Controlled Continuity for Visual Reconstruction
Demetri Terzopoulos
MIT Artificial Intelligence Lab.
545 Technology Square
Cambridge, MA 02139
Abstract:
Controlled continuity is a powerful but nonrestrictive model,
generally applicable to the solution of many visual reconstruction
problems involving both continuous regions and discontinuities.
Summary:
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.