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Object-Image Metrics for Generalized Weak Perspective Projection

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Book cover Statistics and Analysis of Shapes

Abstract

Generalized weak perspective is a common camera model describing the geometric projection for many common scenarios (e.g., 3D to 2D). This chapter describes a metric constructed for comparing (matching) configurations of object features to configurations of image features that is invariant to any affine transformation of the object or image. The natural descriptors are the Plücker coordinates because the Grassmann manifold is the natural shape space for invariance of point features under affine transformations in either the object or image. The objectimage equations detail the relation between the object descriptors and the image descriptors, and an algorithm is provided to compute the distances for all cases.

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Author information

Authors and Affiliations

  1. Air Force Research Lab, AFRL/SNAT, Building 620, 2241 Avionics Circle, Dayton, Ohio, 45433, USA

    Gregory Arnold

  2. Department of Mathematics, Texas A&M University, College Station, Texas, 77843-3368, USA

    Peter F. Stiller

  3. Universal Mathematics, 3274 S. Union Road, Dayton, Ohio, 45418, USA

    Kirk Sturtz

Authors
  1. Gregory Arnold
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  2. Peter F. Stiller
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  3. Kirk Sturtz
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC, 27606-7914, USA

    Hamid Krim

  2. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0250, USA

    Anthony Yezzi Jr.

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© 2006 Birkhäuser Boston

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Arnold, G., Stiller, P.F., Sturtz, K. (2006). Object-Image Metrics for Generalized Weak Perspective Projection. In: Krim, H., Yezzi, A. (eds) Statistics and Analysis of Shapes. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4481-4_10

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