Statistical analysis of locally parameterized shapes
This addresses alignment-induced errors in statistical shape analysis, which is crucial for applications like medical imaging and shape classification, though it is incremental as it builds on existing parameterization methods.
The authors tackled the problem that Procrustes alignment in shape analysis can induce false differences and misleading results, and they proposed a novel hierarchical shape parameterization based on local coordinate systems that avoids these issues, demonstrating its effectiveness on simulated data and Parkinson's disease patient hippocampi.
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.