Minimal Representations of 3D Models in Terms of Image Parameters under Calibrated and Uncalibrated Perspective

Authors:
Vincenzo Caglioti
Affiliations:
IEEE
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
2004

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Abstract

Indexing is a well-known paradigm for object recognition. In indexing, each 3D model is represented as the set of values assumed by a given vector of image parameters in correspondence to all the possible images of the 3D model. An open problem, posed by Jacobs [12], concerned the minimum dimensionality of such sets under perspective. This paper proves that, under calibrated or uncalibrated perspective, the minimum dimensionality of the set representing any 3D modeled point-set is two. Two-dimensional representations are found also for 3D curved objects.