A Statistical Model for Smooth Shapes in Kendall Shape Space

Abstract

AbstractThis paper proposes a novel framework for learning a statistical shape model from image data, automatically without manual annotations. The framework proposes a generative model for image data of individuals within a group, relying on a model of group shape variability. The framework represents shape as an equivalence class of pointsets and models group shape variability in Kendall shape space. The proposed model captures a novel shape-covariance structure that incorporates shape smoothness, relying on Markov regularization. Moreover, the framework employs a novel model for data likelihood, which lends itself to an inference algorithm of low complexity. The framework infers the model via a novel expectation maximization algorithm that samples smooth shapes in the Riemannian space. Furthermore, the inference algorithm normalizes the data (via similarity transforms) by optimal alignment to (sampled) individual shapes. Results on simulated and clinical data show that the proposed framework learns better-fitting compact statistical models as compared to the state of the art.KeywordsStatistical shape modelKendall shape spacegeodesic distanceMarkov modelshape samplingshape alignmentimage data normalization