Time-Varying Linear Autoregressive Models for Segmentation

Tracking highly deforming structures in space and time arises in numerous applications in computer vision. Static Models are often referred to as linear combinations of a mean model and modes of variation learned from training examples. In Dynamic Modeling, the shape is represented as a function of shapes at previous time steps. In this paper, we introduce a novel technique that uses the spatial and the temporal information on the object deformation. We reformulate tracking as a high order time series prediction mechanism that adapts itself on-line to the newest results. Samples (toward dimensionality reduction) are represented in an orthogonal basis, and are introduced in an auto-regressive model that is determined through an optimization process in appropriate metric spaces. Toward capturing evolving deformations as well as cases that have not been part of the learning stage, a process that updates on-line both the orthogonal basis decomposition and the parameters of the autoregressive model is proposed. Experimental results with a nonstationary dynamic system prove adaptive AR models give better results than both stationary models and models learned over the whole sequence.