如何从旋转角度计算OpenCV的透视变换？
我想从旋转角度和到物体的距离开始计算透视变换（warpPerspective函数的矩阵）。
怎么做？
我在OE上找到了代码。示例程序如下：
#include <opencv2/objdetect/objdetect.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <iostream>
#include <math.h>
using namespace std;
using namespace cv;
Mat frame;
int alpha_int;
int dist_int;
int f_int;
double w;
double h;
double alpha;
double dist;
double f;
void redraw() {
alpha = (double)alpha_int/1000.;
//dist = 1./(dist_int+1);
//dist = dist_int+1;
dist = dist_int-50;
f = f_int+1;
cout << "alpha = " << alpha << endl;
cout << "dist = " << dist << endl;
cout << "f = " << f << endl;
// Projection 2D -> 3D matrix
Mat A1 = (Mat_<double>(4,3) <<
1, 0, -w/2,
0, 1, -h/2,
0, 0, 1,
0, 0, 1);
// Rotation matrices around the X axis
Mat R = (Mat_<double>(4, 4) <<
1, 0, 0, 0,
0, cos(alpha), -sin(alpha), 0,
0, sin(alpha), cos(alpha), 0,
0, 0, 0, 1);
// Translation matrix on the Z axis
Mat T = (Mat_<double>(4, 4) <<
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, dist,
0, 0, 0, 1);
// Camera Intrisecs matrix 3D -> 2D
Mat A2 = (Mat_<double>(3,4) <<
f, 0, w/2, 0,
0, f, h/2, 0,
0, 0, 1, 0);
Mat m = A2 * (T * (R * A1));
cout << "R=" << endl << R << endl;
cout << "A1=" << endl << A1 << endl;
cout << "R*A1=" << endl << (R*A1) << endl;
cout << "T=" << endl << T << endl;
cout << "T * (R * A1)=" << endl << (T * (R * A1)) << endl;
cout << "A2=" << endl << A2 << endl;
cout << "A2 * (T * (R * A1))=" << endl << (A2 * (T * (R * A1))) << endl;
cout << "m=" << endl << m << endl;
Mat frame1;
warpPerspective( frame, frame1, m, frame.size(), INTER_CUBIC | WARP_INVERSE_MAP);
imshow("Frame", frame);
imshow("Frame1", frame1);
}
void callback(int, void* ) {
redraw();
}
void main() {
frame = imread("FruitSample_small.png", CV_LOAD_IMAGE_COLOR);
imshow("Frame", frame);
w = frame.size().width;
h = frame.size().height;
createTrackbar("alpha", "Frame", &alpha_int, 100, &callback);
dist_int = 50;
createTrackbar("dist", "Frame", &dist_int, 100, &callback);
createTrackbar("f", "Frame", &f_int, 100, &callback);
redraw();
waitKey(-1);
}
但不幸的是，这种转变确实很奇怪
为什么呢？ alpha>0时上面的另一半图像是什么？以及如何围绕其他轴旋转？为什么dist如此奇怪？
3 个答案:
答案 0 :(得分：38)
我有时间思考数学和代码。我是在一两年前做过的。我甚至在美丽的乳胶中排版它。
我有意设计了我的解决方案，这样无论提供什么样的旋转角度，整个输入图像都包含在输出框内，居中，否则为黑色。
我的warpImage函数的参数是所有3个轴的旋转角度，比例因子和垂直视野角度。该函数在输出图像中输出扭曲矩阵，输出图像和源图像的角。
数学（代码，见下文）
LaTeX源代码是here。
代码（数学，见上）
这是一个扭曲相机的测试应用程序
#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <math.h>
using namespace cv;
using namespace std;
static double rad2Deg(double rad){return rad*(180/M_PI);}//Convert radians to degrees
static double deg2Rad(double deg){return deg*(M_PI/180);}//Convert degrees to radians
void warpMatrix(Size sz,
double theta,
double phi,
double gamma,
double scale,
double fovy,
Mat& M,
vector<Point2f>* corners){
double st=sin(deg2Rad(theta));
double ct=cos(deg2Rad(theta));
double sp=sin(deg2Rad(phi));
double cp=cos(deg2Rad(phi));
double sg=sin(deg2Rad(gamma));
