参考资料：
ORBSLAM2 Initialzer注释
单应矩阵的分解
把看过的看懂的代码弄成素材用起来才行啊，这是积累经验啊。
PS：学和做怎么结合在一块呢？
1.明确输入输出和各个模块。（学）
2.分离模块，解读模块。（学，思考为什么这么做，懂算法背后的数学原理是最基本的，否则根本就用不了，这样才能积累算法经验）
3.知道有哪些模块可以替换，看相关源码，替换模块。（做）
随机选择4对点对，进行计算单应矩阵，循环指定的次数，选择得分最高的单应矩阵，最后进行单应矩阵的分解。
共分成：计算单应矩阵；选择得分最高的单应矩阵；单应矩阵的分解。
// Generate sets of 8 points for each RANSAC iteration
// 步骤2：在所有匹配特征点对中随机选择8对匹配特征点为一组，共选择mMaxIterations组
// 用于FindHomography和FindFundamental求解
// mMaxIterations:200
mvSets = vector< vector<size_t> >(mMaxIterations,vector<size_t>(8,0));
DUtils::Random::SeedRandOnce(0);
for(int it=0; it<mMaxIterations; it++)
{
vAvailableIndices = vAllIndices;
// Select a minimum set
for(size_t j=0; j<8; j++)
{
// 产生0到N-1的随机数
int randi = DUtils::Random::RandomInt(0,vAvailableIndices.size()-1);
// idx表示哪一个索引对应的特征点被选中
int idx = vAvailableIndices[randi];
mvSets[it][j] = idx;
// randi对应的索引已经被选过了，从容器中删除
// randi对应的索引用最后一个元素替换，并删掉最后一个元素
vAvailableIndices[randi] = vAvailableIndices.back();
vAvailableIndices.pop_back();
}
}
/**
* @brief 计算单应矩阵
*
* 假设场景为平面情况下通过前两帧求取Homography矩阵(current frame 2 到 reference frame 1),并得到该模型的评分
*/
void Initializer::FindHomography(vector<bool> &vbMatchesInliers, float &score, cv::Mat &H21)
{
// Number of putative matches
const int N = mvMatches12.size();
// Normalize coordinates
// 将mvKeys1和mvKey2归一化到均值为0，一阶绝对矩为1，归一化矩阵分别为T1、T2
vector<cv::Point2f> vPn1, vPn2;
cv::Mat T1, T2;
Normalize(mvKeys1,vPn1, T1);
Normalize(mvKeys2,vPn2, T2);
cv::Mat T2inv = T2.inv();
// Best Results variables
// 最终最佳的MatchesInliers与得分
score = 0.0;
vbMatchesInliers = vector<bool>(N,false);
// Iteration variables
vector<cv::Point2f> vPn1i(8);
vector<cv::Point2f> vPn2i(8);
cv::Mat H21i, H12i;
// 每次RANSAC的MatchesInliers与得分
vector<bool> vbCurrentInliers(N,false);
float currentScore;
// Perform all RANSAC iterations and save the solution with highest score
for(int it=0; it<mMaxIterations; it++)
{
// Select a minimum set
for(size_t j=0; j<8; j++)
{
int idx = mvSets[it][j];
// vPn1i和vPn2i为匹配的特征点对的坐标
vPn1i[j] = vPn1[mvMatches12[idx].first];
vPn2i[j] = vPn2[mvMatches12[idx].second];
}
cv::Mat Hn = ComputeH21(vPn1i,vPn2i);
// 恢复原始的均值和尺度
H21i = T2inv*Hn*T1;
H12i = H21i.inv();
// 利用重投影误差为当次RANSAC的结果评分
currentScore = CheckHomography(H21i, H12i, vbCurrentInliers, mSigma);
// 得到最优的vbMatchesInliers与score
if(currentScore>score)
{
H21 = H21i.clone();
vbMatchesInliers = vbCurrentInliers;
score = currentScore;
}
}
}
/**
* @brief 从特征点匹配求homography（normalized DLT）
*
* @param vP1 归一化后的点, in reference frame
