Discrete variational scheme for 3D surface modeling

In this paper, we propose a novel discrete variational scheme for 3D surface modeling. The key idea is to consider to utilize an unknown surface from a finite number of normals for surface reconstruction. The algorithm, based on active contours procedure, is obtained without any preprocessing or postprocessing steps and with no restriction on the sets of measurement directions except their number, a limitation dictated only by computing time. We investigate the properties of the regularization functional and illustrate our technique by applying it to converge to the input shape as the number of measurements increases. In addition, we offer linear program version of the novel algorithm that is much more robust, or at least comparable, in performance at low levels of noise and reasonably small numbers of measurements. In contrast to previous works our method can be considered on arbitrary surface and allows the use of variational scheme for 3D surface modeling.