Groups for grouping

Luc J. Van Gool; Marc Proesmans; Theo Moons

doi:10.1117/12.217424

22 August 1995 Groups for grouping

Luc J. Van Gool, Marc Proesmans, Theo Moons

Proceedings Volume 2564, Applications of Digital Image Processing XVIII; (1995) https://doi.org/10.1117/12.217424
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Comparing shapes is important for both recognition and geometry-based grouping. In the case of perspective views of planar shapes, such comparison will typically be based on projective invariants. Yet there are quite a number of practical cases where one can do better and exploit simpler invariants of subgroups of the planar projectivities. This paper tries to sketch a systematic approach, based on subgroups defined by the structures they keep fixed in the image. In particular, this paper focuses on fixed points, fixed lines, lines of fixed points, and pencils of fixed lines. A complete classification of the resulting subgroups is given and the most interesting cases are identified. For these cases invariants are given and examples illustrate their use. In order to illustrate the wider scope, perspectively skewed mirror symmetry is discussed, since it entails a different type of fixed structures.

Citation Download Citation

Luc J. Van Gool, Marc Proesmans, and Theo Moons "Groups for grouping", Proc. SPIE 2564, Applications of Digital Image Processing XVIII, (22 August 1995); https://doi.org/10.1117/12.217424

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