double cg=cos(deg2Rad(gamma));
double halfFovy=fovy*0.5;
double d=hypot(sz.width,sz.height);
double sideLength=scale*d/cos(deg2Rad(halfFovy));
double h=d/(2.0*sin(deg2Rad(halfFovy)));
double n=h-(d/2.0);
double f=h+(d/2.0);
Mat F=Mat(4,4,CV_64FC1);//Allocate 4x4 transformation matrix F
Mat Rtheta=Mat::eye(4,4,CV_64FC1);//Allocate 4x4 rotation matrix around Z-axis by theta degrees
Mat Rphi=Mat::eye(4,4,CV_64FC1);//Allocate 4x4 rotation matrix around X-axis by phi degrees
Mat Rgamma=Mat::eye(4,4,CV_64FC1);//Allocate 4x4 rotation matrix around Y-axis by gamma degrees
Mat T=Mat::eye(4,4,CV_64FC1);//Allocate 4x4 translation matrix along Z-axis by -h units
Mat P=Mat::zeros(4,4,CV_64FC1);//Allocate 4x4 projection matrix
//Rtheta
Rtheta.at<double>(0,0)=Rtheta.at<double>(1,1)=ct;
Rtheta.at<double>(0,1)=-st;Rtheta.at<double>(1,0)=st;
//Rphi
Rphi.at<double>(1,1)=Rphi.at<double>(2,2)=cp;
Rphi.at<double>(1,2)=-sp;Rphi.at<double>(2,1)=sp;
//Rgamma
Rgamma.at<double>(0,0)=Rgamma.at<double>(2,2)=cg;
Rgamma.at<double>(0,2)=-sg;Rgamma.at<double>(2,0)=sg;
//T
T.at<double>(2,3)=-h;
//P
P.at<double>(0,0)=P.at<double>(1,1)=1.0/tan(deg2Rad(halfFovy));
P.at<double>(2,2)=-(f+n)/(f-n);
P.at<double>(2,3)=-(2.0*f*n)/(f-n);
P.at<double>(3,2)=-1.0;
//Compose transformations
F=P*T*Rphi*Rtheta*Rgamma;//Matrix-multiply to produce master matrix
//Transform 4x4 points
double ptsIn [4*3];
double ptsOut[4*3];
double halfW=sz.width/2, halfH=sz.height/2;
ptsIn[0]=-halfW;ptsIn[ 1]= halfH;
ptsIn[3]= halfW;ptsIn[ 4]= halfH;
ptsIn[6]= halfW;ptsIn[ 7]=-halfH;
ptsIn[9]=-halfW;ptsIn[10]=-halfH;
ptsIn[2]=ptsIn[5]=ptsIn[8]=ptsIn[11]=0;//Set Z component to zero for all 4 components
Mat ptsInMat(1,4,CV_64FC3,ptsIn);
Mat ptsOutMat(1,4,CV_64FC3,ptsOut);
perspectiveTransform(ptsInMat,ptsOutMat,F);//Transform points
//Get 3x3 transform and warp image
Point2f ptsInPt2f[4];
Point2f ptsOutPt2f[4];
for(int i=0;i<4;i++){
Point2f ptIn (ptsIn [i*3+0], ptsIn [i*3+1]);
Point2f ptOut(ptsOut[i*3+0], ptsOut[i*3+1]);
ptsInPt2f[i] = ptIn+Point2f(halfW,halfH);
ptsOutPt2f[i] = (ptOut+Point2f(1,1))*(sideLength*0.5);
}
M=getPerspectiveTransform(ptsInPt2f,ptsOutPt2f);
//Load corners vector
if(corners){
corners->clear();
corners->push_back(ptsOutPt2f[0]);//Push Top Left corner
corners->push_back(ptsOutPt2f[1]);//Push Top Right corner
corners->push_back(ptsOutPt2f[2]);//Push Bottom Right corner
corners->push_back(ptsOutPt2f[3]);//Push Bottom Left corner
}
}
void warpImage(const Mat &src,
double theta,
double phi,
double gamma,
double scale,
double fovy,
Mat& dst,
Mat& M,
vector<Point2f> &corners){
double halfFovy=fovy*0.5;
double d=hypot(src.cols,src.rows);
double sideLength=scale*d/cos(deg2Rad(halfFovy));
warpMatrix(src.size(),theta,phi,gamma, scale,fovy,M,&corners);//Compute warp matrix
warpPerspective(src,dst,M,Size(sideLength,sideLength));//Do actual image warp
}
int main(void){
int c = 0;
Mat m, disp, warp;
vector<Point2f> corners;
