透视变换的原理和矩阵求解请参见前一篇《透视变换 Perspective Transformation》。在OpenCV中也实现了透视变换的公式求解和变换函数。

求解变换公式的函数：

Mat getPerspectiveTransform(const Point2f src[], const Point2f dst[])

void perspectiveTransform(InputArray src, OutputArray dst, InputArray m)

int main( )
{
	Mat img=imread("boy.png");
	int img_height = img.rows;
	int img_width = img.cols;
	vector<Point2f> corners(4);
	corners[0] = Point2f(0,0);
	corners[1] = Point2f(img_width-1,0);
	corners[2] = Point2f(0,img_height-1);
	corners[3] = Point2f(img_width-1,img_height-1);
	vector<Point2f> corners_trans(4);
	corners_trans[0] = Point2f(150,250);
	corners_trans[1] = Point2f(771,0);
	corners_trans[2] = Point2f(0,img_height-1);
	corners_trans[3] = Point2f(650,img_height-1);

	Mat transform = getPerspectiveTransform(corners,corners_trans);
	cout<<transform<<endl;
	vector<Point2f> ponits, points_trans;
	for(int i=0;i<img_height;i++){
		for(int j=0;j<img_width;j++){
			ponits.push_back(Point2f(j,i));
		}
	}

	perspectiveTransform( ponits, points_trans, transform);
	Mat img_trans = Mat::zeros(img_height,img_width,CV_8UC3);
	int count = 0;
	for(int i=0;i<img_height;i++){
		uchar* p = img.ptr<uchar>(i);
		for(int j=0;j<img_width;j++){
			int y = points_trans[count].y;
			int x = points_trans[count].x;
			uchar* t = img_trans.ptr<uchar>(y);
			t[x*3]  = p[j*3];
			t[x*3+1]  = p[j*3+1];
			t[x*3+2]  = p[j*3+2];
			count++;
		}
	}
	imwrite("boy_trans.png",img_trans);

	return 0;
}

注意这种将原图变换到对应图像上的方式会有一些没有被填充的点，也就是右图中黑色的小点。解决这种问题一是用差值的方式，再一种比较简单就是不用原图的点变换后对应找新图的坐标，而是直接在新图上找反向变换原图的点。说起来有点绕口，具体见前一篇《透视变换 Perspective Transformation》的代码应该就能懂啦。

除了getPerspectiveTransform()函数，OpenCV还提供了findHomography()的函数，不是用点来找，而是直接用透视平面来找变换公式。这个函数在特征匹配的经典例子中有用到，也非常直观：

int main( int argc, char** argv )
{
	Mat img_object = imread( argv[1], IMREAD_GRAYSCALE );
	Mat img_scene = imread( argv[2], IMREAD_GRAYSCALE );
	if( !img_object.data || !img_scene.data )
	{ std::cout<< " --(!) Error reading images " << std::endl; return -1; }

	//-- Step 1: Detect the keypoints using SURF Detector
	int minHessian = 400;
	SurfFeatureDetector detector( minHessian );
	std::vector<KeyPoint> keypoints_object, keypoints_scene;
	detector.detect( img_object, keypoints_object );
	detector.detect( img_scene, keypoints_scene );

	//-- Step 2: Calculate descriptors (feature vectors)
	SurfDescriptorExtractor extractor;
	Mat descriptors_object, descriptors_scene;
	extractor.compute( img_object, keypoints_object, descriptors_object );
	extractor.compute( img_scene, keypoints_scene, descriptors_scene );

	//-- Step 3: Matching descriptor vectors using FLANN matcher
	FlannBasedMatcher matcher;
	std::vector< DMatch > matches;
	matcher.match( descriptors_object, descriptors_scene, matches );
	double max_dist = 0; double min_dist = 100;

	//-- Quick calculation of max and min distances between keypoints
	for( int i = 0; i < descriptors_object.rows; i++ )
	{ double dist = matches[i].distance;
	if( dist < min_dist ) min_dist = dist;
	if( dist > max_dist ) max_dist = dist;
	}

	printf("-- Max dist : %f \n", max_dist );
	printf("-- Min dist : %f \n", min_dist );

	//-- Draw only "good" matches (i.e. whose distance is less than 3*min_dist )
	std::vector< DMatch > good_matches;

	for( int i = 0; i < descriptors_object.rows; i++ )
	{ if( matches[i].distance < 3*min_dist )
	{ good_matches.push_back( matches[i]); }
	}

	Mat img_matches;
	drawMatches( img_object, keypoints_object, img_scene, keypoints_scene,
		good_matches, img_matches, Scalar::all(-1), Scalar::all(-1),
		vector<char>(), DrawMatchesFlags::NOT_DRAW_SINGLE_POINTS );

	//-- Localize the object from img_1 in img_2
	std::vector<Point2f> obj;
	std::vector<Point2f> scene;

	for( size_t i = 0; i < good_matches.size(); i++ )
	{
		//-- Get the keypoints from the good matches
		obj.push_back( keypoints_object[ good_matches[i].queryIdx ].pt );
		scene.push_back( keypoints_scene[ good_matches[i].trainIdx ].pt );
	}

	Mat H = findHomography( obj, scene, RANSAC );

	//-- Get the corners from the image_1 ( the object to be "detected" )
	std::vector<Point2f> obj_corners(4);
	obj_corners[0] = Point(0,0); obj_corners[1] = Point( img_object.cols, 0 );
	obj_corners[2] = Point( img_object.cols, img_object.rows ); obj_corners[3] = Point( 0, img_object.rows );
	std::vector<Point2f> scene_corners(4);
	perspectiveTransform( obj_corners, scene_corners, H);
	//-- Draw lines between the corners (the mapped object in the scene - image_2 )
	Point2f offset( (float)img_object.cols, 0);
	line( img_matches, scene_corners[0] + offset, scene_corners[1] + offset, Scalar(0, 255, 0), 4 );
	line( img_matches, scene_corners[1] + offset, scene_corners[2] + offset, Scalar( 0, 255, 0), 4 );
	line( img_matches, scene_corners[2] + offset, scene_corners[3] + offset, Scalar( 0, 255, 0), 4 );
	line( img_matches, scene_corners[3] + offset, scene_corners[0] + offset, Scalar( 0, 255, 0), 4 );

	//-- Show detected matches
	imshow( "Good Matches & Object detection", img_matches );
	waitKey(0);
	return 0;
}

findHomography()函数直接通过两个平面上相匹配的特征点求出变换公式，之后代码又对原图的四个边缘点进行变换，在右图上画出对应的矩形。这个图也很好地解释了所谓透视变换的“Viewing Plane”。

（转载请注明作者和出处：http://blog.csdn.net/xiaowei_cqu 未经允许请勿用于商业用途）