We introduce an approach to the representation of curved or
polyhedral 3-D objects and apply this representation to pose
estimation.  The representation is based on
surface patches with uniform curvature properties extracted at
multiple scales. These patches are computed using multiple
alternative decompositions of the surface based on the signs of the mean and
Gaussian curvatures. Initial coarse decompositions are
subsequently refined using a curvature compatibility scheme 
to rectify the effect of noise
and quantization errors.

   The extraction of simple uniform curvature features is limited by the
fact that the optimal scale of processing for a single object  is
very difficult to determine. As a solution we propose the segmentation
of range data into patches at multiple scales.

   A hierarchical ranking of these patches is then used to describe
individual objects based on geometric information. These
geometric descriptors are ranked according to several criteria
expressing their estimated stability and utility.

The applicability of the 
resulting multi-scale description is demonstrated by estimating the
pose of a 3-D object. Pose estimation is cast as an optimal matching problem. 
The geometric pose transformation is computed by matching two representations,
which amounts to finding the three-patch correspondence that produces the best
global consistency.

Examples of the multi-scale representation applied to both
real and simulated
range data are presented. Effective pose estimation is demonstrated
and the algorithms behaviour in the presence 
of noise is validated.