VideoCapture cap(0);
while(c != 033 && cap.isOpened()){
cap >> m;
warpImage(m, 5, 50, 0, 1, 30, disp, warp, corners);
imshow("Disp", disp);
c = waitKey(1);
}
}
答案 1 :(得分：1)
我遇到了类似的问题。问题证明是在反投影到3D坐标后，由于我们没有摄像机的内在参数，我们使用一些猜测值，甚至是矩阵A1中的1。在旋转期间，这可能导致图像平面位于错误的一侧＆＃34;图像平面，具有负深度值（z < 0）。投影后，当你用z划分你的坐标时，你会得到一些像你所展示的那样奇怪的东西。
因此，解决方案最终将focallength缩放为与图像大小相关的东西。
假设您的图片具有尺寸(H, W)，请将focallength设置为H/3。
在这种情况下，您的A1将是
[H/3, 0, W/2]
[0, H/3, H/2]
[0, 0, 1]
答案 2 :(得分：0)
这是流行的C ++示例代码答案的Java转换。除了说这似乎行得通之外，我没有办法知道此Java代码，原始C ++代码或基本方程式的准确性，也没有任何有关调整方程式的评论。这是出于实验目的，与高中生一起进行图像处理。
package app;
import java.util.Arrays;
import java.util.stream.Collectors;
import org.opencv.highgui.HighGui;
import org.opencv.core.Core;
import org.opencv.core.CvType;
import org.opencv.core.Size;
import org.opencv.imgcodecs.Imgcodecs;
import org.opencv.core.Point;
import org.opencv.core.Mat;
import org.opencv.core.MatOfPoint2f;
import org.opencv.imgproc.Imgproc;
import org.opencv.videoio.VideoCapture;
public class App {
static {
System.loadLibrary(Core.NATIVE_LIBRARY_NAME); // Load the native library.
}
static void warpMatrix(Size sz,
double theta,
double phi,
double gamma,
double scale,
double fovy,
Mat M,
MatOfPoint2f corners) {
double st=Math.sin(Math.toRadians(theta));
double ct=Math.cos(Math.toRadians(theta));
double sp=Math.sin(Math.toRadians(phi));
double cp=Math.cos(Math.toRadians(phi));
double sg=Math.sin(Math.toRadians(gamma));
double cg=Math.cos(Math.toRadians(gamma));
double halfFovy=fovy*0.5;
double d=Math.hypot(sz.width,sz.height);
double sideLength=scale*d/Math.cos(Math.toRadians(halfFovy));
double h=d/(2.0*Math.sin(Math.toRadians(halfFovy)));
double n=h-(d/2.0);
double f=h+(d/2.0);
Mat F=new Mat(4,4, CvType.CV_64FC1);//Allocate 4x4 transformation matrix F
Mat Rtheta=Mat.eye(4,4, CvType.CV_64FC1);//Allocate 4x4 rotation matrix around Z-axis by theta degrees
Mat Rphi=Mat.eye(4,4, CvType.CV_64FC1);//Allocate 4x4 rotation matrix around X-axis by phi degrees
Mat Rgamma=Mat.eye(4,4, CvType.CV_64FC1);//Allocate 4x4 rotation matrix around Y-axis by gamma degrees
Mat T=Mat.eye(4,4, CvType.CV_64FC1);//Allocate 4x4 translation matrix along Z-axis by -h units
Mat P=Mat.zeros(4,4, CvType.CV_64FC1);//Allocate 4x4 projection matrix
// zeros instead of eye as in github manisoftwartist/perspectiveproj
//Rtheta Z
Rtheta.put(0,0, ct);
Rtheta.put(1,1, ct);
Rtheta.put(0,1, -st);
Rtheta.put(1,0, st);
//Rphi X
Rphi.put(1,1, cp);
Rphi.put(2,2, cp);
Rphi.put(1,2, -sp);
Rphi.put(2,1, sp);
//Rgamma Y
Rgamma.put(0,0, cg);
Rgamma.put(2,2, cg);
Rgamma.put(0,2, -sg); // sign reversed? Math different convention than computer graphics according to Wikipedia
Rgamma.put(2,0, sg);
//T
T.put(2,3, -h);
//P Perspective Matrix (see also in computer vision a camera matrix or (camera) projection matrix is a 3x4 matrix which describes the mapping of a pinhole camera from 3D points in the world to 2D points in an image.)
