float CalculateError(const Mat_<float>& ground_truth_shape, const Mat_<float>& predicted_shape) {
Mat_<float> temp;
//temp = ground_truth_shape.rowRange(36, 37)-ground_truth_shape.rowRange(45, 46);
temp = ground_truth_shape.rowRange(1, 2) - ground_truth_shape.rowRange(6, 7);
float x = mean(temp.col(0))[0];
float y = mean(temp.col(1))[1];
float interocular_distance = sqrt(x*x + y*y);
float sum = 0;
for (int i = 0; i < ground_truth_shape.rows; i++) {
sum += norm(ground_truth_shape.row(i) - predicted_shape.row(i));
}
return sum / (ground_truth_shape.rows*interocular_distance);
}
// MARK: implement not complete yet.
bool SimpleNN::train(const Mat_<double> &train_X,
const Mat_<double> &train_Y,
string &err_msg)
{
/*
Parameters
----------
- Mat_<double> train_X: the training input data. It should be a NxM matrix
where N is the number of training data, M is the
size of input layer.
- Mat_<double> train_Y: the target training output data. It should be a NxO
matrix where N is the number of training data, O is
the size of output layer.
- string err_msg: error message (if any). It will be "" if there is no error.
*/
int N = train_X.rows;
if (train_Y.rows != N){
err_msg = "the number of training input data does not match the number of output data.";
return false;
}
srand((unsigned int) time(NULL));
vector<Mat_<double> > deltas(this->weights.size());
for (int iter_index = 0; iter_index < this->num_iteration; ++iter_index){
if (iter_index % 100 == 0 && iter_index > 0){
cout << "Iteration " << iter_index << " over total iteration " << this->num_iteration << endl;
}
// back-propagation with Stochastic Gradient Descend.
int rand_index = rand() % N;
Mat_<double> one_sample = train_X.row(rand_index).reshape(0, 1); // make it a column vector.
Mat_<double> one_target = train_Y.row(rand_index).reshape(0, 1);
Mat_<double> output;
string err_msg;
if (!this->predict(one_sample, output, err_msg)){
cerr << err_msg << endl;
return false;
} else {
deltas[this->weights.size() - 1] = 2.0*(one_target - output);
}
}
err_msg = "";
return true;
}
//==============================================================================
vector<uchar> ANN::predict(Mat_<float> &testData)
{
int numberOfSamples = testData.rows;
Mat_<float> classifResult(1, this->numberOfClasses);
vector<uchar> predictedLabels(numberOfSamples);
for(int i = 0; i < numberOfSamples; i++) {
nnetwork->predict(testData.row(i), classifResult);
#if DEBUG
cout << classifResult << endl;
#endif
// int max = 0;
// int maxI = 0;
// for(int j = 0; j < this->numberOfClasses; ++j){
// if( classifResult(0,j) > max){
// max = classifResult(0,j);
// maxI = j;
// }
// }
Point2i max_loc;
minMaxLoc(classifResult, 0, 0, 0, &max_loc);
// add row into predictions
predictions.push_back(classifResult);
//predictedLabels.push_back(maxI);
predictedLabels[i] = static_cast<unsigned char>(max_loc.x);
}
predictLabels.insert(predictLabels.end(),predictedLabels.begin(), predictedLabels.end());
return predictLabels;
}
static Matx31d NLtriangulation(Point2f P1,
Point2f P2,
Matx34f M1,
Matx34f M2)
{
Matx44d A(P1.x*M1(2,0)-M1(0,0), P1.x*M1(2,1)-M1(0,1), P1.x*M1(2,2)-M1(0,2), P1.x*M1(2,3)-M1(0,3),
P1.y*M1(2,0)-M1(1,0), P1.y*M1(2,1)-M1(1,1), P1.y*M1(2,2)-M1(1,2), P1.y*M1(2,3)-M1(1,3),
P2.x*M2(2,0)-M2(0,0), P2.x*M2(2,1)-M2(0,1), P2.x*M2(2,2)-M2(0,2), P2.x*M2(2,3)-M2(0,3),
P2.y*M2(2,0)-M2(1,0), P2.y*M2(2,1)-M2(1,1), P2.y*M2(2,2)-M2(1,2), P2.y*M2(2,3)-M2(1,3)
);
SVD svd(A,cv::SVD::MODIFY_A);
Mat_<double> vt = svd.vt;
Mat_<double> t = vt.row(3);
t = t/t(3);
Matx31d XX(t(0), t(1), t(2));
return XX;
}
/**
* @author JIA Pei
* @version 2010-02-05
* @brief Calculate statistics for all profiles; Computer all landmarks' mean prof and covariance matrix
* @return void
*/
void VO_ASMNDProfiles::VO_CalcStatistics4AllProfiles()
{
// Calcuate Inverse of Sg
for(unsigned int i = 0; i < this->m_iNbOfPyramidLevels; i++)
{
Mat_<float> allProfiles = Mat_<float>::zeros( this->m_iNbOfSamples, this->m_vvvNormalizedProfiles[0][i][0].GetProfileLength() );
Mat_<float> Covar = Mat_<float>::zeros(this->m_vvvNormalizedProfiles[0][i][0].GetProfileLength(),
this->m_vvvNormalizedProfiles[0][i][0].GetProfileLength() );
Mat_<float> Mean = Mat_<float>::zeros(1, this->m_vvvNormalizedProfiles[0][i][0].GetProfileLength() );
for(unsigned int j = 0; j < this->m_iNbOfPoints; j++)
{
for(unsigned int k = 0; k < this->m_iNbOfProfileDim; k++)
{
for(unsigned int l = 0; l < this->m_iNbOfSamples; l++)
{
Mat_<float> tmpRow = allProfiles.row(l);
Mat_<float> tmp = this->m_vvvNormalizedProfiles[l][i][j].GetTheProfile().col(k).t();
tmp.copyTo(tmpRow);
}
// OK! Now We Calculate the Covariance Matrix of prof for Landmark iPoint
cv::calcCovarMatrix( allProfiles, Covar, Mean, CV_COVAR_NORMAL+CV_COVAR_ROWS+CV_COVAR_SCALE, CV_32F);
// cv::calcCovarMatrix( allProfiles, Covar, Mean, CV_COVAR_SCRAMBLED+CV_COVAR_ROWS, CV_32F);
this->m_vvMeanNormalizedProfile[i][j].Set1DimProfile(Mean.t(), k);
// Explained by YAO Wei, 2008-1-29.
