Controlled Continuity for Visual Reconstruction

Demetri Terzopoulos
MIT Artificial Intelligence Lab.
545 Technology Square
Cambridge, MA 02139


Controlled continuity is a powerful but nonrestrictive model, generally applicable to the solution of many visual reconstruction problems involving both continuous regions and discontinuities.


Ill-posed reconstruction problems are the rule rather than the exception in early vision. Image reconstruction begins with a selection of (usually intensity based) 2-D data. In visual surface reconstruction, the raw data comprise local 3-D shape estimates. Generally, the initial information may be available from multiple sources and at multiple resolutions, but it is often sparse and corrupted by noise. The goal of reconstruction is to generate the best possible interpretation of the available visual information, making explicit the continuous regions as well as the locations of bounding discontinuities. Well-posed variational principle formulations may be obtained systematically for this broad class of visual problems by applying a ``controlled continuity'' model. Although this deterministic model provides sufficient constraint to guarantee the existence of unique solutions, it remains generic and is nonrestrictive at discontinuities. It can be expressed mathematically as functional forms involving generalized spline kernels. The constituent kernels are combined with continuity control functions which can be determined optimally according to local criteria. The resulting variational principles may be locally discretized using piecewise, finite element techniques. Fine scale solutions to the reconstruction problems are efficiently computable by multiresolution hierarchies of local-support cooperative processes under concurrent coordination.