Recovering Surfaces from the Restoring Force

We present a new theoretical method and experimental results for direct recovery of the curvatures, the principal curvature directions, and the surface itself by explicit integration of the Gauss map. The method does not rely on polygonal approximations, smoothing of the data, or model tting. It is based on the observation that one can recover the surface restoring force from the Gauss map, and (i) applies to orientable surfaces of arbitrary topology (not necessarily closed); (ii) uses only rst order linear di erential equations; (iii) avoids the use of unstable computations; (iv) provides tools for ltering noise from the sampled data. The method can be used for stable extraction of surfaces and surface shape invariants, in particular, in applications requiring accurate quantitative measurements.