// Actually Covariance Matrix is semi-positive definite. But I am not sure
// whether it is invertible or not!!!
// In my opinion it is un-invert, since C = X.t() * X!!!
cv::invert(Covar, this->m_vvvCVMInverseOfSg[i][j][k], DECOMP_SVD);
}
}
}
}
void KNN::Compute_Centroid_(Mat_<double>& X, Mat_<double>& Centroid, Mat_<int>& Index, Scalar& K)
{
Scalar _Counter_ = 0;
Mat_<double> _Sum_(1, X.cols);
for (int _i_ = 0; _i_ < K[0]; _i_++)
{
Initialize_Zero_(_Sum_);
_Counter_ = 0;
for (int _j_ = 0; _j_ < Index.rows; _j_++)
{
if (Index(_j_, 0) == _i_)
{
add(_Sum_, X.row(_j_), _Sum_);
_Counter_[0]++;
}
}
divide(_Sum_, _Counter_[0], Centroid.row(_i_));
}
}
void KNN::Compute_Closest_(Mat_<double>& X, Mat_<double>& Centroids, Mat_<int>& Indices, Distance type)
{
Scalar _Number_Of_Centroids_ = Centroids.rows;
Mat_<int> _Index_(X.rows, 1);
Mat_<double> _temp_(_Number_Of_Centroids_[0], 1, CV_32F);
Mat_<double> _Mult_temp_(1, X.cols, CV_32F);
double _min_, _max_;
int _minInd_;
for (int _i_ = 0; _i_ < X.rows; _i_++)
{
for (int _j_ = 0; _j_ < _Number_Of_Centroids_[0]; _j_++)
{
multiply(X.row(_i_) - Centroids.row(_j_), X.row(_i_) - Centroids.row(_j_), _Mult_temp_);
_temp_(_j_, 0) = sum(_Mult_temp_)[0];
}
min(_temp_, _minInd_);
Indices(_i_, 0) = _minInd_;
}
}
//==============================================================================
vector<uchar> ANN::predictMouth(Mat_<float> &testData)
{
int numberOfSamples = testData.rows;
Mat_<float> classifResult(1, (int)MOUTH_CLASSES);
vector<uchar> predictedLabels(numberOfSamples);
for(int i = 0; i < numberOfSamples; i++) {
nnetwork->predict(testData.row(i), classifResult);
Point2i max_loc;
minMaxLoc(classifResult, 0, 0, 0, &max_loc);
// add row into predictions
predictions.push_back(classifResult);
predictedLabels[i] = static_cast<unsigned char>(max_loc.x) + 2;
}
predictLabels.insert(predictLabels.end(),predictedLabels.begin(), predictedLabels.end());
return predictedLabels;
}
float TrainableStatModel::leaveOneOutCrossValidation(const Mat_<float> &samples, const Mat_<int> &classes) {
int correctResults = 0;
Mat_<int> sampleIdx(samples.rows - 1, 1);
for (int i = 1; i < samples.rows; i++) {
sampleIdx(i - 1, 0) = i;
}
for (int i = 0; i < samples.rows; i++) {
this->clear();
this->train(samples, classes, sampleIdx);
int actual = (float)this->predict(samples.row(i));
if (actual == classes(i,0)) {
correctResults++;
}
cout<<"actual = "<<actual<<", expected = "<<classes(i,0)<<endl;
sampleIdx(i, 0) = i;
}
return (float)correctResults/(float)samples.rows;
}
void NNLSOptimizer::estimateIdentityParameters(const vector<vector<Point2f> >&featurePointsVector,
const Mat &cameraMatrix, const Mat& lensDist,
Face* face_ptr,const vector<vector<int> >&point_indices_vector,
const vector<Mat> &rotation, const vector<Mat> &translation,
const vector<vector<double> > &weights_ex,
vector<double> &weights_id)
{
Mat_<double> weakCamera(2,3);
//matrices for A_id * w_id = f
Mat_<double> A_id, seg_A_id;
//matrix Z = kron(weights, Identity_matrix)
Mat_<double> Z_id;
Mat_<double> ZU;
Mat_<double> pr, Pt;
//featurePoints converted to 2x1 matrices
Mat_<double> fi;
Mat_<double> f;
int index = 0;
//total number of feature points
int featurePointNum = 0;
const int exr_size = model->getExpSize();
const int id_size = model->getIdSize();
double *w_id = new double[id_size];
double *w_exp = new double[exr_size];
Mat_<double> rmatrix;
Mat_<double> x_t(1,exr_size);
Mat_<double> y_t(1,id_size);
Mat_<double> x(exr_size,1);
Mat_<double> y(id_size,1);
//used for x_t*U_ex and y_t*U_id
Mat_<double> lin_comb_x(exr_size,1);
double Z_avg;
double average_depth;
Mat_<double> proP;
