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Active Contours with Free Endpoints

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Abstract

Image segmentation methods with length regularized edge sets are known to have segments whose endpoints either terminate perpendicularly to the boundary of the domain, terminate at a triple junction where three segments connect, or terminate at a free endpoint where the segment does not connect to any other edges. However, level set based segmentation methods are only able to capture edge structures which contain the first two types of segments. In this work, we propose an extension to the level set based image segmentation method in order to detect free endpoint structures. By generalizing the curve representation used in Chan and Vese (Trans. Image Proces. 10(2):266–277, 2001; Int. J. Comput. Vis. 50(3):271–293, 2002) to also include free endpoint structures, we are able to segment a larger class of edge types. Since our model is formulated using the level set framework, the curve evolution inherits useful properties such as the ability to change its topology by splitting and merging. The numerical method is provided as well as experimental results on both synthetic and real images.

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Acknowledgements

This research was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program and in part by the National Science Foundation Grant DMS 0714945 and CCF/ITR Expeditions Grant 0926127.

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Authors and Affiliations

  1. Los Angeles Department of Mathematics, University of California, Los Angeles, CA, 90095, USA

    Hayden Schaeffer & Luminita Vese

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  1. Hayden Schaeffer
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  2. Luminita Vese
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Correspondence to Hayden Schaeffer.

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Schaeffer, H., Vese, L. Active Contours with Free Endpoints. J Math Imaging Vis 49, 20–36 (2014). https://doi.org/10.1007/s10851-013-0437-4

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