Given a set of 3D points that we know lie on the surface of an object, we can de ne many possible surfaces that pass through all of these points. Even when we consider only surface triangulations, there a r e still an exponential number of valid triangulations that all t the data. Each triangulation will produce a di erent faceted surface c onnecting the points. Our goal is to overcome this ambiguity and nd the particular surface that is closest to the true object surface. We do not know the

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... e surface but instead we assume that we have a set of images of the object. We propose selecting a triangulation based on its consistency with this set of images of the object. We present an algorithm that starts with an initial rough triangulation and re nes the triangulation until it obtains a surface that best accounts for the images of the object. Our method is thus able to overcome the surface ambiguity problem and at the same time capture sharp corners and handle concave regions and occlusions. We show results for a few real objects.