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Abstract

When we look at a polished metal kettle we get a remarkably strong impression of its 3-D shape. The question what are the underlying mechanisms to recover the shape of a mirrored object from a single static image (eg a photograph) remains. In general, this task is ill-posed since infinitely many possible combinations of the illumination pattern from the surrounding scene and surface properties can generate the same image. Here, we present a biologically motivated model for analysing images of mirrored objects to recover 3-D geometric shape properties. In order to constrain the space of possible solutions, we assume that the reflected scene contains isotropic contrast information. When the scene is isotropic, the distortions of the reflected image are related to the surface curvature of the object (second derivatives of the surface function) (Fleming et al, 2004 Journal of Vision 4 798 - 820). First, we use orientation-selective Gabor filters (V1 cells) to extract the raw orientation and strength of the local distortions that are caused by the mirrored surface. Next, we pool context information from the vector field of orientations (inspired by V2 cells with long-range lateral connections) and use this as a feedback signal (Neumann and Sepp, 1999 Biological Cybernetics 81 425 - 444). The recurrent feedforward/feedback loop enhances and smooths the flow patterns of image orientations to recover the characteristic curvature properties. Our simulations demonstrate quantitatively that the model can reliably extract surface curvature information even when the reflected scene is not isotropic (ie the model can withstand violations of the basic assumptions). Our investigations thus provide a simple, neurally inspired mechanism for the representation and processing of mirrored objects by the visual system.