Statistical Shape Model of Nested Structures Based on the Level Set

We propose a method for constructing a multi-shape 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 and ventricle. Most existing multi-shape SSMs can be used to describe these nested shapes; however, none of them guarantees a correct inclusive relationship. The basic concept of the proposed method is to describe nested shapes by applying different thresholds to a single continuous real-valued function in an image space. We demonstrate that there exists a one-to-one mapping from an arbitrary pair of nested shapes to this type of function. We also demonstrate that this method can be easily extended to represent three or more nested structures. We demonstrate the effectiveness of proposed SSM using brain and ventricle volumes obtained from particular stages of human embryos. 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 multi-shape SSMs demonstrates the superiority of the proposed method.