基于SLAM14讲13.3中提到的单目稠密重建方法，重建自己的单目相机图片的深度图。
我们已经制作了自己的数据集，而且我们现在也根据合适的算法得到了对应的相机位姿。那么就已经达到了单目相机深度估计的要求。下面这些例程使用的是公开的REMODE测试数据集。
例程效果如下
dense_mapping.cpp 主程序如下所示
#include <iostream>
#include <vector>
#include <fstream>
using namespace std;
#include <boost/timer.hpp>
// for sophus
#include <sophus/se3.h>
using Sophus::SE3;
// for eigen
#include <Eigen/Core>
#include <Eigen/Geometry>
using namespace Eigen;
#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>
using namespace cv;
/**********************************************
* 本程序演示了单目相机在已知轨迹下的稠密深度估计
* 使用极线搜索 + NCC 匹配的方式，与书本的 13.2 节对应
* 请注意本程序并不完美，你完全可以改进它——我其实在故意暴露一些问题。
***********************************************/
// ------------------------------------------------------------------
// parameters
const int boarder = 20; // 边缘宽度
const int width = 640; // 宽度
const int height = 480; // 高度
const double fx = 481.2f; // 相机内参
const double fy = -480.0f;
const double cx = 319.5f;
const double cy = 239.5f;
const int ncc_window_size = 2; // NCC 取的窗口半宽度
const int ncc_area = (2*ncc_window_size+1)*(2*ncc_window_size+1); // NCC窗口面积
const double min_cov = 0.1; // 收敛判定：最小方差
const double max_cov = 10; // 发散判定：最大方差
// ------------------------------------------------------------------
// 重要的函数
// 从 REMODE 数据集读取数据
bool readDatasetFiles(
const string& path,
vector<string>& color_image_files,
vector<SE3>& poses
);
// 根据新的图像更新深度估计
bool update(
const Mat& ref,
const Mat& curr,
const SE3& T_C_R,
Mat& depth,
Mat& depth_cov
);
// 极线搜索
bool epipolarSearch(
const Mat& ref,
const Mat& curr,
const SE3& T_C_R,
const Vector2d& pt_ref,
const double& depth_mu,
const double& depth_cov,
Vector2d& pt_curr
);
// 更新深度滤波器
bool updateDepthFilter(
const Vector2d& pt_ref,
const Vector2d& pt_curr,
const SE3& T_C_R,
Mat& depth,
Mat& depth_cov
);
// 计算 NCC 评分
double NCC( const Mat& ref, const Mat& curr, const Vector2d& pt_ref, const Vector2d& pt_curr );
// 双线性灰度插值
inline double getBilinearInterpolatedValue( const Mat& img, const Vector2d& pt ) {
uchar* d = & img.data[ int(pt(1,0))*img.step+int(pt(0,0)) ];
double xx = pt(0,0) - floor(pt(0,0));
double yy = pt(1,0) - floor(pt(1,0));
return (( 1-xx ) * ( 1-yy ) * double(d[0]) +
xx* ( 1-yy ) * double(d[1]) +
( 1-xx ) *yy* double(d[img.step]) +
xx*yy*double(d[img.step+1]))/255.0;
}
// ------------------------------------------------------------------
// 一些小工具
// 显示估计的深度图
void plotDepth( const Mat& depth );
// 像素到相机坐标系
inline Vector3d px2cam ( const Vector2d px ) {
return Vector3d (
(px(0,0) - cx)/fx,
(px(1,0) - cy)/fy,
1
);
}
// 相机坐标系到像素
inline Vector2d cam2px ( const Vector3d p_cam ) {
return Vector2d (
p_cam(0,0)*fx/p_cam(2,0) + cx,
p_cam(1,0)*fy/p_cam(2,0) + cy
);
}
// 检测一个点是否在图像边框内
inline bool inside( const Vector2d& pt ) {
return pt(0,0) >= boarder && pt(1,0)>=boarder
&& pt(0,0)+boarder<width && pt(1,0)+boarder<=height;
}
// 显示极线匹配
void showEpipolarMatch( const Mat& ref, const Mat& curr, const Vector2d& px_ref, const Vector2d& px_curr );
// 显示极线
