When is it Possible to Identify 3D Objects From Single Images Using Class Constraints?

  • Authors:
  • Ronen Basri;Yael Moses

  • Affiliations:
  • Department of Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel;Department of Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1999

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Abstract

One approach to recognizing objects seen from arbitrary viewpoint isby extracting invariant properties of the objects from single images.Such properties are found in images of 3D objects only when theobjects are constrained to belong to certain classes (e.g.,bilaterally symmetric objects). Existing studies that follow thisapproach propose how to compute invariant representations for ahandful of classes of objects. A fundamental question regarding theinvariance approach is whether it can be applied to a wide range ofclasses. To answer this question it is essential to study the set ofclasses for which invariance exists. This paper introduces a newmethod for determining the existence of invariant functions forclasses of objects together with the set of images from which theseinvariants can be computed. We develop algebraic tests that determinewhether the objects in a given class can be identified from singleimages. These tests apply to classes of objects undergoing affineprojection. In addition, these tests allow us to determine the set ofviews of the objects which are degenerate. We apply these tests toseveral classes of objects and determine which of them is identifiableand which of their views are degenerate.