【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”。

（转载请注明作者和出处：http://blog.csdn.net/xiaowei_cqu 未经允许请勿用于商业用途）

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”。

（转载请注明作者和出处：http://blog.csdn.net/xiaowei_cqu 未经允许请勿用于商业用途）