Statistical analysis of locally parameterized shapes

TL;DR

This paper introduces a hierarchical local shape parameterization method that avoids alignment issues inherent in global coordinate systems, improving statistical shape analysis accuracy and robustness.

Contribution

A novel local coordinate system-based shape parameterization that is translation and rotation invariant, reducing alignment-induced errors in shape analysis.

Findings

The new method avoids false shape differences caused by alignment.

It improves shape deformation and simulation capabilities.

Demonstrated effectiveness on simulated data and Parkinson's disease hippocampi.

Abstract

The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most commonly used method and state of the art. In this work, we uncover that alignment might seriously affect the statistical analysis. For example, alignment can induce false shape differences and lead to misleading results and interpretations. We propose a novel hierarchical shape parameterization based on local coordinate systems. The local parameterized shapes are translation and rotation invariant. Thus, the inherent alignment problems from the commonly used global coordinate system for shape representation can be avoided using this parameterization. The new parameterization is also superior for shape deformation and simulation. The method's power is demonstrated on the hypothesis testing of simulated data as well as the left hippocampi of patients with Parkinson's disease and controls.