Motion estimation using Statistical Learning Theory

This paper describes a novel application of Statistical Learning Theory (SLT) to single motion estimation and tracking. The problem of motion estimation can be related to statistical model selection, where the goal is to select one (correct) motion model from several possible motion models, given finite noisy samples. SLT, also known as Vapnik-Chervonenkis (VC), theory provides analytic generalization bounds for model selection, which have been used successfully for practical model selection. This paper describes a successful application of an SLT-based model selection approach to the challenging problem of estimating optimal motion models from small data sets of image measurements (flow). We present results of experiments on both synthetic and real image sequences for motion interpolation and extrapolation; these results demonstrate the feasibility and strength of our approach. Our experimental results show that for motion estimation applications, SLT-based model selection compares favorably against alternative model selection methods, such as the Akaike's fpe, Schwartz' criterion (sc), Generalized Cross-Validation (gcv), and Shibata's Model Selector (sms). The paper also shows how to address the aperture problem using SLT-based model selection for penalized linear (ridge regression) formulation.