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

本研究的目标是调查的计划，允许通过紧凑和通用的几何模型，可以模拟一个大类的形状，并服从稳定和有效的数值实现的2D和3D形状的表示。 这些模型将能够表示先验未知拓扑结构的形状。 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，一个功能强大的几何形状meodeling计划进行调查，它允许表示的全球形状与局部细节，并允许通过基于物理的控制以及拓扑变化的模型成形。 这些模型是一个混合的几何和物理为基础的模型，并在精神上“类似”，现在流行的变形超二次曲面，但从他们的表现力和数值稳定性，从而有希望更大的适用性显着不同。

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.