P.put(0,0, 1.0/Math.tan(Math.toRadians(halfFovy)));
P.put(1,1, 1.0/Math.tan(Math.toRadians(halfFovy)));
P.put(2,2, -(f+n)/(f-n));
P.put(2,3, -(2.0*f*n)/(f-n));
P.put(3,2, -1.0);
System.out.println("P " + P.dump());
System.out.println("T " + T.dump());
System.out.println("Rphi " + Rphi.dump());
System.out.println("Rtheta " + Rtheta.dump());
System.out.println("Rgamma " + Rgamma.dump());
//Compose transformations
//F=P*T*Rphi*Rtheta*Rgamma;//Matrix-multiply to produce master matrix
//gemm(Mat src1, Mat src2, double alpha, Mat src3, double beta, Mat dst)
//dst = alpha*src1.t()*src2 + beta*src3.t(); // w or w/o the .t() transpose
// D=α∗AB+β∗C
Mat F1 = new Mat();
Mat F2 = new Mat();
Mat F3 = new Mat();
Core.gemm(P, T, 1, new Mat(), 0, F1);
Core.gemm(F1, Rphi, 1, new Mat(), 0, F2);
Core.gemm(F2, Rtheta, 1, new Mat(), 0, F3);
Core.gemm(F3, Rgamma, 1, new Mat(), 0, F);
P.release();
T.release();
Rphi.release();
Rtheta.release();
Rgamma.release();
F1.release();
F2.release();
F3.release();
//Transform 4x4 points
double[] ptsIn = new double[4*3];
double[] ptsOut = new double[4*3];
double halfW=sz.width/2, halfH=sz.height/2;
ptsIn[0]=-halfW;ptsIn[ 1]= halfH;
ptsIn[3]= halfW;ptsIn[ 4]= halfH;
ptsIn[6]= halfW;ptsIn[ 7]=-halfH;
ptsIn[9]=-halfW;ptsIn[10]=-halfH;
ptsIn[2]=ptsIn[5]=ptsIn[8]=ptsIn[11]=0;//Set Z component to zero for all 4 components
Mat ptsInMat = new Mat(1,4,CvType.CV_64FC3);
ptsInMat.put(0,0, ptsIn);
Mat ptsOutMat = new Mat(1,4,CvType.CV_64FC3);
System.out.println("ptsInMat " + ptsInMat + " " + ptsInMat.dump());
System.out.println("F " + F + " " + F.dump());
Core.perspectiveTransform(ptsInMat, ptsOutMat, F);//Transform points
System.out.println("ptsOutMat " + ptsOutMat + " " + ptsOutMat.dump());
ptsInMat.release();
F.release();
ptsOutMat.get(0, 0, ptsOut);
ptsOutMat.release();
System.out.println(toString(ptsOut));
System.out.println(halfW + " " + halfH);
//Get 3x3 transform and warp image
Point[] ptsInPt2f = new Point[4];
Point[] ptsOutPt2f = new Point[4];
for(int i=0;i<4;i++){
ptsInPt2f[i] = new Point(0, 0);
ptsOutPt2f[i] = new Point(0, 0);
System.out.println(i);
System.out.println("points " + ptsIn [i*3+0] + " " + ptsIn [i*3+1]);
Point ptIn = new Point(ptsIn [i*3+0], ptsIn [i*3+1]);
Point ptOut = new Point(ptsOut[i*3+0], ptsOut[i*3+1]);
ptsInPt2f[i].x = ptIn.x+halfW;
ptsInPt2f[i].y = ptIn.y+halfH;
ptsOutPt2f[i].x = (ptOut.x+1) * sideLength*0.5;
ptsOutPt2f[i].y = (ptOut.y+1) * sideLength*0.5;
System.out.println("ptsOutPt2f " + ptsOutPt2f[i]);
}
Mat ptsInPt2fTemp = Mat.zeros(4,1,CvType.CV_32FC2);
ptsInPt2fTemp.put(0, 0,
ptsInPt2f[0].x,ptsInPt2f[0].y,
ptsInPt2f[1].x,ptsInPt2f[1].y,
ptsInPt2f[2].x,ptsInPt2f[2].y,
ptsInPt2f[3].x,ptsInPt2f[3].y);