* @param vP2 归一化后的点, in current frame
* @return 单应矩阵
* @see Multiple View Geometry in Computer Vision - Algorithm 4.2 p109
*/
cv::Mat Initializer::ComputeH21(const vector<cv::Point2f> &vP1, const vector<cv::Point2f> &vP2)
{
const int N = vP1.size();
cv::Mat A(2*N,9,CV_32F); // 2N*9
for(int i=0; i<N; i++)
{
const float u1 = vP1[i].x;
const float v1 = vP1[i].y;
const float u2 = vP2[i].x;
const float v2 = vP2[i].y;
A.at<float>(2*i,0) = 0.0;
A.at<float>(2*i,1) = 0.0;
A.at<float>(2*i,2) = 0.0;
A.at<float>(2*i,3) = -u1;
A.at<float>(2*i,4) = -v1;
A.at<float>(2*i,5) = -1;
A.at<float>(2*i,6) = v2*u1;
A.at<float>(2*i,7) = v2*v1;
A.at<float>(2*i,8) = v2;
A.at<float>(2*i+1,0) = u1;
A.at<float>(2*i+1,1) = v1;
A.at<float>(2*i+1,2) = 1;
A.at<float>(2*i+1,3) = 0.0;
A.at<float>(2*i+1,4) = 0.0;
A.at<float>(2*i+1,5) = 0.0;
A.at<float>(2*i+1,6) = -u2*u1;
A.at<float>(2*i+1,7) = -u2*v1;
A.at<float>(2*i+1,8) = -u2;
}
cv::Mat u,w,vt;
cv::SVDecomp(A,w,u,vt,cv::SVD::MODIFY_A | cv::SVD::FULL_UV);
return vt.row(8).reshape(0, 3); // v的最后一列
}
// x'Fx = 0 整理可得：Af = 0
// A = | x'x x'y x' y'x y'y y' x y 1 |, f = | f1 f2 f3 f4 f5 f6 f7 f8 f9 |
// 通过SVD求解Af = 0，A'A最小特征值对应的特征向量即为解
/**
* @brief 对给定的homography matrix打分
*
* @see
* - Author's paper - IV. AUTOMATIC MAP INITIALIZATION （2）
* - Multiple View Geometry in Computer Vision - symmetric transfer errors: 4.2.2 Geometric distance
* - Multiple View Geometry in Computer Vision - model selection 4.7.1 RANSAC
*/
float Initializer::CheckHomography(const cv::Mat &H21, const cv::Mat &H12, vector<bool> &vbMatchesInliers, float sigma)
{
const int N = mvMatches12.size();
// |h11 h12 h13|
// |h21 h22 h23|
// |h31 h32 h33|
const float h11 = H21.at<float>(0,0);
const float h12 = H21.at<float>(0,1);
const float h13 = H21.at<float>(0,2);
const float h21 = H21.at<float>(1,0);
const float h22 = H21.at<float>(1,1);
const float h23 = H21.at<float>(1,2);
const float h31 = H21.at<float>(2,0);
const float h32 = H21.at<float>(2,1);
const float h33 = H21.at<float>(2,2);
// |h11inv h12inv h13inv|
// |h21inv h22inv h23inv|
// |h31inv h32inv h33inv|
const float h11inv = H12.at<float>(0,0);
const float h12inv = H12.at<float>(0,1);
const float h13inv = H12.at<float>(0,2);
const float h21inv = H12.at<float>(1,0);
const float h22inv = H12.at<float>(1,1);
const float h23inv = H12.at<float>(1,2);
const float h31inv = H12.at<float>(2,0);
const float h32inv = H12.at<float>(2,1);
const float h33inv = H12.at<float>(2,2);