Mat_<double> pM(3,1);
//get weights from the current face instance
face_ptr->getWeights(w_id,id_size,w_exp,exr_size);
/***************************************************************/
/*create weak-perspecitve camera matrix from camera matrix*/
/***************************************************************/
for(int i=0;i<2;i++)
for(int j=0;j<3;j++)
weakCamera(i,j) = cameraMatrix.at<double>(i,j);
for(unsigned int i=0;i<featurePointsVector.size();i++)
featurePointNum += featurePointsVector[i].size();
f = Mat_<double>(featurePointNum*2,1);
fi = Mat_<double>(2,1);
//preprocess points and core tensor rows
//for points subtract translation too
for(unsigned int i=0, count=0;i<featurePointsVector.size();i++)
{
//precompute translation
Pt = (1./translation[i].at<double>(2,0)) * (weakCamera*translation[i]);
for(unsigned int j=0;j<featurePointsVector[i].size();j++)
{
fi = Mat_<double>(2,1);
fi(0,0) = featurePointsVector[i][j].x;
fi(1,0) = featurePointsVector[i][j].y;
fi = fi - Pt;
f.row(count + 2*j) = fi.row(0) + 0.0;
f.row(count + 2*j+1) = fi.row(1) + 0.0;
}
count += 2*featurePointsVector[i].size();
}
A_id = Mat_<double>(2*featurePointNum,id_size);
seg_A_id = Mat_<double>(2,id_size);
average_depth = face_ptr->getAverageDepth();
pM(0,0) = 1;
pM(1,0) = 1;
pM(2,0) = average_depth;
for(unsigned int i=0, count = 0;i<point_indices_vector.size();++i)
{
Rodrigues(rotation[i],rmatrix);
proP = cameraMatrix*rmatrix*pM;
proP = proP + cameraMatrix*translation[i];
Z_avg = proP(0,2);
pr = (1.0/Z_avg)*weakCamera*rmatrix;
//load the appropriate weights for the i-th frame
for(unsigned int k=0;k<weights_ex[i].size();k++)
x_t(0,k) = weights_ex[i][k];
lin_comb_x = (x_t*u_ex).t();
Z_id = Matrix::kronecker(Mat_<double>::eye(id_size,id_size),lin_comb_x);
ZU = Z_id*(u_id.t());
for(unsigned int j=0;j<point_indices_vector[i].size();++j)
{
index = point_indices_vector[i][j];
seg_A_id = pr*M[index]*ZU;
A_id.row(count + 2*j) = seg_A_id.row(0) + 0.0;
A_id.row(count + 2*j+1) = seg_A_id.row(1) + 0.0;
}
count += 2*point_indices_vector[i].size();
}
//do not use the guess in the first frame but do for every following frame
for(int i=0;i<id_size;i++)
y_t(0,i) = y(i,0) = w_id[i];
// Mat_<double> temp = (A_id*y - f);
// Mat_<double> e = temp.t()*temp;
// cout << "id, error before " << e(0,0)<<endl;
//optimize using sequential coordinate descent
this->scannls(A_id,f,y);
// temp = (A_id*y - f);
// e = temp.t()*temp;
// cout << "id, error after " << e(0,0)<<endl;
for(int i=0;i<id_size;i++){
w_id[i] = y(i,0);
}
for(int i=0;i<exr_size;i++){
w_exp[i] = weights_ex[0][i];
}
for(int i=0;i<id_size;i++){
weights_id.push_back(w_id[i]);
}
face_ptr->setNewIdentityAndExpression(w_id,w_exp);
face_ptr->setAverageDepth(average_depth);
ZU.release();
Z_id.release();
A_id.release();
f.release();
delete[] w_id;
delete[] w_exp;
}
int MultipleGraphsClassifier::predict(DisjointSetForest &segmentation, const Mat_<Vec3b> &image, const Mat_<float> &mask) {
int maxGraphSize = max(segmentation.getNumberOfComponents(), this->maxTrainingGraphSize);
int minGraphSize = min(segmentation.getNumberOfComponents(), this->minTrainingGraphSize);
if (minGraphSize <= this->k) {
cout<<"the smallest graph has size "<<minGraphSize<<", cannot compute "<<this->k<<" eigenvectors"<<endl;
exit(EXIT_FAILURE);
}
// compute each feature graph for the test sample
vector<WeightedGraph> featureGraphs;
featureGraphs.reserve(this->features.size());
for (int i = 0; i < (int)this->features.size(); i++) {
featureGraphs.push_back(this->computeFeatureGraph(i, segmentation, image, mask));
}
// order graphs by feature, to compute pattern vectors feature by
// feature.
