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[])
輸入原始圖像和變換之後的圖像的對應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的輸入並不是圖像，而是圖像對應的坐標。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圖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坐標，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。這個函數在特征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 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;
}
代碼運行效果：
findHomography()函數直接通過兩個平面上相匹配的特征點求出變換公式，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”。
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Ubuntu Linux下安裝OpenCV2.4.1所需包 http://www.linuxidc.com/Linux/2012-08/68184.htm
Ubuntu 12.04 安裝 OpenCV2.4.2 http://www.linuxidc.com/Linux/2012-09/70158.htm
CentOS下OpenCV無法讀取視頻文件 http://www.linuxidc.com/Linux/2011-07/39295.htm
Ubuntu 12.04下安裝OpenCV 2.4.5總結 http://www.linuxidc.com/Linux/2013-06/86704.htm
Ubuntu 10.04中安裝OpenCv2.1九步曲 http://www.linuxidc.com/Linux/2010-09/28678.htm
基於QT和OpenCV的人臉識別系統 http://www.linuxidc.com/Linux/2011-11/47806.htm
[翻譯]Ubuntu 14.04, 13.10 下安裝 OpenCV 2.4.9 http://www.linuxidc.com/Linux/2014-12/110045.htm
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OpenCV的詳細介紹：請點這裡
OpenCV的下載地址：請點這裡
