A Novel and Effective Approach to Shape Analysis: Nonparametric Representation, De-noising and Change-Point Detection, Based on Singular-Spectrum Analysis

Abstract

This paper proposes new very effective methods for building nonparametric, multi-resolution models of 2D closed contours, based on Singular Spectrum Analysis (SSA). Representation, de-noising and change-point detection to automate the landmark selection are simultaneously addressed in three different settings. The basic one is to apply SSA to a shape signature encoded by sampling a real-valued time series from a radius-vector contour function. However, this is only suited for star-shaped contours. A second setting is to generalize SSA so as to apply to a complex-valued trajectory matrix in order to directly represent the contour as a time series path in the complex plan, along with detecting change-points in a complex-valued time series. A third setting is to consider the pairs (x, y) of coordinates as a co-movement of two real-valued time series and to apply SSA to a trajectory matrix defined in such a way to span both of them.