ViSP学习笔记（二十四）：计算两幅图像之间的单应性矩阵

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我是靠谱客的博主会撒娇西牛，最近开发中收集的这篇文章主要介绍ViSP学习笔记（二十四）：计算两幅图像之间的单应性矩阵，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

开发环境：Ubuntu 18.04 LTS + ROS Melodic + ViSP 3.3.1
文章内容主要参考ViSP官方教学文档：https://visp-doc.inria.fr/doxygen/visp-daily/tutorial_mainpage.html

本文主要介绍了如何使用ViSP计算两幅图像之间的单应性矩阵，在已知同一个物体的特征点在两个相机中的图像坐标后，就能够计算两个相机坐标之间的单应性矩阵。如果能够保证两幅图像中的特征点是一一对应匹配的可以采用DLT或HLM算法进行计算。本文主要参考了computer-vision中的tutorial-homography-from-points.cpp例程。首先要获取这个例程文件并编译它

svn export https://github.com/lagadic/visp.git/trunk/tutorial/computer-vision
cd computer-vision/
mkdir build
cd build 
cmake .. -DCMAKE_BUILD_TYPE=Release -DVISP_DIR=$VISP_WS/visp-build
make

执行例程，查看效果

./tutorial-homography-from-points

首先会输出两个相机坐标系之间的单应性矩阵（分别使用DLT和HLM两种算法）

Estimated homography using DLT:
0.9540353246  -0.0911338709  0.5155021269
0.04848747565  0.9605117258  -0.03003809211
-0.3066184621  -0.03490122576  1
Estimated homography using HLM:
0.9540353246  -0.0911338709  0.5155021269
0.04848747565  0.9605117258  -0.03003809211
-0.3066184621  -0.03490122576  1

然后将单应性矩阵拆分成旋转矩阵和平移矩阵

Estimated displacement:
 atb: 0.2016519874  -0.1008259937  0.1008259937
 athetaub: -3 20 5 
 n: 0.2588190451  -7.938094626e-15  0.9659258263

最后给出特征点的输入坐标和估计坐标结果

Ground truth: Point 3 in pixels in frame b: 377.9450564, 193.9928711
Ground truth: Point 3 in pixels in frame a: 353.8501593, 486.1851856
Estimation from homography: Point 3 in pixels in frame a: 353.8501593, 486.1851856

下面介绍一下代码实现过程

#include <visp3/vision/vpHomography.h>
#include <visp3/core/vpMeterPixelConversion.h>
int main()
{
  double L = 0.1;
  std::vector<vpPoint> oP;//新建目标空间坐标容器
  //初始化目标特征点的空间坐标
  oP.push_back(vpPoint(-L, -L, 0));
  oP.push_back(vpPoint(2 * L, -L, 0));
  oP.push_back(vpPoint(L, 3 * L, 0));
  oP.push_back(vpPoint(-L, 4 * L, 0));
  vpHomogeneousMatrix bMo(0.1, 0, 1, 0, vpMath::rad(15), 0);//设置目标坐标系和相机b坐标系之间的齐次变换矩阵
  vpHomogeneousMatrix aMb(0.2, -0.1, 0.1, vpMath::rad(-3), vpMath::rad(20), vpMath::rad(5));//设置相机a坐标系和相机b坐标系之间的齐次变换矩阵
  vpHomogeneousMatrix aMo = aMb * bMo;//计算目标坐标系和相机a坐标系之间的齐次变换矩阵
  std::vector<vpPoint> aP(4), bP(4);//新建两个相机的图像坐标容器
  std::vector<double> xa(4), ya(4), xb(4), yb(4);//新建两个相机的图像x和y坐标容器
  for (unsigned int i = 0; i < 4; i++) {
    oP[i].project(aMo);//根据相机和目标坐标系之间的齐次变换矩阵 与 特征点空间坐标计算得到图像坐标
    xa[i] = oP[i].get_x();
    ya[i] = oP[i].get_y();
    oP[i].project(bMo);
    xb[i] = oP[i].get_x();
    yb[i] = oP[i].get_y();
  }
  vpHomography aHb;
  vpHomography::DLT(xb, yb, xa, ya, aHb, true);//利用DLT算法计算单应性矩阵
  std::cout << "Estimated homography using DLT:n" << aHb / aHb[2][2] << std::endl;
  vpHomography::HLM(xb, yb, xa, ya, true, aHb);//利用HLM算法计算单应性矩阵
  std::cout << "Estimated homography using HLM:n" << aHb / aHb[2][2] << std::endl;
  vpRotationMatrix aRb;
  vpTranslationVector atb;
  vpColVector n;
  aHb.computeDisplacement(aRb, atb, n);//把单应性矩阵分解为平移矩阵和旋转矩阵
  std::cout << "nEstimated displacement:" << std::endl;
  std::cout << " atb: " << atb.t() << std::endl;
  vpThetaUVector atub;
  atub.buildFrom(aRb);
  std::cout << " athetaub: ";
  for (unsigned int i = 0; i < 3; i++)
    std::cout << vpMath::deg(atub[i]) << " ";
  std::cout << std::endl;
  std::cout << " n: " << n.t() << std::endl;
  vpImagePoint iPa, iPb;
  vpCameraParameters cam;
  vpMeterPixelConversion::convertPoint(cam, xb[3], yb[3], iPb);
  vpMeterPixelConversion::convertPoint(cam, xa[3], ya[3], iPa);
  std::cout << "Ground truth: Point 3 in pixels in frame b: " << iPb << std::endl;
  std::cout << "Ground truth: Point 3 in pixels in frame a: " << iPa << std::endl;
  // Project the position in pixel of point 3 from the homography
  std::cout << "Estimation from homography: Point 3 in pixels in frame a: " << vpHomography::project(cam, aHb, iPb)
            << std::endl;//根据单应性矩阵和特征点在相机b坐标系下的坐标估计特征点在相机a坐标系下的坐标
}