vbMatchesInliers.resize(N);
float score = 0;
// 基于卡方检验计算出的阈值（假设测量有一个像素的偏差）
const float th = 5.991;
//信息矩阵，方差平方的倒数
const float invSigmaSquare = 1.0/(sigma*sigma);
// N对特征匹配点
for(int i=0; i<N; i++)
{
bool bIn = true;
const cv::KeyPoint &kp1 = mvKeys1[mvMatches12[i].first];
const cv::KeyPoint &kp2 = mvKeys2[mvMatches12[i].second];
const float u1 = kp1.pt.x;
const float v1 = kp1.pt.y;
const float u2 = kp2.pt.x;
const float v2 = kp2.pt.y;
// Reprojection error in first image
// x2in1 = H12*x2
// 将图像2中的特征点单应到图像1中
// |u1| |h11inv h12inv h13inv||u2|
// |v1| = |h21inv h22inv h23inv||v2|
// |1 | |h31inv h32inv h33inv||1 |
const float w2in1inv = 1.0/(h31inv*u2+h32inv*v2+h33inv);
const float u2in1 = (h11inv*u2+h12inv*v2+h13inv)*w2in1inv;
const float v2in1 = (h21inv*u2+h22inv*v2+h23inv)*w2in1inv;
// 计算重投影误差
const float squareDist1 = (u1-u2in1)*(u1-u2in1)+(v1-v2in1)*(v1-v2in1);
// 根据方差归一化误差
const float chiSquare1 = squareDist1*invSigmaSquare;
if(chiSquare1>th)
bIn = false;
else
score += th - chiSquare1;
// Reprojection error in second image
// x1in2 = H21*x1
// 将图像1中的特征点单应到图像2中
const float w1in2inv = 1.0/(h31*u1+h32*v1+h33);
const float u1in2 = (h11*u1+h12*v1+h13)*w1in2inv;
const float v1in2 = (h21*u1+h22*v1+h23)*w1in2inv;
const float squareDist2 = (u2-u1in2)*(u2-u1in2)+(v2-v1in2)*(v2-v1in2);
const float chiSquare2 = squareDist2*invSigmaSquare;
if(chiSquare2>th)
bIn = false;
else
score += th - chiSquare2;
if(bIn)
vbMatchesInliers[i]=true;
else
vbMatchesInliers[i]=false;
}
return score;
}
// H矩阵分解常见有两种方法：Faugeras SVD-based decomposition 和 Zhang SVD-based decomposition
// 参考文献：Motion and structure from motion in a piecewise plannar environment
// 这篇参考文献和下面的代码使用了Faugeras SVD-based decomposition算法
/**
* @brief 从H恢复R t
*
* @see
* - Faugeras et al, Motion and structure from motion in a piecewise planar environment. International Journal of Pattern Recognition and Artificial Intelligence, 1988.
* - Deeper understanding of the homography decomposition for vision-based control
*/
bool Initializer::ReconstructH(vector<bool> &vbMatchesInliers, cv::Mat &H21, cv::Mat &K,
cv::Mat &R21, cv::Mat &t21, vector<cv::Point3f> &vP3D, vector<bool> &vbTriangulated, float minParallax, int minTriangulated)
{
int N=0;
for(size_t i=0, iend = vbMatchesInliers.size() ; i<iend; i++)
if(vbMatchesInliers[i])
N++;
// We recover 8 motion hypotheses using the method of Faugeras et al.
// Motion and structure from motion in a piecewise planar environment.
