Supervised Motion Segmentation by Spatial-Frequential Analysis and Dynamic Sliced Inverse Regression

In this paper, we propose a new method for supervised motion segmentation based on spatial-frequential analysis and dimension reduction techniques. A sequence of images could contain non-ridge motion in the region of interest and the segmentation of these moving objects with deformation is challenging. The aim is to extract feature vectors that capture the spatialfrequential information in the training set and then to monitor the variations of the feature vectors over time in the test set. Given successive images in the training set, we consider a dynamical model that extends the sliced inverse regression in Li (1991). It is designed to capture the intrinsic dimension of feature vectors that holds over a local time scale. These projected features are then used to classify training images and predict forthcoming images in the test set into distinct categories. Theoretic properties are addressed. Simulation studies and clinical studies of a sequence of magnetic resonance images are reported, which confirm the practical feasibility of this new approach.