vector<vector<WeightedGraph> > graphsByFeatures(this->features.size());
// add feature graphs for the test sample at index 0
for (int i = 0; i < (int)this->features.size(); i++) {
graphsByFeatures[i].reserve(this->trainingFeatureGraphs.size() + 1);
graphsByFeatures[i].push_back(featureGraphs[i]);
}
// add feature graphs for each training sample
for (int i = 0; i < (int)this->trainingFeatureGraphs.size(); i++) {
for (int j = 0; j < (int)this->features.size(); j++) {
graphsByFeatures[j].push_back(get<0>(this->trainingFeatureGraphs[i])[j]);
}
}
// compute the corresponding pattern vectors
vector<vector<VectorXd> > patternsByFeatures(this->features.size());
for (int i = 0; i < (int)this->features.size(); i++) {
patternsByFeatures[i] = patternVectors(graphsByFeatures[i], this->k, maxGraphSize);
}
// concatenate pattern vectors by image, converting to opencv format
// to work with cv's ML module.
Mat_<float> longPatterns = Mat_<float>::zeros(this->trainingFeatureGraphs.size() + 1, maxGraphSize * k * this->features.size());
for (int i = 0; i < (int)this->trainingFeatureGraphs.size() + 1; i++) {
VectorXd longPattern(maxGraphSize * k * this->features.size());
for (int j = 0; j < this->features.size(); j++) {
longPattern.block(j * maxGraphSize * k, 0, maxGraphSize * k, 1) = patternsByFeatures[j][i];
}
Mat_<double> cvLongPattern;
eigenToCv(longPattern, cvLongPattern);
Mat_<float> castLongPattern = Mat_<float>(cvLongPattern);
castLongPattern.copyTo(longPatterns.row(i));
}
// classification of long patterns using SVM
CvKNearest svmClassifier;
Mat_<int> classes(this->trainingFeatureGraphs.size(), 1);
for (int i = 0; i < (int)this->trainingFeatureGraphs.size(); i++) {
classes(i,0) = get<1>(this->trainingFeatureGraphs[i]);
}
svmClassifier.train(longPatterns.rowRange(1, longPatterns.rows), classes);
return (int)svmClassifier.find_nearest(longPatterns.row(0), 1);
}
void NNLSOptimizer::estimateExpressionParameters(const vector<Point2f> &featurePoints,
const Mat &cameraMatrix, const Mat& lensDist,
Face* face_ptr,const vector<int> &point_indices,
const Mat &rotation, const Mat &translation,
vector<double> &weights_ex)
{
Mat_<double> weakCamera(2,3);
//matrices for A_ex * w_ex = f and A_id * w_id = f
Mat_<double> A_ex, seg_A_ex;
//matrix Z = kron(weights, Identity_matrix)
Mat_<double> Z_ex;
Mat_<double> ZU;
Mat_<double> pr, Pt;
//core tensor rows
Mat_<double> Mi;
//featurePoints converted to 2x1 matrices
Mat_<double> fi;
Mat_<double> f;
int index = 0;
const int exr_size = model->getExpSize();
const int id_size = model->getIdSize();
double *w_id = new double[id_size];
double *w_exp = new double[exr_size];
Mat_<double> rmatrix;
Mat_<double> x_t(1,exr_size);
Mat_<double> y_t(1,id_size);
Mat_<double> x(exr_size,1);
Mat_<double> y(id_size,1);
//used for x_t*U_ex and y_t*U_id
Mat_<double> lin_comb_x(exr_size,1);
Mat_<double> lin_comb_y(id_size,1);
double Z_avg;
double average_depth;
Point3f p;
Mat_<double> proP;
Mat_<double> pM(3,1);
Rodrigues(rotation,rmatrix);
//get weights from the current face instance
face_ptr->getWeights(w_id,id_size,w_exp,exr_size);
//find average depth
average_depth = face_ptr->getAverageDepth();
pM(0,0) = 1;
pM(1,0) = 1;
pM(2,0) = average_depth;
proP = cameraMatrix*rmatrix*pM;
proP = proP + cameraMatrix*translation;
Z_avg = proP(0,2);
/***************************************************************/
/*create weak-perspecitve camera matrix from camera matrix*/
/***************************************************************/
for(int i=0;i<2;i++)
for(int j=0;j<3;j++)
weakCamera(i,j) = cameraMatrix.at<double>(i,j);
f = Mat_<double>(featurePoints.size()*2,1);
fi = Mat_<double>(2,1);
//precompute translation