// International Journal of Pattern Recognition and Artificial Intelligence, 1988
// 因为特征点是图像坐标系，所以讲H矩阵由相机坐标系换算到图像坐标系
cv::Mat invK = K.inv();
cv::Mat A = invK*H21*K;
cv::Mat U,w,Vt,V;
cv::SVD::compute(A,w,U,Vt,cv::SVD::FULL_UV);
V=Vt.t();
float s = cv::determinant(U)*cv::determinant(Vt);
float d1 = w.at<float>(0);
float d2 = w.at<float>(1);
float d3 = w.at<float>(2);
// SVD分解的正常情况是特征值降序排列
if(d1/d2<1.00001 || d2/d3<1.00001)
{
return false;
}
vector<cv::Mat> vR, vt, vn;
vR.reserve(8);
vt.reserve(8);
vn.reserve(8);
//n'=[x1 0 x3] 4 posibilities e1=e3=1, e1=1 e3=-1, e1=-1 e3=1, e1=e3=-1
// 法向量n'= [x1 0 x3] 对应ppt的公式17
float aux1 = sqrt((d1*d1-d2*d2)/(d1*d1-d3*d3));
float aux3 = sqrt((d2*d2-d3*d3)/(d1*d1-d3*d3));
float x1[] = {aux1,aux1,-aux1,-aux1};
float x3[] = {aux3,-aux3,aux3,-aux3};
//case d'=d2
// 计算ppt中公式19
float aux_stheta = sqrt((d1*d1-d2*d2)*(d2*d2-d3*d3))/((d1+d3)*d2);
float ctheta = (d2*d2+d1*d3)/((d1+d3)*d2);
float stheta[] = {aux_stheta, -aux_stheta, -aux_stheta, aux_stheta};
// 计算旋转矩阵 R‘，计算ppt中公式18
// | ctheta 0 -aux_stheta| | aux1|
// Rp = | 0 1 0 | tp = | 0 |
// | aux_stheta 0 ctheta | |-aux3|
// | ctheta 0 aux_stheta| | aux1|
// Rp = | 0 1 0 | tp = | 0 |
// |-aux_stheta 0 ctheta | | aux3|
// | ctheta 0 aux_stheta| |-aux1|
// Rp = | 0 1 0 | tp = | 0 |
// |-aux_stheta 0 ctheta | |-aux3|
// | ctheta 0 -aux_stheta| |-aux1|
// Rp = | 0 1 0 | tp = | 0 |
// | aux_stheta 0 ctheta | | aux3|
for(int i=0; i<4; i++)
{
cv::Mat Rp=cv::Mat::eye(3,3,CV_32F);
Rp.at<float>(0,0)=ctheta;
Rp.at<float>(0,2)=-stheta[i];
Rp.at<float>(2,0)=stheta[i];
Rp.at<float>(2,2)=ctheta;
cv::Mat R = s*U*Rp*Vt;
vR.push_back(R);
cv::Mat tp(3,1,CV_32F);
tp.at<float>(0)=x1[i];
tp.at<float>(1)=0;
tp.at<float>(2)=-x3[i];
tp*=d1-d3;
// 这里虽然对t有归一化，并没有决定单目整个SLAM过程的尺度
// 因为CreateInitialMapMonocular函数对3D点深度会缩放，然后反过来对 t 有改变
cv::Mat t = U*tp;
vt.push_back(t/cv::norm(t));
cv::Mat np(3,1,CV_32F);
np.at<float>(0)=x1[i];
np.at<float>(1)=0;
np.at<float>(2)=x3[i];
cv::Mat n = V*np;
if(n.at<float>(2)<0)
n=-n;
vn.push_back(n);
}
//case d'=-d2
// 计算ppt中公式22
float aux_sphi = sqrt((d1*d1-d2*d2)*(d2*d2-d3*d3))/((d1-d3)*d2);
float cphi = (d1*d3-d2*d2)/((d1-d3)*d2);
float sphi[] = {aux_sphi, -aux_sphi, -aux_sphi, aux_sphi};
// 计算旋转矩阵 R‘，计算ppt中公式21
for(int i=0; i<4; i++)
{
cv::Mat Rp=cv::Mat::eye(3,3,CV_32F);
Rp.at<float>(0,0)=cphi;
Rp.at<float>(0,2)=sphi[i];
Rp.at<float>(1,1)=-1;
Rp.at<float>(2,0)=sphi[i];
Rp.at<float>(2,2)=-cphi;
cv::Mat R = s*U*Rp*Vt;
vR.push_back(R);
cv::Mat tp(3,1,CV_32F);
tp.at<float>(0)=x1[i];