void showEpipolarLine( const Mat& ref, const Mat& curr, const Vector2d& px_ref, const Vector2d& px_min_curr, const Vector2d& px_max_curr );
// ------------------------------------------------------------------
int main( int argc, char** argv )
{
if ( argc != 2 )
{
cout<<"Usage: dense_mapping path_to_test_dataset"<<endl;
return -1;
}
// 从数据集读取数据
vector<string> color_image_files;
vector<SE3> poses_TWC;
bool ret = readDatasetFiles( argv[1], color_image_files, poses_TWC );
if ( ret==false )
{
cout<<"Reading image files failed!"<<endl;
return -1;
}
cout<<"read total "<<color_image_files.size()<<" files."<<endl;
// 第一张图
Mat ref = imread( color_image_files[0], 0 ); // gray-scale image
SE3 pose_ref_TWC = poses_TWC[0];
double init_depth = 3.0; // 深度初始值
double init_cov2 = 3.0; // 方差初始值
Mat depth( height, width, CV_64F, init_depth ); // 深度图
Mat depth_cov( height, width, CV_64F, init_cov2 ); // 深度图方差
for ( int index=1; index<color_image_files.size(); index++ )
{
cout<<"*** loop "<<index<<" ***"<<endl;
Mat curr = imread( color_image_files[index], 0 );
if (curr.data == nullptr) continue;
SE3 pose_curr_TWC = poses_TWC[index];
SE3 pose_T_C_R = pose_curr_TWC.inverse() * pose_ref_TWC; // 坐标转换关系： T_C_W * T_W_R = T_C_R
update( ref, curr, pose_T_C_R, depth, depth_cov );
plotDepth( depth );
imshow("image", curr);
waitKey(1);
}
cout<<"estimation returns, saving depth map ..."<<endl;
imwrite( "depth.pgm", depth );
cout<<"done."<<endl;
return 0;
}
bool readDatasetFiles(
const string& path,
vector< string >& color_image_files,
std::vector<SE3>& poses
)
{
ifstream fin( path+"/first_200_frames_traj_over_table_input_sequence.txt");
if ( !fin ) return false;
while ( !fin.eof() )
{
// 数据格式：图像文件名 tx, ty, tz, qx, qy, qz, qw ，注意是 TWC 而非 TCW
string image;
fin>>image;
double data[7];
for ( double& d:data ) fin>>d;
color_image_files.push_back( path+string("/images/")+image );
poses.push_back(
SE3( Quaterniond(data[6], data[3], data[4], data[5]),
Vector3d(data[0], data[1], data[2]))
);
if ( !fin.good() ) break;
}
return true;
}
// 对整个深度图进行更新
bool update(const Mat& ref, const Mat& curr, const SE3& T_C_R, Mat& depth, Mat& depth_cov )
{
#pragma omp parallel for
for ( int x=boarder; x<width-boarder; x++ )
#pragma omp parallel for
for ( int y=boarder; y<height-boarder; y++ )
{
// 遍历每个像素
if ( depth_cov.ptr<double>(y)[x] < min_cov || depth_cov.ptr<double>(y)[x] > max_cov ) // 深度已收敛或发散
continue;
// 在极线上搜索 (x,y) 的匹配
Vector2d pt_curr;
bool ret = epipolarSearch (
ref,
curr,
T_C_R,
Vector2d(x,y),
depth.ptr<double>(y)[x],
sqrt(depth_cov.ptr<double>(y)[x]),
pt_curr
);
if ( ret == false ) // 匹配失败
continue;
// 取消该注释以显示匹配
// showEpipolarMatch( ref, curr, Vector2d(x,y), pt_curr );
// 匹配成功，更新深度图
updateDepthFilter( Vector2d(x,y), pt_curr, T_C_R, depth, depth_cov );
}
}
// 极线搜索
// 方法见书 13.2 13.3 两节
bool epipolarSearch(
const Mat& ref, const Mat& curr,
const SE3& T_C_R, const Vector2d& pt_ref,
const double& depth_mu, const double& depth_cov,
Vector2d& pt_curr )
{
Vector3d f_ref = px2cam( pt_ref );
f_ref.normalize();
Vector3d P_ref = f_ref*depth_mu; // 参考帧的 P 向量
Vector2d px_mean_curr = cam2px( T_C_R*P_ref ); // 按深度均值投影的像素