Pt = (1./translation.at<double>(2,0)) * (weakCamera*translation);
//preprocess points and core tensor rows
//for points subtract translation too
for(unsigned int i=0;i<featurePoints.size();i++)
{
fi = Mat_<double>(2,1);
fi(0,0) = featurePoints[i].x;
fi(1,0) = featurePoints[i].y;
fi = fi - Pt;
f.row(2*i) = fi.row(0) + 0.0;
f.row(2*i+1) = fi.row(1) + 0.0;
}
pr = (1.0/Z_avg)*weakCamera*rmatrix;
A_ex = Mat_<double>::zeros(2*featurePoints.size(),exr_size);
seg_A_ex = Mat_<double>::zeros(2*featurePoints.size(),exr_size);
for(int i=0;i<id_size;i++)
y_t(0,i) = w_id[i];
lin_comb_y = (y_t*u_id).t();
Z_ex = Matrix::kronecker(lin_comb_y,Mat_<double>::eye(exr_size,exr_size));
ZU = Z_ex*(u_ex.t());
for(unsigned int i=0;i<point_indices.size();++i)
{
index = point_indices[i];
seg_A_ex = pr*M[index]*ZU;
A_ex.row(2*i) = seg_A_ex.row(0) + 0.0;
A_ex.row(2*i+1) = seg_A_ex.row(1) + 0.0;
}
//do not use the guess in the first frame but do for every following frame
for(int i=0;i<exr_size;i++)
x_t(0,i) = x(i,0) = w_exp[i];
// Mat_<double> temp = (A_ex*x - f);
// Mat_<double> e = temp.t()*temp;
// cout << "exp, error before " << e(0,0)<<endl;
//op .. lets see if we get here
this->scannls(A_ex,f,x);
// temp = (A_ex*x - f);
// e = temp.t()*temp;
// cout << "exp, error after " << e(0,0)<<endl;
for(int i=0;i<exr_size;i++){
w_exp[i] = x(i,0);
}
for(int i=0;i<exr_size;i++){
weights_ex.push_back(w_exp[i]);
}
face_ptr->setNewIdentityAndExpression(w_id,w_exp);
//unecessary it seems
face_ptr->setAverageDepth(average_depth);
ZU.release();
Z_ex.release();
A_ex.release();
f.release();
delete[] w_id;
delete[] w_exp;
}
// Need to move this all to opengl
void DrawBox(Mat image, Vec6d pose, Scalar color, int thickness, float fx, float fy, float cx, float cy)
{
float boxVerts[] = {-1, 1, -1,
1, 1, -1,
1, 1, 1,
-1, 1, 1,
1, -1, 1,
1, -1, -1,
-1, -1, -1,
-1, -1, 1};
Mat_<float> box = Mat(8, 3, CV_32F, boxVerts).clone() * 100;
Matx33f rot = Euler2RotMat(Vec3d(pose[3], pose[4], pose[5]));
Mat_<float> rotBox;
Mat((Mat(rot) * box.t())).copyTo(rotBox);
rotBox = rotBox.t();
rotBox.col(0) = rotBox.col(0) + pose[0];
rotBox.col(1) = rotBox.col(1) + pose[1];
rotBox.col(2) = rotBox.col(2) + pose[2];
// draw the lines
Mat_<float> rotBoxProj;
Project(rotBoxProj, rotBox, image.size(), fx, fy, cx, cy);
Mat begin;
Mat end;
rotBoxProj.row(0).copyTo(begin);
rotBoxProj.row(1).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(1).copyTo(begin);
rotBoxProj.row(2).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(2).copyTo(begin);
rotBoxProj.row(3).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(0).copyTo(begin);
rotBoxProj.row(3).copyTo(end);
//std::cout << begin <<endl;
//std::cout << end <<endl;
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(2).copyTo(begin);
rotBoxProj.row(4).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(1).copyTo(begin);
rotBoxProj.row(5).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(0).copyTo(begin);
rotBoxProj.row(6).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(3).copyTo(begin);
rotBoxProj.row(7).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(6).copyTo(begin);
rotBoxProj.row(5).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(5).copyTo(begin);
rotBoxProj.row(4).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(4).copyTo(begin);
rotBoxProj.row(7).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
rotBoxProj.row(7).copyTo(begin);
rotBoxProj.row(6).copyTo(end);
cv::line(image, Point((int)begin.at<float>(0), (int)begin.at<float>(1)), Point((int)end.at<float>(0), (int)end.at<float>(1)), color, thickness);
}
static int initialize_simplex(Mat_<double>& c, Mat_<double>& b,double& v,vector<int>& N,vector<int>& B,vector<unsigned int>& indexToRow){
