Nondeterministic Deformation Analysis Using Quasiconformal Geometry

Abstract

Deformation analysis is crucial in many applications, especially in medical image analysis. Analyzing the deformation pattern of anatomical structures provides important information for disease analysis. With degraded images or uncertainties, getting a deterministic solution of the deformation is challenging. In some cases, there may also be multiple solutions with different probabilities. As such, it is important to analyze the probability distribution of deformations, given data information with uncertainty. In this work, we propose to use computational Quasiconformal (QC) Teichmuller theories to parameterize the space of deformations. A distribution over the space of special features, called the QC features, can be computed and applied for deformation analysis. Extensive experiments are carried out on both synthetic data and real medical images, which demonstrate the efficacy of the proposed framework.