An eigenvector method for shape-from-shading

We explore how spectral methods for graph seriation can be used to develop a new shape-from-shading algorithm. We characterise the field of surface normals using a transition matrix whose elements are computed from the sectional curvature between different image locations. We use a graph seriation method to define a curvature minimising surface integration path for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadric patches to the height data. 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.