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1. 基本原理

  透视变换（Perspective Transformation）的本质是将图像投影到一个新的视平面，其通用变换公式为：

  

  （u，v）为原始图像像素坐标，（x=x’/w’，y=y’/w’）为变换之后的图像像素坐标。透视变换矩阵图解如下：

  

  仿射变换（Affine Transformation）可以理解为透视变换的特殊形式。透视变换的数学表达式为：

  

  所以，给定透视变换对应的四对像素点坐标，即可求得透视变换矩阵；反之，给定透视变换矩阵，即可对图像或像素点坐标完成透视变换，如下图所示：

  

2. OpenCV透视变换函数

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mat getPerspectiveTransform(const Point2f* src, const Point2f* dst) // Calculate a perspective transform from four pairs of the corresponding points. // src – Coordinates of quadrangle vertices in the source image. // dst – Coordinates of the corresponding quadrangle vertices in the destination image.   void warpPerspective(InputArray src, OutputArray dst, InputArray M, Size dsize, int flags=INTER_LINEAR, int borderMode=BORDER_CONSTANT, const Scalar& borderValue=Scalar()) // Apply a perspective transform to an image. // src – Source image. // dst – Destination image that has the size dsize and the same type as src. // M – 3*3 transformation matrix. // dsize – Size of the destination image. // flags – Combination of interpolation methods and the optional flag WARP_INVERSE_MAP that means that M is the inverse transformation (dstsrc). // borderMode – Pixel extrapolation method. When borderMode=BORDER_TRANSPARENT, it means that the pixels in the destination image that corresponds to the “outliers” in the source image are not modified by the function. // borderValue – Value used in case of a constant border. By default, it is 0.

3. 程序

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 #include <iostream>   #include "highgui.h" #include "opencv2/imgproc/imgproc.hpp"   int main() {     // get original image.     cv::Mat originalImage = cv::imread("road.png");           // perspective image.     cv::Mat perspectiveImage;           // perspective transform     cv::Point2f objectivePoints[4], imagePoints[4];       // original image points.     imagePoints[0].x = 10.0; imagePoints[0].y = 457.0;     imagePoints[1].x = 395.0; imagePoints[1].y = 291.0;     imagePoints[2].x = 624.0; imagePoints[2].y = 291.0;     imagePoints[3].x = 1000.0; imagePoints[3].y = 457.0;       // objective points of perspective image.     // move up the perspective image : objectivePoints.y - value .     // move left the perspective image : objectivePoints.x - value.     double moveValueX = 0.0;     double moveValueY = 0.0;       objectivePoints[0].x = 46.0 + moveValueX; objectivePoints[0].y = 920.0 + moveValueY;     objectivePoints[1].x = 46.0 + moveValueX; objectivePoints[1].y = 100.0 + moveValueY;     objectivePoints[2].x = 600.0 + moveValueX; objectivePoints[2].y = 100.0 + moveValueY;     objectivePoints[3].x = 600.0 + moveValueX; objectivePoints[3].y = 920.0 + moveValueY;       cv::Mat transform = cv::getPerspectiveTransform(objectivePoints, imagePoints);       // perspective.     cv::warpPerspective(originalImage,                         perspectiveImage,                         transform,                         cv::Size(originalImage.rows, originalImage.cols),                         cv::INTER_LINEAR | cv::WARP_INVERSE_MAP);       // cv::imshow("perspective image", perspectiveImage);     // cvWaitKey(0);       cv::imwrite("perspectiveImage.png", perspectiveImage);       return 0; }

  原始图像及其透视变换结果：

  

  

本文标签： 透视 perspective transformation

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