Finding tree structures by grouping symmetries

Hiroshi Ishikawa*, Davi Geiger, Richard Cole

*Corresponding author for this work

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

8 Citations (Scopus)


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
Title of host publicationProceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005
Number of pages8
Publication statusPublished - 2005
Externally publishedYes
EventProceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 - Beijing, China
Duration: 2005 Oct 172005 Oct 20

Publication series

NameProceedings of the IEEE International Conference on Computer Vision


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

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition


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