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Algebraic geometry and object representation in computer vision

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Book cover Object Representation in Computer Vision (ORCV 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 994))

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Abstract

The goal of algebraic geometry is to gain an understanding of the behaviour of functions related by polynomial relationships. Algebraic curves and surfaces having considerable advantages as objects of study in computer vision, the relevance of algebraic geometry when dealing with the representation of polynomial objects seems only natural. However, due to its high level of abstraction, this mathematical field has seen only few applications in computer vision in comparison to its huge achievements, by contrast with differential geometry for instance. In this paper, we examine several methods that we think could see some developments in object representation. An example of their use is presented for the construction of aspect graphs of smooth surfaces and for the understanding of the complexity of this representation.

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Authors and Affiliations

  1. CRIN/INRIA Lorraine, B timent LORIA Campus Scientifique, BP 239, 54506, Vandœuvre-les-Nancy cedex, France

    Sylvain Petitjean

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  1. Sylvain Petitjean
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Martial Hebert Jean Ponce Terry Boult Ari Gross

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© 1995 Springer-Verlag Berlin Heidelberg

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Petitjean, S. (1995). Algebraic geometry and object representation in computer vision. In: Hebert, M., Ponce, J., Boult, T., Gross, A. (eds) Object Representation in Computer Vision. ORCV 1994. Lecture Notes in Computer Science, vol 994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60477-4_11

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  • DOI: https://doi.org/10.1007/3-540-60477-4_11

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  • Print ISBN: 978-3-540-60477-8

  • Online ISBN: 978-3-540-47526-2

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