In this paper, we present a new method for representing and recognizing objects, based on invariants of the object's regions. We apply the method to articulated objects in low-resolution, noisy range images. Articulated objects such as a back-hoe can have many degrees of freedom, in addition to the unknown variables of viewpoint. Recognizing such an object in an image can involve a search in a high-dimensional space that involves all these unknown variables. Here, we use invariance to reduce this search space to a manageable size. The low resolution of our range images makes it hard to use common features such as edges to find invariants. We have thus developed a new "featureless" method that does not depend on feature detection. Instead of local features, we deal with whole regions of the object. We define a "transform" that converts the image into an invariant representation on a grid, based on invariant descriptors of entire regions centered around the grid points. We use these region-based invariants for indexing and recognition. While the focus here is on articulation, the method can be easily applied to other problems such as the occlusion of fixed objects.

In this work, we treat major problems of object recognition which have received relatively little attention lately. Among them are the loss of depth information in the projection from a 3D object to a single 2D image, and the complexity of finding feature correspondences between images. We use geometric invariants to reduce the complexity of these problems. There are no geometric invariants of a projection from 3D to 2D. However, given certain 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 use such assumptions for single-view recognition. We find algebraic relations between the invariants of a 3D model and those of its 2D image under general projective projection. These relations can be described geometrically as invariant models in a 3D invariant space, illuminated by invariant "light rays," and projected onto an invariant version of the given image. We apply the method to real images.

Articulated objects can have many degrees of freedom. Recognizing such an object in a single image can involve a search in a high-dimensional space that involves all these degrees of freedom, in addition to the usual unknown viewpoint. In this paper we use invariance to reduce this search space to a manageable size. Our method avoids feature detection for improved robustness. We apply the method to range images of objects such as back-hoes.

A method has been developed for overcoming some of the major obstacles of object recognition. It represents both 2D images and 3D models from a database by viewpoint invariant descriptors in the same invariant space. As there is a large number of possible matches between the image and model invariants, there is a crucial need to perform this match efficiently. We answer this need by using an adaptation of spatial sorting based on the octree representation of the model points and image lines in three-dimensional space. We show the advantage of the octree method over the traditional "brute-force" approach and we compare the merits of the two methods. This makes it possible for the recognition task to be performed in a reasonable time for a large number of models.