Random Subspace Supervised Descent Method for Regression Problems in Computer Vision

Supervised Descent Method (SDM) has shown good performance in solving non-linear least squares problems in computer vision, giving state of the art results for the problem of face alignment. However, when SDM learns the generic descent maps, it is very difficult to avoid over-fitting due to the high dimensionality of the input features. In this paper we propose a Random Subspace SDM (RSSDM) that maintains the high accuracy on the training data and improves the generalization accuracy. Instead of using all the features for descent learning at each iteration, we randomly select sub-sets of the features and learn an ensemble of descent maps in the corresponding subspaces, one in each subspace. Then, we average the ensemble of descents to calculate the update of the iteration. We test the proposed methods on two representative regression problems, namely, 3D pose estimation and face alignment and show that RSSDM consistently outperforms SDM in both tasks in terms of accuracy (e.g., RSSDM is able to localize 4% more landmarks at error level of 0.1 on the challenging iBug dataset). RSSDM also holds several useful generalization properties: 1) it is more effective when the number of training samples is small-with 3 Monte-Carlo permutations RSSDM can achieve similar performance to SDM with 9 Monte-Carlo permutations; 2) it is less sensitive to the changes of the strength of the regularization-when the regularization parameter is changed to 10 times larger, the mean error increases 9.0% for SDM vs. 3.4% for RSSDM.