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1 A Graph-Spectral Approach to Shape-from-shading

By Antonio Robles-kelly and Edwin Hancock


Abstract — In this paper we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterise the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalise large change in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximises the sum of curvature dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert’s law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery. Index Terms — Shape-from-shading, graph seriation, graphspectral methods

Year: 2014
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