Campus Event Calendar
Event Entry
What and Who
Homologically Persistent Skeleton in Computer Vision and beyond
Vitaliy Kurlin
Durham University, UK
AG1 Mittagsseminar (own work)
AG 1, AG 2, AG 3, AG 4, AG 5, RG1, SWS, MMCI
MPI Audience
English
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Date, Time and Location
Tuesday, 19 May 2015
13:00
30 Minutes
E1 4
024
Saarbrücken
Abstract
2D images often contain irregular salient features and interest points with non-integer coordinates. Our skeletonization problem for such a noisy sparse cloud is to summarize the topology of a given 2D cloud across all scales in the form of a graph, which can be used for combining local features into a more powerful object-wide descriptor.
We extend a classical Minimum Spanning Tree of a cloud to the new fundamental concept of a Homologically Persistent Skeleton, which is scale-and-rotation invariant and depends only on the given cloud without extra parameters. This graph
(1) is computable in time O(n log n) for any n points in the plane;
(2) has the minimum total length among all graphs that span a 2D cloud at any scale and also have most persistent 1-dimensional cycles;
(3) is geometrically stable for noisy samples around planar graphs.
The preprint is at http://kurlin.org/projects/hopes.pdf
Contact
Michael Kerber
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Michael Kerber, 03/26/2015 15:03 -- Created document.