Mat ptsOutPt2fTemp = Mat.zeros(4,1,CvType.CV_32FC2);
ptsOutPt2fTemp.put(0, 0,
ptsOutPt2f[0].x,ptsOutPt2f[0].y,
ptsOutPt2f[1].x,ptsOutPt2f[1].y,
ptsOutPt2f[2].x,ptsOutPt2f[2].y,
ptsOutPt2f[3].x,ptsOutPt2f[3].y);
System.out.println("ptsInPt2fTemp " + ptsInPt2fTemp.dump());
System.out.println("ptsOutPt2fTemp " + ptsOutPt2fTemp.dump());
Mat warp=Imgproc.getPerspectiveTransform(ptsInPt2fTemp, ptsOutPt2fTemp);
warp.copyTo(M);
ptsInPt2fTemp.release();
warp.release();
//Load corners vector
if(corners != null)
{
corners.put(0,0, ptsOutPt2f[0].x, ptsOutPt2f[0].y//Push Top Left corner
, ptsOutPt2f[1].x, ptsOutPt2f[1].y//Push Top Right corner
, ptsOutPt2f[2].x, ptsOutPt2f[2].y//Push Bottom Right corner
, ptsOutPt2f[3].x, ptsOutPt2f[3].y);//Push Bottom Left corner
}
ptsOutPt2fTemp.release();
System.out.println("corners " + corners + " " + corners.dump());
}
static void warpImage(Mat src,
double theta,
double phi,
double gamma,
double scale,
double fovy,
Mat dst,
Mat M,
MatOfPoint2f corners){
double halfFovy=fovy*0.5;
double d=Math.hypot(src.cols(),src.rows());
double sideLength=scale*d/Math.cos(Math.toRadians(halfFovy));
System.out.println("d " + d + ", sideLength " + sideLength);
warpMatrix(src.size(), theta, phi, gamma, scale, fovy, M, corners);//Compute warp matrix
System.out.println("M " + M + " " + M.dump());
Imgproc.warpPerspective(src, dst, M, new Size(sideLength,sideLength));//Do actual image warp
}
public static void main(String[] args)
{
int c = 0;
Mat m = new Mat();
Mat disp = new Mat();
Mat warp = new Mat();
MatOfPoint2f corners = new MatOfPoint2f(new Point(0,0),new Point(0,0),new Point(0,0),new Point(0,0));
String filename = "lena.jpg";
m = Imgcodecs.imread(filename, Imgcodecs.IMREAD_COLOR);
if (m.empty()) {
System.out.println("Error opening image");
System.exit(-1);
}
double scale = 1.;
double fovy = 53.;
double halfFovy=fovy*0.5;
VideoCapture cap;
cap = new VideoCapture();
cap.open(0);
cap.read(m);
warpImage(m, 5, 50, 0, 1, 30, disp, warp, corners); // fovy = rad2deg(arctan2(640,480)) = 53 ??
while(true) {
cap.read(m);
double d=Math.hypot(m.cols(),m.rows());
double sideLength=scale*d/Math.cos(Math.toRadians(halfFovy));
Imgproc.warpPerspective(m, disp, warp, new Size(sideLength,sideLength));//Do actual image warp
HighGui.imshow("Disp", disp);
HighGui.imshow("Orig", m);
c = HighGui.waitKey(25);
if (c != -1) break;
}
m.release();
disp.release();
warp.release();
corners.release();
System.exit(0);
}
static String toString(double[] array) {
return Arrays.stream(array)
.mapToObj(i -> String.format("%5.2f", i))
.collect(Collectors.joining(", ", "[", "]"));
//.collect(Collectors.joining("|", "|", "|"));
}
}
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