Conditional Visual Tracking in Kernel Space

Abstract

We present a conditional temporal probabilistic framework for recon- structing 3D human motion in monocular video based on descriptors en- coding image silhouette observations. For computational efficiency we restrict visual inference to low-dimensional kernel induced non-linear state spaces. Our methodology (kBME) combines kernel PCA-based non-linear dimensionality reduction (kPCA) and Conditional Bayesian Mixture of Experts (BME) in order to learn complex multivalued pre- dictors between observations and model hidden states. This is necessary for accurate, inverse, visual perception inferences, where several proba- ble, distant 3D solutions exist due to noise or the uncertainty of monoc- ular perspective projection. Low-dimensional models are appropriate because many visual processes exhibit strong non-linear correlations in both the image observations and the target, hidden state variables. The learned predictors are temporally combined within a conditional graphi- cal model in order to allow a principled propagation of uncertainty. We study several predictors and empirically show that the proposed algo- rithm positively compares with techniques based on regression, Kernel Dependency Estimation (KDE) or PCA alone, and gives results competi- tive to those of high-dimensional mixture predictors at a fraction of their computational cost. We show that the method successfully reconstructs the complex 3D motion of humans in real monocular video sequences.