In the past four decades, computerized image segmentation has played an increasingly important role in medical imaging. Segmented images are now used routinely in a multitude of different applications, such as the quantification of tissue volumes, diagnosis, localization of pathology, study of anatomical structure, treatment planning, partial volume correction of functional imaging data, and computer-assisted surgery. Image segmentation remains a difficult task, however, due to both the tremendous variability of object shapes and the variation in image quality. In particular, medical images are often corrupted by noise and sampling artifacts, which can cause considerable difficulties when applying classical segmentation techniques such as edge detection and thresholding. As a result, these techniques either fail completely or require some kind of postprocessing step to remove invalid object boundaries in the segmentation results.
To address these difficulties, deformable models have been extensively studied and widely used in medical image segmentation, with promising results. Deformable models are curves or surfaces defined within an image domain that can move under the influence of internal forces, which are defined within the curve or surface itself, and external forces, which are computed from the image data. By constraining extracted boundaries to be smooth and incorporating other prior information about the object shape, deformable models offer robustness to both image noise and boundary gaps and allow integrating boundary elements into a coherent and consistent mathematical description. Such a boundary description can then be readily used by subsequent applications. Since its introduction 15 years ago, deformable models have grown to be one of the most active and successful research areas in image segmentation.
There are basically two types of deformable models: parametric deformable models and geometric deformable models. Parametric deformable models represent curves and surfaces explicitly in their parametric forms during deformation. This representation allows direct interaction with the model and can lead to a compact representation for fast real-time implementation. Adaptation of the model topology, however, such as splitting or merging parts during the deformation, can be difficult using parametric models. Geometric deformable models, on the other hand, can handle topological changes naturally. These models, based on the theory of curve evolution and the level set method, represent curves and surfaces implicitly as a level set of a higher-dimensional scalar function. Their parameterizations are computed only after complete deformation, thereby allowing topological adaptivity to be easily accommodated. Despite this fundamental difference, the underlying principles of both methods are very similar.
In this talk, I will present an overall description of the development in deformable models research and their applications in medical imaging. I will first introduce parametric deformable models, and then describe geometric deformable models. Next, I will present an explicit mathematical relationship between parametric deformable models and geometric deformable models. Finally, I will present several extensions to these deformable models by various researchers and point out future research directions.