INTRINSIC PARAMETERS FOR SURFACE REPRESENTATION USING DEFORMABLE MODELS

Three-dimensional viewpoint invariance is an important requirement on the representation of surfaces for recognition tasks. Parameterized surfaces possess this desirable property. In general, the parameters in a parametric surface representation can be arbitrarily defined. A canonical, intrinsic parameterization provides a consistent, invariant form for describing surfaces. Our goal here is to define and construct such a parameterization. A new technique for achieving this goal is presented by using an elastically deformable model. The salient features of our method am that it provides a unified and general framework for reparameterization of a surface and easily allows for incorporation of multiview data sets. The canonical parameterization of the surface is defined in terms of the surface lines of curvature. Depth constraints are first imposed as an external force field on the deformable model that molds itself to be consistent with the data. Principal vectors computed from this conformed model surface are then imposed as a force field on the parameter curves of the model. The parameter curves deform to become tangential to the principal vectors thereby yielding an invariant surface parameterized by the lines of curvature. Extension of the canonical parametric grid to multiple views is then demonstrated by incorporating depth and curvature constraints from multiple views.