Bazin Pierre-Louis, Ellingsen Lotta Maria, Pham Dzung L
Johns Hopkins University, Baltimore, USA.
Inf Process Med Imaging. 2007;20:211-22. doi: 10.1007/978-3-540-73273-0_18.
A common goal in deformable registration applications is to produce a spatial transformation that is diffeomorphic, thereby preserving the topology of structures being transformed. Because this constraint is typically enforced only on the continuum, however, topological changes can still occur within discretely sampled images. This work discusses the notion of homeomorphisms in digital images, and how it differs from the diffeomorphic/homeomorphic concepts in continuous spaces commonly used in medical imaging. We review the differences and problems brought by considering functions defined on a discrete grid, and propose a practical criterion for enforcing digital homeomorphisms in the context of atlas-based segmentation.
可变形配准应用中的一个常见目标是生成一个微分同胚的空间变换，从而保留被变换结构的拓扑结构。然而，由于这种约束通常仅在连续统上实施，离散采样图像中仍可能发生拓扑变化。本文讨论了数字图像中同胚的概念，以及它与医学成像中常用的连续空间中的微分同胚/同胚概念有何不同。我们回顾了考虑在离散网格上定义的函数所带来的差异和问题，并提出了在基于图谱的分割背景下实施数字同胚的实用标准。
