【OpenCV】透视变换 Perspective Transformation（续）

「爱情、让人受尽委屈。」 2022-08-27 08:48 179阅读 0赞

透视变换的原理和矩阵求解请参见前一篇[《透视变换 Perspective Transformation》][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[])

输入原始图像和变换之后的图像的对应4个点，便可以得到变换矩阵。之后用求解得到的矩阵输入perspectiveTransform便可以对一组点进行变换：

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

注意这里src和dst的输入并不是图像，而是图像对应的坐标。应用前一篇的例子，做个相反的变换：

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;
    }

得到变换之后的图片：

![20140521152755093][]

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》][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;
    }

代码运行效果：

![20140521153450140][]

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][http_blog.csdn.net_xiaowei_cqu] 未经允许请勿用于商业用途） ###

[Perspective Transformation]: http://blog.csdn.net/xiaowei_cqu/article/details/26471527
[20140521152755093]: /images/20220824/629ece5830f54ff6a40e95fd679ba536.png
[20140521153450140]: /images/20220824/205e9c67f3d64552b889231951e667c9.png
[http_blog.csdn.net_xiaowei_cqu]: http://blog.csdn.net/xiaowei_cqu