Added a parameter to the linear shape fitting to start it from a different face than the mean-face

This is used for example when we fit blendshapes and want to fit the PCA shape given current blendshape parameters.

include/eos/fitting/linear_shape_fitting.hpp

@@ -50,13 +50,14 @@ namespace eos {
  * @param[in] affine_camera_matrix A 3x4 affine camera matrix from model to screen-space (should probably be of type CV_32FC1 as all our calculations are done with float).
  * @param[in] landmarks 2D landmarks from an image to fit the model to.
  * @param[in] vertex_ids The vertex ids in the model that correspond to the 2D points.
+ * @param[in] base_face The base or reference face from where the fitting is started. Usually this would be the models mean face.
  * @param[in] lambda The regularisation parameter (weight of the prior towards the mean).
  * @param[in] num_coefficients_to_fit How many shape-coefficients to fit (all others will stay 0). Not tested thoroughly.
  * @param[in] detector_standard_deviation The standard deviation of the 2D landmarks given (e.g. of the detector used), in pixels.
  * @param[in] model_standard_deviation The standard deviation of the 3D vertex points in the 3D model, projected to 2D (so the value is in pixels).
  * @return The estimated shape-coefficients (alphas).
  */
-inline std::vector<float> fit_shape_to_landmarks_linear(morphablemodel::MorphableModel morphable_model, cv::Mat affine_camera_matrix, std::vector<cv::Vec2f> landmarks, std::vector<int> vertex_ids, float lambda=3.0f, boost::optional<int> num_coefficients_to_fit=boost::optional<int>(), boost::optional<float> detector_standard_deviation=boost::optional<float>(), boost::optional<float> model_standard_deviation=boost::optional<float>())
+inline std::vector<float> fit_shape_to_landmarks_linear(morphablemodel::MorphableModel morphable_model, cv::Mat affine_camera_matrix, std::vector<cv::Vec2f> landmarks, std::vector<int> vertex_ids, cv::Mat base_face, float lambda=3.0f, boost::optional<int> num_coefficients_to_fit=boost::optional<int>(), boost::optional<float> detector_standard_deviation=boost::optional<float>(), boost::optional<float> model_standard_deviation=boost::optional<float>())
 {
 	using cv::Mat;
 	assert(landmarks.size() == vertex_ids.size());
@@ -101,7 +102,8 @@ inline std::vector<float> fit_shape_to_landmarks_linear(morphablemodel::Morphabl
 	// The mean, with an added homogeneous coordinate (x_1, y_1, z_1, 1, x_2, ...)^t
 	Mat v_bar = Mat::ones(4 * num_landmarks, 1, CV_32FC1);
 	for (int i = 0; i < num_landmarks; ++i) {
-		cv::Vec4f model_mean = morphable_model.get_shape_model().get_mean_at_point(vertex_ids[i]);
+		//cv::Vec4f model_mean = morphable_model.get_shape_model().get_mean_at_point(vertex_ids[i]);
+		cv::Vec4f model_mean(base_face.at<float>(vertex_ids[i] * 3), base_face.at<float>(vertex_ids[i] * 3 + 1), base_face.at<float>(vertex_ids[i] * 3 + 2), 1.0f);
 		v_bar.at<float>(4 * i, 0) = model_mean[0];
 		v_bar.at<float>((4 * i) + 1, 0) = model_mean[1];
 		v_bar.at<float>((4 * i) + 2, 0) = model_mean[2];