tp.at<float>(1)=0;
tp.at<float>(2)=x3[i];
tp*=d1+d3;
cv::Mat t = U*tp;
vt.push_back(t/cv::norm(t));
cv::Mat np(3,1,CV_32F);
np.at<float>(0)=x1[i];
np.at<float>(1)=0;
np.at<float>(2)=x3[i];
cv::Mat n = V*np;
if(n.at<float>(2)<0)
n=-n;
vn.push_back(n);
}
int bestGood = 0;
int secondBestGood = 0;
int bestSolutionIdx = -1;
float bestParallax = -1;
vector<cv::Point3f> bestP3D;
vector<bool> bestTriangulated;
// Instead of applying the visibility constraints proposed in the Faugeras' paper (which could fail for points seen with low parallax)
// We reconstruct all hypotheses and check in terms of triangulated points and parallax
// d'=d2和d'=-d2分别对应8组(R t)
for(size_t i=0; i<8; i++)
{
float parallaxi;
vector<cv::Point3f> vP3Di;
vector<bool> vbTriangulatedi;
int nGood = CheckRT(vR[i],vt[i],mvKeys1,mvKeys2,mvMatches12,vbMatchesInliers,K,vP3Di, 4.0*mSigma2, vbTriangulatedi, parallaxi);
// 保留最优的和次优的
if(nGood>bestGood)
{
secondBestGood = bestGood;
bestGood = nGood;
bestSolutionIdx = i;
bestParallax = parallaxi;
bestP3D = vP3Di;
bestTriangulated = vbTriangulatedi;
}
else if(nGood>secondBestGood)
{
secondBestGood = nGood;
}
}
if(secondBestGood<0.75*bestGood && bestParallax>=minParallax && bestGood>minTriangulated && bestGood>0.9*N)
{
vR[bestSolutionIdx].copyTo(R21);
vt[bestSolutionIdx].copyTo(t21);
vP3D = bestP3D;
vbTriangulated = bestTriangulated;
return true;
}
return false;
}
// Trianularization: 已知匹配特征点对{x x'} 和 各自相机矩阵{P P'}, 估计三维点 X
// x' = P'X x = PX
// 它们都属于 x = aPX模型
// |X|
// |x| |p1 p2 p3 p4 ||Y| |x| |--p0--||.|
// |y| = a |p5 p6 p7 p8 ||Z| ===>|y| = a|--p1--||X|
// |z| |p9 p10 p11 p12||1| |z| |--p2--||.|
// 采用DLT的方法：x叉乘PX = 0
// |yp2 - p1| |0|
// |p0 - xp2| X = |0|
// |xp1 - yp0| |0|
// 两个点:
// |yp2 - p1 | |0|
// |p0 - xp2 | X = |0| ===> AX = 0
// |y'p2' - p1' | |0|
// |p0' - x'p2'| |0|
// 变成程序中的形式：
// |xp2 - p0 | |0|
// |yp2 - p1 | X = |0| ===> AX = 0
// |x'p2'- p0'| |0|
// |y'p2'- p1'| |0|
/**
* @brief 给定投影矩阵P1,P2和图像上的点kp1,kp2，从而恢复3D坐标
*
* @param kp1 特征点, in reference frame
* @param kp2 特征点, in current frame
* @param P1 投影矩阵P1
* @param P2 投影矩阵P２
* @param x3D 三维点
* @see Multiple View Geometry in Computer Vision - 12.2 Linear triangulation methods p312
*/
void Initializer::Triangulate(const cv::KeyPoint &kp1, const cv::KeyPoint &kp2, const cv::Mat &P1, const cv::Mat &P2, cv::Mat &x3D)
{
// 在DecomposeE函数和ReconstructH函数中对t有归一化
// 这里三角化过程中恢复的3D点深度取决于 t 的尺度，
// 但是这里恢复的3D点并没有决定单目整个SLAM过程的尺度
// 因为CreateInitialMapMonocular函数对3D点深度会缩放，然后反过来对 t 有改变
cv::Mat A(4,4,CV_32F);
