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Minimal Representations of 3D Models in Terms of Image Parameters under Calibrated and Uncalibrated Perspective
September 2004 (vol. 26 no. 9)
pp. 1234-1238
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.

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Index Terms:
Object recognition, indexing, 3D point sets, perspective, uncalibrated perspective, minimum-dimensional representations, curved objects.
Citation:
Vincenzo Caglioti, "Minimal Representations of 3D Models in Terms of Image Parameters under Calibrated and Uncalibrated Perspective," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1234-1238, Sept. 2004, doi:10.1109/TPAMI.2004.69
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