Rough interface reconstruction using the level set method

We present a new level set method for reconstructing interfaces from point aggregations. Although level-set-based methods are advantageous because they can handle complicated topologies and noisy data, most tend to smooth the inherent roughness of the original data. Our objective is to enhance the quality of a reconstructed surface by preserving certain roughness-related characteristics of the original dataset. Our formulation employs the total variation of the surface as a roughness measure. The algorithm consists of two steps: a roughness-capturing flow and a roughness-preserving flow. The roughness capturing step attempts to construct a surface for which the original roughness is captured - distance flow is well suited for roughness capturing. Surface reconstruction is enhanced by using a total variation preserving (TVP) scheme for the roughness-preserving flow. The shock filter formulation of Osher and Rudin is exploited to achieve this goal. In practice, we have found that better results arc obtained by balancing the TVP term with a smoothing term based on curvature. The algorithm is applied to both fractal surface growth simulations and scanned data sets to demonstrate the efficacy of our approach.