Geometric deformable models using the level set method.

摘要

Geometric deformable models for active contours have brought tremendous impact to classical problems in image processing such as providing ways to devise efficient computational algorithms for automatic segmentation. This is achieved by using the level set method, which allows handling automatic changes in topology while providing a frame-work for very fast numerical schemes. However, topological flexibility is not desired when an object with known topology is sought. It is natural to capture the target in a way that gives the correct topology. A geometric deformable model with topology preserving is developed that can guarantee the topology will be preserved while all the computational advantages of the level set approach are maintained.; A key issue in object detection using the shape of the object's boundary and surface reconstruction using slice contours is the ability to identify the complete boundaries of the segmented objects in the scene. The segmentation results provided by geometric deformable models are usually dependent on the contour initialization, and in most cases, the results of the segmentation will only provide partial objects boundaries. A new method based on digital topology is proposed to detect the complete boundary information of the segmented objects. By carrying out a topological analysis of the objects, this method can provide the right initialization that can capture all the boundaries of the objects in certain cases.; In an effort to facilitate a clear and full understanding of these powerful applied mathematical tools, this thesis tries to explore these geometric deformable models and their implementations. The deformable model with topology analysis and some experimental results are also presented. To have a more clear picture on these works, the algorithms of surface reconstruction and volume rendering are simply discussed and implemented on the resulting data sets from geometric deformable models.