Level set distribution model of nested structures using logarithmic transformation.

Abstract

In this study, we propose a method for constructing a multishape statistical shape model (SSM) for nested structures such that each is a subset or superset of another. The proposed method has potential application to any pair of shapes with an inclusive relationship. These types of shapes are often found in anatomy, such as the brain surface and ventricles. The main contribution of this paper is to introduce a new shape representation called log-transformed level set function (LT-LSF), which has a vector space structure that preserves the correct inclusive relationship of the nested shape. In addition, our method is applicable to an arbitrary number of nested shapes. We demonstrate the effectiveness of the proposed shape representation by modeling the anatomy of human embryos, including the brain, ventricles, and choroid plexus volumes. The performance of the SSM was evaluated in terms of generalization and specificity ability. Additionally, we measured leakage criteria to assess the ability to preserve inclusive relationships. A quantitative comparison of our SSM with conventional multishape SSMs demonstrates the superiority of the proposed method.