Combining Geometric and Topological Information in Image Segmentation
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A fundamental problem in computer vision is image segmentation, where the goal is to delineate the boundary of the object in the image. The focus of this work is on the segmentation of grayscale images and its purpose is two-fold. First, we conduct an in-depth study comparing active contour and topologically-based methods, two popular approaches for boundary detection of 2-dimensional images. Certain properties of the image dataset may favor one method over the other, both from an interpretability perspective as well as through evaluation of performance measures. Second, we propose the use of topological knowledge to assist an active contour method, which can potentially incorporate prior shape information. The latter is known to be extremely sensitive to algorithm initialization, and thus, we use a topological model to provide an automatic initialization. In addition, our proposed model can handle objects in images with more complex topological structures. We demonstrate this on artificially-constructed image datasets from computer vision, as well as real medical image data.
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