A SSA-Based New Framework Allowing for Smoothing and Automatic Change-Points Detection in the Fuzzy Closed Contours of 2D Fuzzy Objects

摘要

The aim of this paper is to propose a new framework, based on Singular-Spectrum Analysis, allowing for smoothing and automatic change-point detection in the fuzzy closed contours of 2D fuzzy objects. The representation of fuzzy objects is first addressed, by distinguishing between fuzzy regions and fuzzy closed curves. Fuzzy shape signatures are derived in special cases, from which fuzzy time series can be subsequently sampled. Geodesic and Euclidean fuzzy paths and distances between two points in a fuzzy region are next contrasted. Finally, a novel approach to decomposing and reconstructing a fuzzy shape and to automatic change-point detection is proposed, based on a generalization of Singular-Spectrum Analysis so as to deal with complex-valued trajectory matrices. The coordinates themselves, represented as complex numbers are used as a shape signature. This approach is suitable for non-convex and non-star-shaped fuzzy contours.