【OpenCV】透视变换 Perspective Transformation

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[])

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：

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;



}

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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