Multilinear Model Estimation with L 2-Regularization

Many challenging computer vision problems can be formulated as a multilinear model. Classical methods like principal component analysis use singular value decomposition to infer model parameters. Although it can solve a given problem easily if all measurements are known this prerequisite is usually violated for computer vision applications. In the current work, a standard tool to estimate singular vectors under incomplete data is reformulated as an energy minimization problem. This admits for a simple and fast gradient descent optimization with guaranteed convergence. Furthermore, the energy function is generalized by introducing an L-regularization on the parameter space. We show a quantitative and qualitative evaluation of the proposed approach on an application from structure-from-motion using synthetic and real image data, and compare it with other works.