Regularization ofInverseVisualProblemsInvolving Discontinuities

Inverse problems, suchasthereconstruction problems thatarise inearly vision, tendtobemathematically ill-posed. Through regularization, theymaybereformulated aswell-posed variational principles whosesolutions arecomputable. Standard regularization theory employs quadratic stabilizing functionals thatimpose global smoothness constraints onpossible solutions. Discontinuities present serious difficulties tostandard regularization, however, since their re- construction requires a precise spatial control overthesmoothing properties ofstabilizers. Thispaperproposes ageneral class ofcon- trolled-continuity stabilizers whichprovide thenecessary control over smoothness. Thesenonquadratic stabilizing functionals comprise mul- tiple generalized spline kernels combined with(noncontinuous) conti- nuity control functions. Inthecontext ofcomputational vision, they maybethought ofascontrolled-continuity constraints. Thesegeneric constraints areapplicable tovisual reconstruction problems thatin- volvebothcontinuous regions anddiscontinuities, forwhichglobal smoothness constraints fail.