double d_min = depth_mu-3*depth_cov, d_max = depth_mu+3*depth_cov;
if ( d_min<0.1 ) d_min = 0.1;
Vector2d px_min_curr = cam2px( T_C_R*(f_ref*d_min) ); // 按最小深度投影的像素
Vector2d px_max_curr = cam2px( T_C_R*(f_ref*d_max) ); // 按最大深度投影的像素
Vector2d epipolar_line = px_max_curr - px_min_curr; // 极线（线段形式）
Vector2d epipolar_direction = epipolar_line; // 极线方向
epipolar_direction.normalize();
double half_length = 0.5*epipolar_line.norm(); // 极线线段的半长度
if ( half_length>100 ) half_length = 100; // 我们不希望搜索太多东西
// 取消此句注释以显示极线（线段）
// showEpipolarLine( ref, curr, pt_ref, px_min_curr, px_max_curr );
// 在极线上搜索，以深度均值点为中心，左右各取半长度
double best_ncc = -1.0;
Vector2d best_px_curr;
for ( double l=-half_length; l<=half_length; l+=0.7 ) // l+=sqrt(2)
{
Vector2d px_curr = px_mean_curr + l*epipolar_direction; // 待匹配点
if ( !inside(px_curr) )
continue;
// 计算待匹配点与参考帧的 NCC
double ncc = NCC( ref, curr, pt_ref, px_curr );
if ( ncc>best_ncc )
{
best_ncc = ncc;
best_px_curr = px_curr;
}
}
if ( best_ncc < 0.85f ) // 只相信 NCC 很高的匹配
return false;
pt_curr = best_px_curr;
return true;
}
double NCC (
const Mat& ref, const Mat& curr,
const Vector2d& pt_ref, const Vector2d& pt_curr
)
{
// 零均值-归一化互相关
// 先算均值
double mean_ref = 0, mean_curr = 0;
vector<double> values_ref, values_curr; // 参考帧和当前帧的均值
for ( int x=-ncc_window_size; x<=ncc_window_size; x++ )
for ( int y=-ncc_window_size; y<=ncc_window_size; y++ )
{
double value_ref = double(ref.ptr<uchar>( int(y+pt_ref(1,0)) )[ int(x+pt_ref(0,0)) ])/255.0;
mean_ref += value_ref;
double value_curr = getBilinearInterpolatedValue( curr, pt_curr+Vector2d(x,y) );
mean_curr += value_curr;
values_ref.push_back(value_ref);
values_curr.push_back(value_curr);
}
mean_ref /= ncc_area;
mean_curr /= ncc_area;
// 计算 Zero mean NCC
double numerator = 0, demoniator1 = 0, demoniator2 = 0;
for ( int i=0; i<values_ref.size(); i++ )
{
double n = (values_ref[i]-mean_ref) * (values_curr[i]-mean_curr);
numerator += n;
demoniator1 += (values_ref[i]-mean_ref)*(values_ref[i]-mean_ref);
demoniator2 += (values_curr[i]-mean_curr)*(values_curr[i]-mean_curr);
}
return numerator / sqrt( demoniator1*demoniator2+1e-10 ); // 防止分母出现零
}
bool updateDepthFilter(
const Vector2d& pt_ref,
const Vector2d& pt_curr,
const SE3& T_C_R,
Mat& depth,
Mat& depth_cov
)
{
// 我是一只喵
// 不知道这段还有没有人看
// 用三角化计算深度
SE3 T_R_C = T_C_R.inverse();
Vector3d f_ref = px2cam( pt_ref );
f_ref.normalize();
Vector3d f_curr = px2cam( pt_curr );
f_curr.normalize();
// 方程
// d_ref * f_ref = d_cur * ( R_RC * f_cur ) + t_RC
// => [ f_ref^T f_ref, -f_ref^T f_cur ] [d_ref] = [f_ref^T t]
// [ f_cur^T f_ref, -f_cur^T f_cur ] [d_cur] = [f_cur^T t]
// 二阶方程用克莱默法则求解并解之
Vector3d t = T_R_C.translation();
Vector3d f2 = T_R_C.rotation_matrix() * f_curr;
Vector2d b = Vector2d ( t.dot ( f_ref ), t.dot ( f2 ) );
double A[4];
A[0] = f_ref.dot ( f_ref );
A[2] = f_ref.dot ( f2 );
A[1] = -A[2];
A[3] = - f2.dot ( f2 );
double d = A[0]*A[3]-A[1]*A[2];
Vector2d lambdavec =
Vector2d ( A[3] * b ( 0,0 ) - A[1] * b ( 1,0 ),
-A[2] * b ( 0,0 ) + A[0] * b ( 1,0 )) /d;
