Minimal representations of 3D models in terms of image parameters under calibrated and uncalibrated perspective

Indexing is a well-known paradigm for object recognition. In indexing, each 3D model is repre- sented 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 [14], 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.