Recognition of configurations of lines I: weak perspective case

Peter F. Stiller

doi:10.1117/12.617168

30 August 2005 Recognition of configurations of lines I: weak perspective case

Peter F. Stiller

Proceedings Volume 5916, Mathematical Methods in Pattern and Image Analysis; 59160A (2005) https://doi.org/10.1117/12.617168
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

In this paper we examine the problem of single-view recognition for sets of line features under generalized weak perspective projection. Our ultimate goal is to understand metrically the shape spaces for various labeled and unlabeled feature sets of lines and to represent those shapes using global shape coordinates. The later are "invariants" that provide an isometric embedding of the shape space in question (be it the object space or the image space) into an ambient Euclidean or projective space. The metrics involved are natural variants of the Procrustes metric of classical shape theory that is used in object recognition and image understanding tasks. In this first paper of what will be a series, we derive a fundamental set of equations that express the relationship between the 3D geometry of our lines and its "residual" in a 2D generalized weak perspective image. These equations are known as object/image relations. They completely and invariantly describe the mutual 3D/2D constraints, and can be exploited in a number of ways. For example, from a given 2D configuration of edges (lines) in an image, we can determine a set of nonlinear constraints on the geometric invariants of all 3D configurations capable of producing the given 2D configuration, and thus arrive at a test for determining the object being viewed. Conversely, given a 3D geometric configuration of lines (features on an object), we can derive a set of equations that constrain the invariants of the images of that object; helping us to determine if that particular object appears in various images.

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Peter F. Stiller "Recognition of configurations of lines I: weak perspective case", Proc. SPIE 5916, Mathematical Methods in Pattern and Image Analysis, 59160A (30 August 2005); https://doi.org/10.1117/12.617168

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KEYWORDS

3D image processing

3D imaging standards

Matrices

Atrial fibrillation

Cameras

Image understanding

Object recognition

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