N.resize(c.cols);
N[0]=0;
for (std::vector<int>::iterator it = N.begin()+1 ; it != N.end(); ++it){
*it=it[-1]+1;
}
B.resize(b.rows);
B[0]=(int)N.size();
for (std::vector<int>::iterator it = B.begin()+1 ; it != B.end(); ++it){
*it=it[-1]+1;
}
indexToRow.resize(c.cols+b.rows);
indexToRow[0]=0;
for (std::vector<unsigned int>::iterator it = indexToRow.begin()+1 ; it != indexToRow.end(); ++it){
*it=it[-1]+1;
}
v=0;
int k=0;
{
double min=DBL_MAX;
for(int i=0;i<b.rows;i++){
if(b(i,b.cols-1)<min){
min=b(i,b.cols-1);
k=i;
}
}
}
if(b(k,b.cols-1)>=0){
N.erase(N.begin());
for (std::vector<unsigned int>::iterator it = indexToRow.begin()+1 ; it != indexToRow.end(); ++it){
--(*it);
}
return 0;
}
Mat_<double> old_c=c.clone();
c=0;
c(0,0)=-1;
for(int i=0;i<b.rows;i++){
b(i,0)=-1;
}
print_simplex_state(c,b,v,N,B);
dprintf(("\tWE MAKE PIVOT\n"));
pivot(c,b,v,N,B,k,0,indexToRow);
print_simplex_state(c,b,v,N,B);
inner_simplex(c,b,v,N,B,indexToRow);
dprintf(("\tAFTER INNER_SIMPLEX\n"));
print_simplex_state(c,b,v,N,B);
unsigned int nsize = (unsigned int)N.size();
if(indexToRow[0]>=nsize){
int iterator_offset=indexToRow[0]-nsize;
if(b(iterator_offset,b.cols-1)>0){
return SOLVELP_UNFEASIBLE;
}
pivot(c,b,v,N,B,iterator_offset,0,indexToRow);
}
vector<int>::iterator iterator;
{
int iterator_offset=indexToRow[0];
iterator=N.begin()+iterator_offset;
std::iter_swap(iterator,N.begin());
SWAP(int,indexToRow[*iterator],indexToRow[0]);
swap_columns(c,iterator_offset,0);
swap_columns(b,iterator_offset,0);
}
dprintf(("after swaps\n"));
print_simplex_state(c,b,v,N,B);
//start from 1, because we ignore x_0
c=0;
v=0;
for(int I=1;I<old_c.cols;I++){
if(indexToRow[I]<nsize){
dprintf(("I=%d from nonbasic\n",I));
int iterator_offset=indexToRow[I];
c(0,iterator_offset)+=old_c(0,I);
print_matrix(c);
}else{
dprintf(("I=%d from basic\n",I));
int iterator_offset=indexToRow[I]-nsize;
c-=old_c(0,I)*b.row(iterator_offset).colRange(0,b.cols-1);
v+=old_c(0,I)*b(iterator_offset,b.cols-1);
print_matrix(c);
}
}
dprintf(("after restore\n"));
print_simplex_state(c,b,v,N,B);
N.erase(N.begin());
for (std::vector<unsigned int>::iterator it = indexToRow.begin()+1 ; it != indexToRow.end(); ++it){
--(*it);
}
return 0;
}
void locallyLinearEmbeddings(const Mat_<float> &samples, int outDim, Mat_<float> &embeddings, int k) {
assert(outDim < samples.cols);
assert(k >= 1);
Mat_<int> nearestNeighbors(samples.rows, k);
// determining k nearest neighbors for each sample
flann::Index flannIndex(samples, flann::LinearIndexParams());
for (int i = 0; i < samples.rows; i++) {
Mat_<int> nearest;
Mat dists;
flannIndex.knnSearch(samples.row(i), nearest, dists, k + 1);
nearest.colRange(1, nearest.cols).copyTo(nearestNeighbors.row(i));
}
// determining weights for each sample
vector<Triplet<double> > tripletList;
tripletList.reserve(samples.rows * k);
for (int i = 0; i < samples.rows; i++) {
Mat_<double> C(k,k);
for (int u = 0; u < k; u++) {
for (int v = u; v < k; v++) {
C(u,v) = (samples.row(i) - samples.row(nearestNeighbors(i,u))).dot(samples.row(i) - samples.row(nearestNeighbors(i,v)));
C(v,u) = C(u,v);
}
}
// regularize when the number of neighbors is greater than the input
// dimension
if (k > samples.cols) {
C = C + Mat_<double>::eye(k,k) * 10E-3 * trace(C)[0];
}
Map<MatrixXd,RowMajor> eigC((double*)C.data, C.rows, C.cols);
LDLT<MatrixXd> solver(eigC);
Mat_<double> weights(k,1);
Map<MatrixXd,RowMajor> eigWeights((double*)weights.data, weights.rows, weights.cols);
eigWeights = solver.solve(MatrixXd::Ones(k,1));
Mat_<double> normWeights;
double weightsSum = sum(weights)[0];
if (weightsSum == 0) {
cout<<"error: cannot reconstruct point "<<i<<" from its neighbors"<<endl;
exit(EXIT_FAILURE);
}
