Image Segmentation Using Topological Persistence

  • David Letscher
  • Jason Fritts
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4673)


This paper presents a new hybrid split-and-merge image segmentation method based on computational geometry and topology using persistent homology. The algorithm uses edge-directed topology to initially split the image into a set of regions based on the Delaunay triangulations of the points in the edge map. Persistent homology is used to generate three types of regions: p-persistent regions, p-transient regions, and d-triangles. The p-persistent regions correspond to core objects in the image, while p-transient regions and d-triangles are smaller regions that may be combined in the merge phase, either with p-persistent regions to refine the core or with other p-transient and d-triangles regions to potentially form new core objects. Performing image segmentation based on topology and persistent homology guarantees several nice properties, and initial results demonstrate high quality image segmentation.


Image Segmentation Voronoi Diagram Delaunay Triangulation Betti Number Edge Detection Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • David Letscher
    • 1
  • Jason Fritts
    • 1
  1. 1.Saint Louis University, Department of Mathematics and Computer Science 

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