A.row(0) = kp1.pt.x*P1.row(2)-P1.row(0);
A.row(1) = kp1.pt.y*P1.row(2)-P1.row(1);
A.row(2) = kp2.pt.x*P2.row(2)-P2.row(0);
A.row(3) = kp2.pt.y*P2.row(2)-P2.row(1);
cv::Mat u,w,vt;
cv::SVD::compute(A,w,u,vt,cv::SVD::MODIFY_A| cv::SVD::FULL_UV);
x3D = vt.row(3).t();
x3D = x3D.rowRange(0,3)/x3D.at<float>(3);
}
/**
* ＠brief 归一化特征点到同一尺度（作为normalize DLT的输入）
*
* [x' y' 1]' = T * [x y 1]' \n
* 归一化后x', y'的均值为0，sum(abs(x_i'-0))=1，sum(abs((y_i'-0))=1
*
* @param vKeys 特征点在图像上的坐标
* @param vNormalizedPoints 特征点归一化后的坐标
* @param T 将特征点归一化的矩阵
*/
void Initializer::Normalize(const vector<cv::KeyPoint> &vKeys, vector<cv::Point2f> &vNormalizedPoints, cv::Mat &T)
{
float meanX = 0;
float meanY = 0;
const int N = vKeys.size();
vNormalizedPoints.resize(N);
for(int i=0; i<N; i++)
{
meanX += vKeys[i].pt.x;
meanY += vKeys[i].pt.y;
}
meanX = meanX/N;
meanY = meanY/N;
float meanDevX = 0;
float meanDevY = 0;
// 将所有vKeys点减去中心坐标，使x坐标和y坐标均值分别为0
for(int i=0; i<N; i++)
{
vNormalizedPoints[i].x = vKeys[i].pt.x - meanX;
vNormalizedPoints[i].y = vKeys[i].pt.y - meanY;
meanDevX += fabs(vNormalizedPoints[i].x);
meanDevY += fabs(vNormalizedPoints[i].y);
}
meanDevX = meanDevX/N;
meanDevY = meanDevY/N;
float sX = 1.0/meanDevX;
float sY = 1.0/meanDevY;
// 将x坐标和y坐标分别进行尺度缩放，使得x坐标和y坐标的一阶绝对矩分别为1
for(int i=0; i<N; i++)
{
vNormalizedPoints[i].x = vNormalizedPoints[i].x * sX;
vNormalizedPoints[i].y = vNormalizedPoints[i].y * sY;
}
// |sX 0 -meanx*sX|
// |0 sY -meany*sY|
// |0 0 1 |
T = cv::Mat::eye(3,3,CV_32F);
T.at<float>(0,0) = sX;
T.at<float>(1,1) = sY;
T.at<float>(0,2) = -meanX*sX;
T.at<float>(1,2) = -meanY*sY;
}
/**
* @brief 进行cheirality check，从而进一步找出F分解后最合适的解
*/
int Initializer::CheckRT(const cv::Mat &R, const cv::Mat &t, const vector<cv::KeyPoint> &vKeys1, const vector<cv::KeyPoint> &vKeys2,
const vector<Match> &vMatches12, vector<bool> &vbMatchesInliers,
const cv::Mat &K, vector<cv::Point3f> &vP3D, float th2, vector<bool> &vbGood, float ¶llax)
{
// Calibration parameters
const float fx = K.at<float>(0,0);
const float fy = K.at<float>(1,1);
const float cx = K.at<float>(0,2);
const float cy = K.at<float>(1,2);
vbGood = vector<bool>(vKeys1.size(),false);
vP3D.resize(vKeys1.size());
vector<float> vCosParallax;
vCosParallax.reserve(vKeys1.size());
// Camera 1 Projection Matrix K[I|0]
// 步骤1：得到一个相机的投影矩阵
// 以第一个相机的光心作为世界坐标系
cv::Mat P1(3,4,CV_32F,cv::Scalar(0));
K.copyTo(P1.rowRange(0,3).colRange(0,3));
// 第一个相机的光心在世界坐标系下的坐标
cv::Mat O1 = cv::Mat::zeros(3,1,CV_32F);
// Camera 2 Projection Matrix K[R|t]
// 步骤2：得到第二个相机的投影矩阵
