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圖像幾何變換之透視變換

 百眼通 2017-10-29

1. 基本原理

  透視變換(Perspective Transformation)的本質(zhì)是將圖像投影到一個新的視平面,,其通用變換公式為:

  

  (u,,v)為原始圖像像素坐標,,(x=x’/w’,y=y’/w’)為變換之后的圖像像素坐標,。透視變換矩陣圖解如下:

  

  仿射變換(Affine Transformation)可以理解為透視變換的特殊形式,。透視變換的數(shù)學表達式為:

  

  所以,,給定透視變換對應(yīng)的四對像素點坐標,即可求得透視變換矩陣,;反之,,給定透視變換矩陣,即可對圖像或像素點坐標完成透視變換,,如下圖所示:

  

2. OpenCV透視變換函數(shù)

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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

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#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;
}

  原始圖像及其透視變換結(jié)果:

  

  

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