【OpenCV】透视变换 Perspective Transformation(续)


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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