Stochastic fusion of multi-view gradient fields

Image gradients form powerful cues in a host of vision and graphics applications. In this paper, we consider multiple views of a textured planar scene and consider the problem of estimating the scene texture map using these multi-view inputs. Modeling each camera view as a projective transformation of the scene, we show that the problem is equivalent to that of studying the effect of noise (and the projective imaging) on the gradient fields induced by this texture map. We show that these noisy gradient fields can be modeled as complete observers of the scene radiance. Further, the corrupting noise can be shown to be additive and linear, although spatially varying. However, the specific form of the noise term can be exploited to design linear estimators that fuse the gradient fields obtained from each of the individual views. The fused gradient field forms a robust estimate of the scene gradients and can be used for scene reconstruction.