Finding tree structures by grouping symmetries

Hiroshi Ishikawa, Davi Geiger, Richard Cole

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The representation of objects in images as tree structures is of great interest to vision, as they can represent articulated objects such as people as well as other structured objects like arteries in human bodies, roads, circuit board patterns, etc. Tree structures are often related to the symmetry axis representation of shapes, which captures their local symmetries. Algorithms have been introduced to detect (i) open contours in images in quadratic time (ii) closed contours in images in cubic time, and (in) tree structures from contours in quadratic time. The algorithms are based on dynamic programming and Single Source Shortest Path algorithms. However, in this paper, we show that the problem of finding tree structures in images in a principled manner is a much harder problem. We argue that the optimization problem of finding tree structures in images is essentially equivalent to a variant of the Steiner Tree problem, which is NP-hard. Nevertheless, an approximate polynomial-time algorithm for this problem exists: we apply a fast implementation of the Goemans-Williamson approximate algorithm to the problem of finding a tree representation after an image is transformed by a local symmetry mapping. Examples of extracting tree structures from images illustrate the idea and applicability of the approximate method.

Original languageEnglish (US)
Title of host publicationProceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005
Number of pages8
StatePublished - 2005
EventProceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 - Beijing, China
Duration: Oct 17 2005Oct 20 2005

Publication series

NameProceedings of the IEEE International Conference on Computer Vision


OtherProceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition


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