Topology-preserving geometric deformable models (TGDMs) are used to segment objects that have a known topology. Their accuracy is inherently limited, however, by the resolution of the underlying computational grid. Although this can be overcome by using fine-resolution grids, both the computational cost and the size of the resulting contour increase dramatically. In order to maintain computational efficiency and to keep the contour size manageable, we have developed a new framework, termed QTGDMs, for topology-preserving geometric deformable models on balanced quadtree grids (BQGs). In order to do this, definitions and concepts from digital topology on regular grids were extended to BQGs so that characterization of simple points could be made. Other issues critical to the implementation of geometric deformable models are also addressed and a strategy for adapting a BQG during contour evolution is presented. We demonstrate the performance of the QTGDM method using both mathematical phantoms and real medical images.

Geometric deformable models based on the level set method have become very popular. To overcome an inherent limitation in accuracy while maintaining computational efficiency, adaptive grid techniques using local grid refinement have been developed for use with these models. However, this strategy requires a very complex data structure, yields large numbers of contour points, and is inconsistent with our previously presented topology-preserving geometric deformable model (TGDM). In this paper, we incorporate an alternative adaptive grid technique called the moving grid method into the geometric deformable model framework. We find that it is simpler to implement than grid refinement, requiring no large, complex, hierarchical data structures. It also limits the number of contour vertices in the final contour and supports the incorporation of the topology-preserving constraint of TGDM. After presenting the algorithm, we demonstrate its performance using both simulated and real images.

Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models-the ability to automatically handle topology changes-turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved. We present a new class of geometric deformable models designed using a novel topology-preserving level set method, which achieves topology preservation by applying the simple point concept from digital topology. These new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces. Moreover, since the topology-preserving constraint is enforced efficiently through local computations, the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models. Several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm.

Reconstructing an accurate and topologically correct representation of the cortical surface of the brain is an important objective in various neuroscience applications. Most cortical surface reconstruction methods either ignore topology or correct it using manual editing or methods that lead to inaccurate reconstructions. Shattuck and Leahy recently reported a fully automatic method that yields a topologically correct representation with little distortion of the underlying segmentation. We provide an alternate approach that has several advantages over their approach, including the use of arbitrary digital connectivities, a flexible morphology-based multiscale approach, and the option of foreground-only or background-only correction. A detailed analysis of the method's performance on 15 magnetic resonance brain images is provided.

Active contour and surface models, also known as deformable models, constitute a class of powerful segmentation techniques. Geometric deformable models implemented via level-set methods have advantages over parametric ones due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models, the ability to automatically handle topology changes, turns out to be a liability in applications where the objects to be segmented have a known topology that must be preserved. In this paper, we present a geometric deformable model that preserves topology using the simple point concept from digital topology. This algorithm maintains the other advantages of standard geometric deformable models including sub-pixel accuracy and production of nonintersecting curves (or surfaces). Several experiments on simulated and real data are provided to demonstrate the performance of the proposed algorithm.