Model-based recognition of 3D objects from single images

In this work, we treat major problems of object recognition which have rece ived relatively little attention lately. Among them are the loss of depth i nformation in the projection from a 3D object to a single 2D image, and the complexity of finding feature correspondences between images. We use geome tric invariants to reduce the complexity of these problems. There are no ge ometric invariants of a projection from 3D to 2D. However, given certain mo deling assumptions about the 3D object, such invariants can be found. The m odeling assumptions can be either a particular model or a generic assumptio n about a class of models. Here, we use such assumptions for single-view re cognition. We find algebraic relations between the invariants of a 3D model and those of its 2D image under general projective projection. These relat ions can be described geometrically as invariant models in a 3D invariant s pace, illuminated by invariant "light rays, and projected onto an invariant version of the given image. We apply the method to real images.