Segmenting images and triangular meshes using meth
2016-08-23
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My task was to get acquainted with image and mesh segmentation algorithms that use algebraic topology. Algebraic topology examines the topology of spaces by studying abstract algebraic structures, while Morse theory constructs the space sequentially, taking note of changes in its topology. Persistence theory is what makes the connection between these approaches quantitative, by assigning to each topological feature its lifetime in a step-by step construction of the space. This theory can be utilized for segmentation purposes mostly through watershed-based methods. Essentially, the watershed procedure considers the image or mesh as a topographical landscape being flooded by water, with lakes emerging in the basins. As the level rises, the waters from adjacent basins meet along watershed lines, forming the segment boundaries. This usually leads to oversegmentation, so a merging step is neccessary, for which we can use persistence theory. The consid
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