Principal Geodesic Analysis for the Study of Nonlinear Minimum Description Length

Abstract

The essential goal for Statistical Shape Model (SSM) is to describe and extract the shape variations from the landmarks cloud. A standard technique for such variation extraction is by using Principal Component Analysis (PCA). However, PCA assumes that variations are linear in Euclidean vector space, which is not true or insufficient on many medical data. Therefore, we developed a new Geodesic Active Shape (GAS) mode by using Principal Geodesic Analysis (PGA) as an alternative of PCA. The new GAS model is combined with Minimum Description Length approach to find correspondence points across datasets automatically. The results are compared between original MDL and our proposed GAS MDL approach by using the measure of Specificity. Our preliminary results showed that our proposed GAS model achieved better scores on both datasets. Therefore, we conclude that our GAS model can capture shape variations reasonably more specifically than the original Active Shape Model (ASM). Further, analysis on the study of facial profiles dataset showed that our GAS model did not encounter the so-called "Pile Up" problem, whereas original MDL did.