仿射变换及OpenCV实现

本文由 @lonelyrains出品，转载请注明出处。
文章链接： http://blog.csdn.net/lonelyrains/article/details/49847623

翻译自opencv官网，对原文有删改

仿射变换是什么

• 可以用矩阵相乘或者向量叠加到矩阵表示的所有操作
• 所以可以用来做的操作有：
  – 旋转
  – 平移（向量叠加）
  – 缩放
• 数学表达
  – 利用如下矩阵：

A=[a00a10a01a11]2×2，B=[b00b10]2×1

M=[AB]=[a00a10a01a11b00b10]2×3

对一个2D向量

X=[xy]

进行操作，可以列出如下等式：

T=A⋅[xy]+B

或者

T=M⋅[x,y,1]T

T=[a00x+a01y+b00a10x+a11y+b10]

如何得到仿射变换

• 由 T 的公式可知，一共有六个未知参数，所以需要3个2D点的映射关系，即一共六个一次方程，来决定平面。如下图：
  

用OpenCV实现

#include "opencv2/highgui/highgui.hpp"#include "opencv2/imgproc/imgproc.hpp"#include <iostream>#include <stdio.h>using namespace cv;using namespace std;/// Global variableschar* source_window = "Source image";char* warp_window = "Warp";char* warp_rotate_window = "Warp + Rotate";/** @function main */ int main( int argc, char** argv ) {   Point2f srcTri[3];   Point2f dstTri[3];   Mat rot_mat( 2, 3, CV_32FC1 );   Mat warp_mat( 2, 3, CV_32FC1 );   Mat src, warp_dst, warp_rotate_dst;   /// Load the image   src = imread( argv[1], 1 );   /// Set the dst image the same type and size as src   warp_dst = Mat::zeros( src.rows, src.cols, src.type() );   /// Set your 3 points to calculate the  Affine Transform   srcTri[0] = Point2f( 0,0 );   srcTri[1] = Point2f( src.cols - 1, 0 );   srcTri[2] = Point2f( 0, src.rows - 1 );   dstTri[0] = Point2f( src.cols*0.0, src.rows*0.33 );   dstTri[1] = Point2f( src.cols*0.85, src.rows*0.25 );   dstTri[2] = Point2f( src.cols*0.15, src.rows*0.7 );   /// Get the Affine Transform   warp_mat = getAffineTransform( srcTri, dstTri );   /// Apply the Affine Transform just found to the src image   warpAffine( src, warp_dst, warp_mat, warp_dst.size() );   /** Rotating the image after Warp */   /// Compute a rotation matrix with respect to the center of the image   Point center = Point( warp_dst.cols/2, warp_dst.rows/2 );   double angle = -50.0;   double scale = 0.6;   /// Get the rotation matrix with the specifications above   rot_mat = getRotationMatrix2D( center, angle, scale );   /// Rotate the warped image   warpAffine( warp_dst, warp_rotate_dst, rot_mat, warp_dst.size() );   /// Show what you got   namedWindow( source_window, CV_WINDOW_AUTOSIZE );   imshow( source_window, src );   namedWindow( warp_window, CV_WINDOW_AUTOSIZE );   imshow( warp_window, warp_dst );   namedWindow( warp_rotate_window, CV_WINDOW_AUTOSIZE );   imshow( warp_rotate_window, warp_rotate_dst );   /// Wait until user exits the program   waitKey(0);   return 0;  }

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