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Integrating algebraic curves and surfaces, algebraic invariants and Bayesian methods for 2D and 3D object recognition

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Applications of Invariance in Computer Vision (AICV 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 825))

Abstract

This paper presents a new low-computational-cost approach to minimum probability of error recognition of freeform objects in 3D range data or in 2D curve data in the image plane. Objects are represented by implicit polynomials (i.e., 3D algebraic surfaces or 2D algebraic curves) of degrees greater than 2, and are recognized by computing and matching vectors of their algebraic invariants (which are functions of their coefficients that are invariant to translations, rotations, and general linear transformations). Such polynomials of 4th degree can represent objects considerably more complicated than superquadrics and realize object recognition at significantly lower computational cost. This paper presents the Bayesian (i.e., minimum probability of error) recognizers for these models and their invariants, which requires the use of asymptotic methods little used in computer vision previously, and presents a new approach to discovering suitable invariants. Our sytem results in practical recognizers that are robust to noise, considerable partial occlusion, arbitrary sensor viewpoint, and other a priori unknown perturbations of the data sets.

This work was partially supported by NSF Grant #IRI-8715774, NSF-DARPA Grant #IRI-8905436, USAF Grant #F49620-93-1-0501ARPA, and NSF Grant #IRI-9224963

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Authors and Affiliations

  1. Laboratory for Engineering Man/Machine Systems, Division of Engineering, Brown University, 02912, Providence, RI, USA

    Daniel Keren, Jayashree Subrahmonia & David B. Cooper

Authors
  1. Daniel Keren
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  2. Jayashree Subrahmonia
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  3. David B. Cooper
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Editor information

Joseph L. Mundy Andrew Zisserman David Forsyth

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© 1994 Springer-Verlag Berlin Heidelberg

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Keren, D., Subrahmonia, J., Cooper, D.B. (1994). Integrating algebraic curves and surfaces, algebraic invariants and Bayesian methods for 2D and 3D object recognition. In: Mundy, J.L., Zisserman, A., Forsyth, D. (eds) Applications of Invariance in Computer Vision. AICV 1993. Lecture Notes in Computer Science, vol 825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58240-1_26

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  • DOI: https://doi.org/10.1007/3-540-58240-1_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58240-3

  • Online ISBN: 978-3-540-48583-4

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