A bstract

We present a new thcoretical method and experimcntal re-sults for direct recovery of the curvatures,the principal curvature direc-tions,and the surface itself by explicit integration of the Gaulss map.The method docs not rcly on polygonal approximnations,sinoothing of thc data,or modcl fitting.It is bascd on thc obscrvation that onc can recover the surface restoring force froun the Gauss map,and(i)applies to oricntablc surfaccs of arbitrary topology(not ncccssarily closcd);(ii)uscs only first order lincar diffcrcntial cquations:(iii)avoids the usc of unstablc computations:(iv)providcs tools for filtcring noisc from the sampled data.The method can be used for stable extraction of surfaces and surface shape invariants,in particular,in applications requiring ac-curate quantitative measurements