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OpenCV】透视变换 Perspective Transformation（续）

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【OpenCV】透视变换 Perspective Transformation（续）

分类： 【图像处理】 【编程语言】 2014-05-27 09:39 2776人阅读 评论(13) 收藏 举报

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：

 

[cpp] view plaincopyprint?在CODE上查看代码片派生到我的代码片
  1. Mat getPerspectiveTransform(const Point2f src[], const Point2f dst[])  
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：

 

 

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  1. void perspectiveTransform(InputArray src, OutputArray dst, InputArray m)  
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：

 

 

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  1. int main( )  
  2. {  
  3.     Mat img=imread("boy.png");  
  4.     int img_height = img.rows;  
  5.     int img_width = img.cols;  
  6.     vector<Point2f> corners(4);  
  7.     corners[0] = Point2f(0,0);  
  8.     corners[1] = Point2f(img_width-1,0);  
  9.     corners[2] = Point2f(0,img_height-1);  
  10.     corners[3] = Point2f(img_width-1,img_height-1);  
  11.     vector<Point2f> corners_trans(4);  
  12.     corners_trans[0] = Point2f(150,250);  
  13.     corners_trans[1] = Point2f(771,0);  
  14.     corners_trans[2] = Point2f(0,img_height-1);  
  15.     corners_trans[3] = Point2f(650,img_height-1);  
  16.   
  17.     Mat transform = getPerspectiveTransform(corners,corners_trans);  
  18.     cout<<transform<<endl;  
  19.     vector<Point2f> ponits, points_trans;  
  20.     for(int i=0;i<img_height;i++){  
  21.         for(int j=0;j<img_width;j++){  
  22.             ponits.push_back(Point2f(j,i));  
  23.         }  
  24.     }  
  25.   
  26.     perspectiveTransform( ponits, points_trans, transform);  
  27.     Mat img_trans = Mat::zeros(img_height,img_width,CV_8UC3);  
  28.     int count = 0;  
  29.     for(int i=0;i<img_height;i++){  
  30.         uchar* p = img.ptr<uchar>(i);  
  31.         for(int j=0;j<img_width;j++){  
  32.             int y = points_trans[count].y;  
  33.             int x = points_trans[count].x;  
  34.             uchar* t = img_trans.ptr<uchar>(y);  
  35.             t[x*3]  = p[j*3];  
  36.             t[x*3+1]  = p[j*3+1];  
  37.             t[x*3+2]  = p[j*3+2];  
  38.             count++;  
  39.         }  
  40.     }  
  41.     imwrite("boy_trans.png",img_trans);  
  42.   
  43.     return 0;  
  44. }  
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：

 

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：

 

[cpp] view plaincopyprint?在CODE上查看代码片派生到我的代码片
  1. int main( int argc, char** argv )  
  2. {  
  3.     Mat img_object = imread( argv[1], IMREAD_GRAYSCALE );  
  4.     Mat img_scene = imread( argv[2], IMREAD_GRAYSCALE );  
  5.     if( !img_object.data || !img_scene.data )  
  6.     { std::cout<< " --(!) Error reading images " << std::endl; return -1; }  
  7.   
  8.     //-- Step 1: Detect the keypoints using SURF Detector   
  9.     int minHessian = 400;  
  10.     SurfFeatureDetector detector( minHessian );  
  11.     std::vector<KeyPoint> keypoints_object, keypoints_scene;  
  12.     detector.detect( img_object, keypoints_object );  
  13.     detector.detect( img_scene, keypoints_scene );  
  14.   
  15.     //-- Step 2: Calculate descriptors (feature vectors)   
  16.     SurfDescriptorExtractor extractor;  
  17.     Mat descriptors_object, descriptors_scene;  
  18.     extractor.compute( img_object, keypoints_object, descriptors_object );  
  19.     extractor.compute( img_scene, keypoints_scene, descriptors_scene );  
  20.   
  21.     //-- Step 3: Matching descriptor vectors using FLANN matcher   
  22.     FlannBasedMatcher matcher;  
  23.     std::vector< DMatch > matches;  
  24.     matcher.match( descriptors_object, descriptors_scene, matches );  
  25.     double max_dist = 0; double min_dist = 100;  
  26.   
  27.     //-- Quick calculation of max and min distances between keypoints   
  28.     for( int i = 0; i < descriptors_object.rows; i++ )  
  29.     { double dist = matches[i].distance;  
  30.     if( dist < min_dist ) min_dist = dist;  
  31.     if( dist > max_dist ) max_dist = dist;  
  32.     }  
  33.   
  34.     printf("-- Max dist : %f \n", max_dist );  
  35.     printf("-- Min dist : %f \n", min_dist );  
  36.   
  37.     //-- Draw only "good" matches (i.e. whose distance is less than 3*min_dist )   
  38.     std::vector< DMatch > good_matches;  
  39.   
  40.     for( int i = 0; i < descriptors_object.rows; i++ )  
  41.     { if( matches[i].distance < 3*min_dist )  
  42.     { good_matches.push_back( matches[i]); }  
  43.     }  
  44.   
  45.     Mat img_matches;  
  46.     drawMatches( img_object, keypoints_object, img_scene, keypoints_scene,  
  47.         good_matches, img_matches, Scalar::all(-1), Scalar::all(-1),  
  48.         vector<char>(), DrawMatchesFlags::NOT_DRAW_SINGLE_POINTS );  
  49.   
  50.     //-- Localize the object from img_1 in img_2   
  51.     std::vector<Point2f> obj;  
  52.     std::vector<Point2f> scene;  
  53.   
  54.     for( size_t i = 0; i < good_matches.size(); i++ )  
  55.     {  
  56.         //-- Get the keypoints from the good matches   
  57.         obj.push_back( keypoints_object[ good_matches[i].queryIdx ].pt );  
  58.         scene.push_back( keypoints_scene[ good_matches[i].trainIdx ].pt );  
  59.     }  
  60.   
  61.     Mat H = findHomography( obj, scene, RANSAC );  
  62.   
  63.     //-- Get the corners from the image_1 ( the object to be "detected" )   
  64.     std::vector<Point2f> obj_corners(4);  
  65.     obj_corners[0] = Point(0,0); obj_corners[1] = Point( img_object.cols, 0 );  
  66.     obj_corners[2] = Point( img_object.cols, img_object.rows ); obj_corners[3] = Point( 0, img_object.rows );  
  67.     std::vector<Point2f> scene_corners(4);  
  68.     perspectiveTransform( obj_corners, scene_corners, H);  
  69.     //-- Draw lines between the corners (the mapped object in the scene - image_2 )   
  70.     Point2f offset( (float)img_object.cols, 0);  
  71.     line( img_matches, scene_corners[0] + offset, scene_corners[1] + offset, Scalar(0, 255, 0), 4 );  
  72.     line( img_matches, scene_corners[1] + offset, scene_corners[2] + offset, Scalar( 0, 255, 0), 4 );  
  73.     line( img_matches, scene_corners[2] + offset, scene_corners[3] + offset, Scalar( 0, 255, 0), 4 );  
  74.     line( img_matches, scene_corners[3] + offset, scene_corners[0] + offset, Scalar( 0, 255, 0), 4 );  
  75.   
  76.     //-- Show detected matches   
  77.     imshow( "Good Matches & Object detection", img_matches );  
  78.     waitKey(0);  
  79.     return 0;  
  80. }  
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：

 

 

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”。


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