      if ((y_before < 0) || (y_before >= height)){
        continue;
      }

      // assign pixel to new position
      for (int _c = 0; _c < channel; _c++){
        out.at<cv::Vec3b>(y, x)[_c] = img.at<cv::Vec3b>(y_before, x_before)[_c];
      }
    }
  }

  return out;
}


int main(int argc, const char* argv[]){
  // read image
  cv::Mat img = cv::imread("imori.jpg", cv::IMREAD_COLOR);

  // affine
  cv::Mat out = affine(img, 1, 0, 0, 1, 0, 0, 0, 30, 30);

  //cv::imwrite("out.jpg", out);
  cv::imshow("answer", out);
  cv::waitKey(0);
  cv::destroyAllWindows();

  return 0;
}

输入：

输出1：

输出2：

输出3：