A new algorithm is described for the reconstruction of visual surfaces from sparse data. An important aspect of this algorithm is that the surface estimated from the sparse data is approximately invariant with respect to rigid transformation of the surface in three-dimensional space. To form a surface estimate which is invariant with respect to viewpoint the stabilizing information is based on invariant surface characteristics. With appropriate approximations this results in a convex functional which must be minimized. The relationship of this algorithm to several previously proposed reconstruction algorithms is discussed, and several examples are given which demonstrate the effectiveness of the proposed algorithm in reconstructing viewpoint invariant surface estimates.
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