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Abstract:
When we look at a perfectly mirrored object, such as a polished kettle, we generally have a
remarkably strong impression of its 3D shape. This leads to the question of whether there is
a mechanism to completely recover the shape of a mirrored object from a single static image
(e.g. a photograph). Without explicit knowledge of the surrounding scene, this is theoretically
impossible because many possible combinations of illumination from the surrounding scene
and surface properties can generate the same image (i.e. it is an ill-posed problem). Therefore,
the only way to extract information about object shape is to constrain the possible combinations
of object shape and illumination. If we assume that the reflected scene contains isotropic
contrast information, then there is a close relation between the surface curvature of an object
(specifically the second derivatives of the surface function) and the distortions of the reflected
scenery [1]. In this contribution we present two different computational methods for analysing
images of mirrored objects to recover certain properties of 3D shape. Our first method is a
statistical approach, based on principal components of the image gradient computed in a local
neighborhood, known as the structure tensor. In this context, the eigenvectors of the tensor
tell us the orientation of curvature and the eigenvalues of the tensor give us information about
the anisotropy of curvature (ratio of maximal and minimal curvature). Our second method is
a biologically motivated approach, based on Gabor filters and grouping. We apply an iterative
refinement in a simple model of cortical feedforward/feedback processing [2]. Context information
is collected by cells with long-range lateral connections. This information is fed back to
enhance regions where local information matches the top-down reentry pattern provided by the
larger context. Our approach shows that under the assumption mentioned above, it is possible
to recover two characteristic curvature properties of mirrored objects: (i) the direction of maximal
and minimal curvature and (ii) the anisotropy of curvature. Our simulations demonstrate
that both methods (the statistical and biological motivated approach) lead to comparable results
and that the models perform well even if the assumption of isotropic contrasts in the scenery is
violated to a certain degree.
