【OpenCV】透視變換 Perspective Transformation（續）

透視變換的原理和矩陣求解請參見前一篇《透視變換 Perspective Transformation》。在OpenCV中也實現了透視變換的公式求解和變換函數。

求解變換公式的函數：

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

輸入原始映像和變換之後的映像的對應4個點，便可以得到變換矩陣。之後用求解得到的矩陣輸入perspectiveTransform便可以對一組點進行變換：

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

注意這裡src和dst的輸入並不是映像，而是映像對應的座標。應用前一篇的例子，做個相反的變換：

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;}

得到變換之後的圖片：

注意這種將原圖變換到對應映像上的方式會有一些沒有被填充的點，也就是右圖中黑色的小點。解決這種問題一是用差值的方式，再一種比較簡單就是不用原圖的點變換後對應找新圖的座標，而是直接在新圖上找反向變換原圖的點。說起來有點繞口，具體見前一篇《透視變換 Perspective Transformation》的代碼應該就能懂啦。

除了getPerspectiveTransform()函數，OpenCV還提供了findHomography()的函數，不是用點來找，而是直接用透視平面來找變換公式。這個函數在特徵匹配的經典例子中有用到，也非常直觀：

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 Detectorint 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 matcherFlannBasedMatcher 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 keypointsfor( 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_2std::vector<Point2f> obj;std::vector<Point2f> scene;for( size_t i = 0; i < good_matches.size(); i++ ){//-- Get the keypoints from the good matchesobj.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 matchesimshow( "Good Matches & Object detection", img_matches );waitKey(0);return 0;}

代碼運行效果：

findHomography()函數直接通過兩個平面上相匹配的特徵點求出變換公式，之後代碼又對原圖的四個邊緣點進行變換，在右圖上畫出對應的矩形。這個圖也很好地解釋了所謂透視變換的“Viewing Plane”。

（轉載請註明作者和出處：http://blog.csdn.net/xiaowei_cqu 未經允許請勿用於商業用途）