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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.
Object recognition, indexing, 3D point sets, perspective, uncalibrated perspective, minimum-dimensional representations, curved objects.
Vincenzo Caglioti, "Minimal Representations of 3D Models in Terms of Image Parameters under Calibrated and Uncalibrated Perspective", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 26, no. , pp. 1234-1238, September 2004, doi:10.1109/TPAMI.2004.69
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