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.