Compact & Versatile Geometric Models for 3D Shape Recovery from Medical Images

这项研究的目标是研究一种方案，该方案允许通过紧凑和通用的几何模型来表示2D和3D形状，该几何模型可以对大类形状进行建模，并且易于稳定和高效的数值实现。这些模型将能够表示其拓扑结构事先未知的形状。传统上，几何模型非常适合表示全局形状，但不适合表示局部细节。在这项工作中，研究了一种强大的几何形状重塑方案，该方案允许用局部细节来表示全局形状，并允许通过基于物理的控制和拓扑变化来进行模型塑造。这些模型混合了几何模型和基于物理的模型，在精神上与现在流行的可变形超二次曲面“相似”，但在表现力和数值稳定性方面与它们有很大的不同，因此有望获得更大的适用性。

The goal of this research is the investigation of a scheme that allows for the representation of 2D and 3D shapes via compact and versatile geometric models which can model a large class of shapes and are amenable to stable and efficient numerical implementations. The models are to be capable of representing shapes whose topology is not known a priori. Geometric models are traditionally well suited for representing global shapes but not the local details. In this work, a powerful geometric shape meodeling scheme is investigated which allows for the representation of global shapes with local detail and permits model shaping via physics-based control as well as topological changes. These models are a blend of geometric and physics-based models, and are in spirit "similar" to the now popular deformable superquadrics, but differ from them considerably in their expressiveness and numerical stability, thereby promising greater applicability.