cv::Mat P2(3,4,CV_32F);
R.copyTo(P2.rowRange(0,3).colRange(0,3));
t.copyTo(P2.rowRange(0,3).col(3));
P2 = K*P2;
// 第二个相机的光心在世界坐标系下的坐标
cv::Mat O2 = -R.t()*t;
int nGood=0;
for(size_t i=0, iend=vMatches12.size();i<iend;i++)
{
if(!vbMatchesInliers[i])
continue;
// kp1和kp2是匹配特征点
const cv::KeyPoint &kp1 = vKeys1[vMatches12[i].first];
const cv::KeyPoint &kp2 = vKeys2[vMatches12[i].second];
cv::Mat p3dC1;
// 步骤3：利用三角法恢复三维点p3dC1
Triangulate(kp1,kp2,P1,P2,p3dC1);
if(!isfinite(p3dC1.at<float>(0)) || !isfinite(p3dC1.at<float>(1)) || !isfinite(p3dC1.at<float>(2)))
{
vbGood[vMatches12[i].first]=false;
continue;
}
// Check parallax
// 步骤4：计算视差角余弦值
cv::Mat normal1 = p3dC1 - O1;
float dist1 = cv::norm(normal1);
cv::Mat normal2 = p3dC1 - O2;
float dist2 = cv::norm(normal2);
float cosParallax = normal1.dot(normal2)/(dist1*dist2);
// 步骤5：判断3D点是否在两个摄像头前方
// Check depth in front of first camera (only if enough parallax, as "infinite" points can easily go to negative depth)
// 步骤5.1：3D点深度为负，在第一个摄像头后方，淘汰
if(p3dC1.at<float>(2)<=0 && cosParallax<0.99998)
continue;
// Check depth in front of second camera (only if enough parallax, as "infinite" points can easily go to negative depth)
// 步骤5.2：3D点深度为负，在第二个摄像头后方，淘汰
cv::Mat p3dC2 = R*p3dC1+t;
if(p3dC2.at<float>(2)<=0 && cosParallax<0.99998)
continue;
// 步骤6：计算重投影误差
// Check reprojection error in first image
// 计算3D点在第一个图像上的投影误差
float im1x, im1y;
float invZ1 = 1.0/p3dC1.at<float>(2);
im1x = fx*p3dC1.at<float>(0)*invZ1+cx;
im1y = fy*p3dC1.at<float>(1)*invZ1+cy;
float squareError1 = (im1x-kp1.pt.x)*(im1x-kp1.pt.x)+(im1y-kp1.pt.y)*(im1y-kp1.pt.y);
// 步骤6.1：重投影误差太大，跳过淘汰
// 一般视差角比较小时重投影误差比较大
if(squareError1>th2)
continue;
// Check reprojection error in second image
// 计算3D点在第二个图像上的投影误差
float im2x, im2y;
float invZ2 = 1.0/p3dC2.at<float>(2);
im2x = fx*p3dC2.at<float>(0)*invZ2+cx;
im2y = fy*p3dC2.at<float>(1)*invZ2+cy;
float squareError2 = (im2x-kp2.pt.x)*(im2x-kp2.pt.x)+(im2y-kp2.pt.y)*(im2y-kp2.pt.y);
// 步骤6.2：重投影误差太大，跳过淘汰
// 一般视差角比较小时重投影误差比较大
if(squareError2>th2)
continue;
// 步骤7：统计经过检验的3D点个数，记录3D点视差角
vCosParallax.push_back(cosParallax);
vP3D[vMatches12[i].first] = cv::Point3f(p3dC1.at<float>(0),p3dC1.at<float>(1),p3dC1.at<float>(2));
nGood++;
if(cosParallax<0.99998)
vbGood[vMatches12[i].first]=true;
}
// 步骤8：得到3D点中较大的视差角
if(nGood>0)
{
// 从小到大排序
sort(vCosParallax.begin(),vCosParallax.end());
// trick! 排序后并没有取最大的视差角
// 取一个较大的视差角
size_t idx = min(50,int(vCosParallax.size()-1));
parallax = acos(vCosParallax[idx])*180/CV_PI;
}
else
parallax=0;
return nGood;
}
