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Proceedings Paper

Recognizing point configurations in full perspective
Author(s): Kevin Abbott; Peter F. Stiller
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Paper Abstract

In this paper we examine two fundamental problems related to object recognition for point features under full perspective projection. The first problem involves the geometric constraints (object-image equations) that must hold between a set of object feature points (object configuration) and any image of those points under a full perspective projection, which is just a pinhole camera model for image formation. These constraints are formulated in an invariant way, so that object pose, image orientation, or the choice of coordinates used to express the feature point locations either on the object or in the image are irrelevant. These constraints turn out to be expressions in the shape coordinates calculated from the feature point coordinates. The second problem concerns the notion of shape and a description of the resulting shape spaces. These spaces aquire certain natural metrics, but the metrics are often hard to compute. We will discuss certain cases where the computations are managable, but will leave the general case to a future paper. Taken all together, the results in this paper provide a way to understand the relationship that exists between 3D geometry and its "residual" in a 2D image. This relationship is completely characterized (for a particular combination of features) by the above set of fundamental equations in the 3D and 2D shape coordinates. The equations can be used to test for the geometric consistency between an object and an image. For example, by fixing point features on a known object, we get constraints on the 2D shape coordinates of possible images of those features. Conversely, if we have specific 2D features in an image, we will get constraints on the 3D shape coordinates of objects with feature points capable of producing that image. This yields a test for which object is being viewed. The object-image equations are thus a fundamental tool for attacking identification/recognition problems in computer vision and automatic target recognition applications.

Paper Details

Date Published: 29 January 2007
PDF: 12 pages
Proc. SPIE 6499, Vision Geometry XV, 64990C (29 January 2007); doi: 10.1117/12.704308
Show Author Affiliations
Kevin Abbott, Texas A&M Univ. (United States)
Peter F. Stiller, Texas A&M Univ. (United States)

Published in SPIE Proceedings Vol. 6499:
Vision Geometry XV
Longin Jan Latecki; David M. Mount; Angela Y. Wu, Editor(s)

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