Fixed storage order bug with Eigen in the shape and blendshape fitting

When switching the shape and blendshape fitting to use the new Eigen models, these matrices weren't correctly mapped to cv::Mat. Eigen uses col-major storage order by default, and OpenCV row-major - so we now convert to a row-major Eigen matrix before mapping to a cv::Mat.
This caused the fitting to produce faulty/meaningless results since the switch to Eigen.
The output of the linear shape and blendshape fitting functions are now again identical before and after the switch to Eigen. (after 50 iterations, the result is marginally different, most likely because of small rounding differences.)

include/eos/fitting/blendshape_fitting.hpp

@@ -67,14 +67,15 @@ inline std::vector<float> fit_blendshapes_to_landmarks_linear(const std::vector<
 	const int num_landmarks = static_cast<int>(landmarks.size());
 
 	// Copy all blendshapes into a "basis" matrix with each blendshape being a column:
-	MatrixXf blendshapes_as_basis = morphablemodel::to_matrix(blendshapes);
+	Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> blendshapes_as_basis = morphablemodel::to_matrix(blendshapes);
+	// Above converts to a RowMajor matrix on return - for now, since the core algorithm still uses cv::Mat (and OpenCV stores data in row-major memory order).
+	Mat blendshapes_basis_as_mat = Mat(blendshapes_as_basis.rows(), blendshapes_as_basis.cols(), CV_32FC1, blendshapes_as_basis.data());
 
 	// $\hat{V} \in R^{3N\times m-1}$, subselect the rows of the eigenvector matrix $V$ associated with the $N$ feature points
 	// And we insert a row of zeros after every third row, resulting in matrix $\hat{V}_h \in R^{4N\times m-1}$:
 	Mat V_hat_h = Mat::zeros(4 * num_landmarks, num_blendshapes, CV_32FC1);
 	int row_index = 0;
 	for (int i = 0; i < num_landmarks; ++i) {
-		Mat blendshapes_basis_as_mat = Mat(blendshapes_as_basis.rows(), blendshapes_as_basis.cols(), CV_32FC1, blendshapes_as_basis.data());
 		Mat basis_rows = blendshapes_basis_as_mat.rowRange(vertex_ids[i] * 3, (vertex_ids[i] * 3) + 3);
 		basis_rows.copyTo(V_hat_h.rowRange(row_index, row_index + 3));
 		row_index += 4; // replace 3 rows and skip the 4th one, it has all zeros
@@ -145,14 +146,15 @@ inline std::vector<float> fit_blendshapes_to_landmarks_nnls(const std::vector<eo
 	const int num_landmarks = static_cast<int>(landmarks.size());
 
 	// Copy all blendshapes into a "basis" matrix with each blendshape being a column:
-	MatrixXf blendshapes_as_basis = morphablemodel::to_matrix(blendshapes);
+	Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> blendshapes_as_basis = morphablemodel::to_matrix(blendshapes);
+	// Above converts to a RowMajor matrix on return - for now, since the core algorithm still uses cv::Mat (and OpenCV stores data in row-major memory order).
+	Mat blendshapes_basis_as_mat = Mat(blendshapes_as_basis.rows(), blendshapes_as_basis.cols(), CV_32FC1, blendshapes_as_basis.data());
 
 	// $\hat{V} \in R^{3N\times m-1}$, subselect the rows of the eigenvector matrix $V$ associated with the $N$ feature points
 	// And we insert a row of zeros after every third row, resulting in matrix $\hat{V}_h \in R^{4N\times m-1}$:
 	Mat V_hat_h = Mat::zeros(4 * num_landmarks, num_blendshapes, CV_32FC1);
 	int row_index = 0;
 	for (int i = 0; i < num_landmarks; ++i) {
-		Mat blendshapes_basis_as_mat = Mat(blendshapes_as_basis.rows(), blendshapes_as_basis.cols(), CV_32FC1, blendshapes_as_basis.data());
 		Mat basis_rows = blendshapes_basis_as_mat.rowRange(vertex_ids[i] * 3, (vertex_ids[i] * 3) + 3);
 		basis_rows.copyTo(V_hat_h.rowRange(row_index, row_index + 3));
 		row_index += 4; // replace 3 rows and skip the 4th one, it has all zeros

include/eos/fitting/linear_shape_fitting.hpp

@@ -75,7 +75,8 @@ inline std::vector<float> fit_shape_to_landmarks_linear(const morphablemodel::Mo
 	Mat V_hat_h = Mat::zeros(4 * num_landmarks, num_coeffs_to_fit, CV_32FC1);
 	int row_index = 0;
 	for (int i = 0; i < num_landmarks; ++i) {
-		auto basis_rows_ = morphable_model.get_shape_model().get_rescaled_pca_basis_at_point(vertex_ids[i]); // In the paper, the orthonormal basis might be used? I'm not sure, check it. It's even a mess in the paper. PH 26.5.2014: I think the rescaled basis is fine/better.
+		Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> basis_rows_ = morphable_model.get_shape_model().get_rescaled_pca_basis_at_point(vertex_ids[i]); // In the paper, the orthonormal basis might be used? I'm not sure, check it. It's even a mess in the paper. PH 26.5.2014: I think the rescaled basis is fine/better.
+		// Above converts to a RowMajor matrix on return - for now, since the core algorithm still uses cv::Mat (and OpenCV stores data in row-major memory order).
 		Mat basis_rows = Mat(basis_rows_.rows(), basis_rows_.cols(), CV_32FC1, basis_rows_.data());
 		//basisRows.copyTo(V_hat_h.rowRange(rowIndex, rowIndex + 3));
 		basis_rows.colRange(0, num_coeffs_to_fit).copyTo(V_hat_h.rowRange(row_index, row_index + 3));