Core Shape modelling of a set of curves

Abstract

A new method for shape and time variability modelling of a set of curves is presented. Shape variability is captured via warping functions after time realignment of the curves. These warping functions relate normalized integrals but their meaning is different from those described in previously proposed methods for curve registration. For this purpose, a semi-parametric model, namely the Core Shape (CS) model, is proposed for shape variability characterization of a sample of curves. The curve variability is modelled as the composition of a polynomial term that accounts for time support variability and another term that accounts for intrinsic shape variability of the normalized integrals. This formalism provides specific statistical tools for shape dispersion analysis which are typically a mean shape curve, the Core Shape (CS) curve, and a shape distance, the so-called CS distance, according to the degree of specific polynomial time functions. These tools are invariant to time support variability and allow a direct access to intrinsic shape variability obtained at this polynomial degree. Also, a method for estimating shape parameters and functions of the model is presented and illustrated with simulated data. The influence of the polynomial choice is analyzed by simulation. Finally, usefulness of the proposed model for functional curve analysis is demonstrated through a real case study on Auditory Cortex Responses (ACR) analysis. A comparative study with a Curve Registration (CR) approach, namely the Self-Modelling Registration (SMR) method, is performed to better define differences in characterizing time and shape variability.