GEOMETRIC SHOCK-CAPTURING ENO SCHEMES FOR SUBPIXEL INTERPOLATION, COMPUTATION AND CURVE EVOLUTION

Subpixel methods that locate curves and their singularities, and that accurately measure geometric quantities, such as orientation and curva ture, are of significant importance in computer vision and graphics. S uch methods often use local surface fits or structural models for a lo cal neighborhood of the curve to obtain the interpolated curve. Wherea s their performance is good in smooth regions of the curve, it is typi cally poor in the vicinity of singularities. Similarly, the computatio n of geometric quantities is often regularized to deal with noise pres ent in discrete data. However, in the process, discontinuities are blu rred over, leading to poor estimates at them and in their vicinity. In this paper we propose a geometric interpolation technique to overcome these limitations by locating curves and obtaining geometric estimate s while (1) not blurring across discontinuities and (2) explicitly and accurately placing them, The essential idea is to avoid the propagati on of information across singularities. This is accomplished by a one- sided smoothing technique, where information is propagated from the di rection of the side with the ''smoother'' neighborhood. When both side s are nonsmooth, the two existing discontinuities are relieved by plac ing a single discontinuity, or shock. The placement of shacks is guide d by geometric continuity constraints, resulting in subpixel interpola tion with accurate geometric estimates. Since the technique was origin ally motivated by curve evolution applications, we demonstrate its use fulness in capturing not only smooth evolving curves, but also ones wi th orientation discontinuities. In particular, the technique is shown to be far better than traditional methods when multiple or entire curv es are present in a very small neighborhood. (C) 1997 Academic Press.