Facial Landmark Detection Using Supervised Descent Method

The patent segments the complex non-linear least squares optimization problem into multiple linear regression steps. Instead of solving one complex non-linear problem, the method performs several simpler linear regressions sequentially, where each step refines the landmark positions. This segmentation transforms the computationally intensive 2nd order descent into multiple manageable 1st order linear steps, achieving real-time performance while maintaining robustness.

The patent uses computationally inexpensive linear regression models that can be quickly computed and discarded, replacing the need for expensive 2nd order descent methods. Each linear regression step uses simple matrix operations that are computationally lightweight, allowing rapid iteration and convergence without the heavy computational burden of Hessian matrix calculations.

The patent replaces the mechanical search process (searching for each landmark along the diagonal) with a mathematical substitution approach using linear regression. Instead of physically searching through shape subspaces, the method uses learned linear models that directly predict landmark positions based on input features, dramatically speeding up processing while maintaining adaptability to perspective and 3D variations.

The patent performs preliminary action by pre-training linear regression models on diverse facial images that capture various perspectives and 3D movements. These pre-learned models encode the relationships between image features and landmark positions under different transformations, allowing the system to handle perspective projection and 3D movements efficiently during runtime without performing complex searches.