Model-Based Recognition of 3D Objects from One View

Abstract

In this work we treat major problems of object recognition which have previously received little attention. Among them are the loss of depth information in the projection from 3D to 2D, and the complexity of finding feature correspondences in general cases. This treatment enables us to recognize objects in difficult real-world situations. It is well known that there are no geometric invariants of a projection from 3D to 2D. However, given some modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions can be either a particular model or a generic assumption about a class of models. Here we deal with both situations. We find invariant connections between a 2D image and a 3D model under general projective projection. We give a geometric interpretation of the method as an invariant model in 3D invariant space, illuminated by invariant light rays, converging to an invariant camera center in the same space. We demonstrate the method on real images. This work differs from related work in the following ways: 1) Most work in invariants has concentrated on transformations of the same dimensionality, mainly 2D to 2D projections. We deal here with the problem of projecting a 3D object onto a 2D image, which is of greater relevance to object recognition. 2) Much of the previous work is done on multiple images, such as the work on camera calibration. This usually requires knowledge of the correspondence between images. We concentrate on single images, but we also apply our method to finding correspondences in multiple images without prior knowledge or expensive search.