normWeights = weights / weightsSum;
for (int j = 0; j < k; j++) {
tripletList.push_back(Triplet<double>(nearestNeighbors(i,j), i, normWeights(j)));
}
}
SparseMatrix<double> W(samples.rows, samples.rows);
W.setFromTriplets(tripletList.begin(), tripletList.end());
// constructing vectors in lower dimensional space from the weights
VectorXd eigenvalues;
MatrixXd eigenvectors;
LLEMult mult(&W);
symmetricSparseEigenSolver(samples.rows, "SM", outDim + 1, samples.rows, eigenvalues, eigenvectors, mult);
embeddings = Mat_<double>(samples.rows, outDim);
if (DEBUG_LLE) {
cout<<"actual eigenvalues : "<<eigenvalues<<endl;
cout<<"actual : "<<endl<<eigenvectors<<endl;
MatrixXd denseW(W);
MatrixXd tmp = MatrixXd::Identity(W.rows(), W.cols()) - denseW;
MatrixXd M = tmp.transpose() * tmp;
SelfAdjointEigenSolver<MatrixXd> eigenSolver(M);
MatrixXd expectedEigenvectors = eigenSolver.eigenvectors();
cout<<"expected eigenvalues : "<<eigenSolver.eigenvalues()<<endl;
cout<<"expected : "<<endl<<expectedEigenvectors<<endl;
}
for (int i = 0; i < samples.rows; i++) {
for (int j = 0; j < outDim; j++) {
embeddings(i,j) = eigenvectors(i, j + 1);
}
}
}
/**
* @param avgSParam - input mean shape parameters
* @param icovSParam - input covariance matrix of shape parameters
* @param avgTParam - input mean texture parameters
* @param icovTParam - input covariance matrix of texture parameters
* @param iSParams - input the vector of multiple input shape parameters
* @param iTParams - input the vector of multiple input texture parameter
* @param ShapeDistMean - input mean texture parameters
* @param ShapeDistStddev - input covariance matrix of texture parameters
* @param TextureDistMean - input the input shape parameter
* @param TextureDistStddev - input the input texture parameter
* @param WeakFitting - input only shape parameter is used?
* @return whether the fitting is acceptable
*/
bool CRecognitionAlgs::CalcFittingEffect4ImageSequence(
const Mat_<float>& avgSParam,
const Mat_<float>& icovSParam,
const Mat_<float>& avgTParam,
const Mat_<float>& icovTParam,
const Mat_<float>& iSParams,
const Mat_<float>& iTParams,
const Scalar& ShapeDistMean,
const Scalar& ShapeDistStddev,
const Scalar& TextureDistMean,
const Scalar& TextureDistStddev,
bool WeakFitting )
{
assert(iSParams.rows == iTParams.rows);
unsigned int NbOfSamples = iSParams.rows;
vector<float> sDists, tDists;
sDists.resize(NbOfSamples);
tDists.resize(NbOfSamples);
for(unsigned int i = 0; i < NbOfSamples; ++i)
{
CRecognitionAlgs::CalcFittingEffect4StaticImage(
avgSParam,
icovSParam,
avgTParam,
icovTParam,
iSParams.row(i),
iTParams.row(i),
ShapeDistMean,
ShapeDistStddev,
TextureDistMean,
TextureDistStddev,
sDists[i],
tDists[i],
WeakFitting );
}
unsigned int NbOfGood1 = 0;
unsigned int NbOfGood2 = 0;
for(unsigned int i = 0; i < NbOfSamples; ++i)
{
if( ( fabs( sDists[i] - ShapeDistMean.val[0] )
< 1.5f * ShapeDistStddev.val[0] ) )
{
NbOfGood1++;
if( ( fabs( tDists[i] - TextureDistMean.val[0] )
< 3.0f*TextureDistStddev.val[0] ) )
{
NbOfGood2++;
}
}
}
if(WeakFitting)
{
if(NbOfGood1 >= (unsigned int )(0.75*NbOfSamples) )
return true;
else
return false;
}
else
{
if(NbOfGood2 >= (unsigned int )(0.75*NbOfGood1) )
return true;
else
return false;
}
}
void NNLSOptimizer::estimateModelParameters(const vector<Point2f> &featurePoints,
const Mat &cameraMatrix, const Mat& lensDist,
Face* face_ptr,const vector<int> &point_indices,
const Mat &rotation, const Mat &translation,
vector<double> &weights_id, vector<double> &weights_ex)
{
Mat_<double> weakCamera(2,3);
//matrices for A_ex * w_ex = f and A_id * w_id = f
Mat_<double> A_ex , A_id;
//matrix Z = kron(weights, Identity_matrix)
Mat_<double> Z_ex, Z_id;
Mat_<double> ZU;
Mat_<double> pr, Pt, PRM, prm;
