OpenCV Tutorials —— Affine Transformations

仿射变换

Affine Transformation

1. 1，It is any transformation that can be expressed in the form of a matrix multiplication (linear transformation) followed by a vector addition (translation).
2. 2，From the above, We can use an Affine Transformation to express:
3. 1. Rotations (linear transformation)   旋转
   2. Translations (vector addition)   平移
   3. Scale operations (linear transformation)  缩放

   you can see that, in essence, an Affine Transformation represents a relation between two images.

4. 3，The usual way to represent an Affine Transform is by using a matrix.

   

   Considering that we want to transform a 2D vector by using and , we can do it equivalently with:

   or

   

We mentioned that an Affine Transformation is basically a relation between two images. The information about this relation can come, roughly, in two ways:

1. 1，We know both and T and we also know that they are related. Then our job is to find

2，We know and . To obtain we only need to apply . Our information for may be explicit (i.e. have the 2-by-3 matrix) or it can come as a geometric relation between points.

通过参考点找到映射关系 M

对整幅图像应用 M，得到目标图像

warp_mat = getAffineTransform( srcTri, dstTri );

warpAffine( src, warp_dst, warp_mat, warp_dst.size() );

rot_mat = getRotationMatrix2D( center, angle, scale );

Code

#include "stdafx.h"

#include "opencv2/highgui/highgui.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include <iostream>
#include <stdio.h>

using namespace cv;
using namespace std;

/// Global variables
char* 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( "img2.jpg", 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 );	// 通过参考点对应关系获得仿射矩阵

	/// Apply the Affine Transform just found to the src image
	warpAffine( src, warp_dst, warp_mat, warp_dst.size() );	// 应用仿射变换

	/** 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 );	// 通过中心点，偏角，尺度来获得旋转矩阵

	/// Rotate the warped image
	warpAffine( warp_dst, warp_rotate_dst, rot_mat, warp_dst.size() );	// 应用仿射变换

	/// 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;
}