Visibility constraints on features of 3D objects

To recognize three-dimensional objects it is important to model how their appearances can change due to changes in viewpoint. A key aspect of this involves understanding which object features can be simultaneously visible under different viewpoints. We address this problem in an image- based framework, in which we use a limited number of im- ages of an object taken from unknown viewpoints to deter- mine which subsets of features might be simultaneously vis- ible in other views. This leads to the problem of determining whether a set of images, each containing a set of features, is consistent with a single 3D object. We assume that each feature is visible from a disk of viewpoints on the viewing sphere. In this case we show the problem is NP-hard in general, but can be solved efficiently when all views come from a circle on the viewing sphere. We also give iterative algorithms that can handle noisy data and converge to lo- cally optimal solutions in the general case. Our techniques can also be used to recover viewpoint information from the set of features that are visible in different images. We show that these algorithms perform well both on synthetic data and images from the COIL dataset.