//core tensor rows
Mat_<double> Mi;
//featurePoints converted to 2x1 matrices
Mat_<double> fi;
Mat_<double> f;
Mat_<double> O;
int index = 0;
const int exr_size = model->getExpSize();
const int id_size = model->getIdSize();
double *w_id = new double[id_size];
double *w_exp = new double[exr_size];
Mat_<double> rmatrix;
Mat_<double> x_t(1,exr_size);
Mat_<double> y_t(1,id_size);
Mat_<double> x(exr_size,1);
Mat_<double> y(id_size,1);
//used for x_t*U_ex and y_t*U_id
Mat_<double> lin_comb_x(exr_size,1);
Mat_<double> lin_comb_y(id_size,1);
double Z_avg;
double average_depth;
Point3f p;
Mat_<double> proP;
Mat_<double> pM(3,1);
Rodrigues(rotation,rmatrix);
//get weights from the current face instance
face_ptr->getWeights(w_id,id_size,w_exp,exr_size);
average_depth = face_ptr->getAverageDepth();
pM(0,0) = 1;
pM(1,0) = 1;
pM(2,0) = average_depth;
proP = cameraMatrix*rmatrix*pM;
proP = proP + cameraMatrix*translation;
Z_avg = proP(0,2);
/***************************************************************/
/*create weak-perspecitve camera matrix from camera matrix*/
/***************************************************************/
for(int i=0;i<2;i++)
for(int j=0;j<3;j++)
weakCamera(i,j) = cameraMatrix.at<double>(i,j);
f = Mat_<double>(featurePoints.size()*2,1);
fi = Mat_<double>(2,1);
//precompute translation
Pt = (1./translation.at<double>(2,0)) * (weakCamera*translation);
//preprocess points and core tensor rows
//for points subtract translation too
for(unsigned int i=0;i<featurePoints.size();i++)
{
fi = Mat_<double>(2,1);
fi(0,0) = featurePoints[i].x;
fi(1,0) = featurePoints[i].y;
fi = fi - Pt;
f.row(2*i) = fi.row(0) + 0.0;
f.row(2*i+1) = fi.row(1) + 0.0;
}
pr = (1.0/Z_avg)*weakCamera*rmatrix;
PRM = Mat_<double>(2*featurePoints.size(),exr_size*id_size);
prm = Mat_<double>(2,exr_size*id_size);
for(unsigned int i=0;i<point_indices.size();++i)
{
index = point_indices[i];
prm = pr*M[index];
PRM.row(2*i) = prm.row(0) + 0.0;
PRM.row(2*i+1) = prm.row(1) + 0.0;
}
//do not use the guess in the first frame but do for every following frame
for(int i=0;i<exr_size;i++)
x_t(0,i) = x(i,0) = w_exp[i];
for(int i=0;i<id_size;i++)
y_t(0,i) = y(i,0) = w_id[i];
A_ex = Mat_<double>::zeros(2*featurePoints.size(),exr_size);
A_id = Mat_<double>::zeros(2*featurePoints.size(),id_size);
for(int count = 0;count < max_iterations; count++)
{
//put the guesses into matrix y and x
y_t = y.t();
lin_comb_y = (y_t*u_id).t();
Z_ex = Matrix::kronecker(lin_comb_y,Mat_<double>::eye(exr_size,exr_size));
ZU = Z_ex*(u_ex.t());
A_ex = PRM*ZU;
this->scannls(A_ex,f,x);
x_t = x.t();
lin_comb_x = (x_t*u_ex).t();
Z_id = Matrix::kronecker(Mat_<double>::eye(id_size,id_size),lin_comb_x);
ZU = Z_id*(u_id.t());
/* compute the formula :
* Sum( U*Z'*Mi'*R'*PW'*PW*R*Mi*Z*U' )*y = Sum( U*Z'*Mi'*R'*PW'*fi - (1/tz)*U*Z'*Mi'*R'*PW'*PW'*t )
*/
A_id = PRM*ZU;
// Mat_<double> temp = (A_id*y - f);
// Mat_<double> e = temp.t()*temp;
// cout << "id, error before " << e(0,0)<<endl;
this->scannls(A_id,f,y);
// temp = (A_id*y - f);
// e = temp.t()*temp;
// cout << "id, error after " << e(0,0)<<endl;
}
for(int i=0;i<exr_size;i++){
w_exp[i] = x(i,0);
}
for(int i=0;i<id_size;i++){
w_id[i] = y(i,0);
}
//we cannot normalize because then we lose 1/z_avg which is the scale
// Vector3::normalize(w_exp, exr_size);
// Vector3::normalize(w_id, id_size);
for(int i=0;i<exr_size;i++){
weights_ex.push_back(w_exp[i]);
}
for(int i=0;i<id_size;i++){
weights_id.push_back(w_id[i]);
}
face_ptr->setNewIdentityAndExpression(w_id,w_exp);
face_ptr->setAverageDepth(average_depth);
prm.release();
PRM.release();
ZU.release();
Z_id.release();
A_id.release();
Z_ex.release();
A_ex.release();
f.release();
delete[] w_id;
delete[] w_exp;
}