sWe show that we can optimally represent the set of 2D images producedsby the point features of a rigid 3D model as two lines in twoshigh-dimensional spaces. We then decribe a working recognition systemsin which we represent these spaces discretely in a hash table. We cansaccess this table at run time to find all the groups of model featuressthat could match a group of image features, accounting for the effectssof sensing error. We also use this representation of a model's imagessto demonstrate significant new limitations of two other approaches tosrecognition: invariants, and non-accidental properties.

Animating by hand can be a long and challenging process in part because of the necessity of drawing every frame by hand. 3D animation media minimize this problem with the use of automatically interpolated frames, but despite significant research no universally acceptable techniques have been demonstrated for 2 dimensional interpolation. In this paper we explore computer-assisted optimizations to the animation pipeline. Specifically, we utilize 3D motion fields to create more realistic in-between frames for sets of 2D ``key frames.'' We demonstrate our method by using it to create 2D special effects for a 30-second clip of an animated short film.