Vector3d xm = lambdavec ( 0,0 ) * f_ref;
Vector3d xn = t + lambdavec ( 1,0 ) * f2;
Vector3d d_esti = ( xm+xn ) / 2.0; // 三角化算得的深度向量
double depth_estimation = d_esti.norm(); // 深度值
// 计算不确定性（以一个像素为误差）
Vector3d p = f_ref*depth_estimation;
Vector3d a = p - t;
double t_norm = t.norm();
double a_norm = a.norm();
double alpha = acos( f_ref.dot(t)/t_norm );
double beta = acos( -a.dot(t)/(a_norm*t_norm));
double beta_prime = beta + atan(1/fx);
double gamma = M_PI - alpha - beta_prime;
double p_prime = t_norm * sin(beta_prime) / sin(gamma);
double d_cov = p_prime - depth_estimation;
double d_cov2 = d_cov*d_cov;
// 高斯融合
double mu = depth.ptr<double>( int(pt_ref(1,0)) )[ int(pt_ref(0,0)) ];
double sigma2 = depth_cov.ptr<double>( int(pt_ref(1,0)) )[ int(pt_ref(0,0)) ];
double mu_fuse = (d_cov2*mu+sigma2*depth_estimation) / ( sigma2+d_cov2);
double sigma_fuse2 = ( sigma2 * d_cov2 ) / ( sigma2 + d_cov2 );
depth.ptr<double>( int(pt_ref(1,0)) )[ int(pt_ref(0,0)) ] = mu_fuse;
depth_cov.ptr<double>( int(pt_ref(1,0)) )[ int(pt_ref(0,0)) ] = sigma_fuse2;
return true;
}
// 后面这些太简单我就不注释了（其实是因为懒）
void plotDepth(const Mat& depth)
{
imshow( "depth", depth*0.4 );
waitKey(1);
}
void showEpipolarMatch(const Mat& ref, const Mat& curr, const Vector2d& px_ref, const Vector2d& px_curr)
{
Mat ref_show, curr_show;
cv::cvtColor( ref, ref_show, CV_GRAY2BGR );
cv::cvtColor( curr, curr_show, CV_GRAY2BGR );
cv::circle( ref_show, cv::Point2f(px_ref(0,0), px_ref(1,0)), 5, cv::Scalar(0,0,250), 2);
cv::circle( curr_show, cv::Point2f(px_curr(0,0), px_curr(1,0)), 5, cv::Scalar(0,0,250), 2);
imshow("ref", ref_show );
imshow("curr", curr_show );
waitKey(1);
}
void showEpipolarLine(const Mat& ref, const Mat& curr, const Vector2d& px_ref, const Vector2d& px_min_curr, const Vector2d& px_max_curr)
{
Mat ref_show, curr_show;
cv::cvtColor( ref, ref_show, CV_GRAY2BGR );
cv::cvtColor( curr, curr_show, CV_GRAY2BGR );
cv::circle( ref_show, cv::Point2f(px_ref(0,0), px_ref(1,0)), 5, cv::Scalar(0,255,0), 2);
cv::circle( curr_show, cv::Point2f(px_min_curr(0,0), px_min_curr(1,0)), 5, cv::Scalar(0,255,0), 2);
cv::circle( curr_show, cv::Point2f(px_max_curr(0,0), px_max_curr(1,0)), 5, cv::Scalar(0,255,0), 2);
cv::line( curr_show, Point2f(px_min_curr(0,0), px_min_curr(1,0)), Point2f(px_max_curr(0,0), px_max_curr(1,0)), Scalar(0,255,0), 1);
imshow("ref", ref_show );
imshow("curr", curr_show );
waitKey(1);
}
CMakeLists.txt 如下所示
cmake_minimum_required( VERSION 2.8 )
project( dense_monocular )
set(CMAKE_BUILD_TYPE "Release")
set( CMAKE_CXX_FLAGS "-std=c++11 -march=native -O3 -fopenmp" )
############### dependencies ######################
# Eigen
include_directories( "/usr/include/eigen3" )
# OpenCV
find_package( OpenCV REQUIRED )
include_directories( ${OpenCV_INCLUDE_DIRS} )
# Sophus
find_package( Sophus REQUIRED )
include_directories( ${Sophus_INCLUDE_DIRS} )
set( THIRD_PARTY_LIBS
${OpenCV_LIBS}
${Sophus_LIBRARIES}
)
add_executable( dense_mapping dense_mapping.cpp )
target_link_libraries( dense_mapping ${THIRD_PARTY_LIBS} )