Surface height recovery from surface normals using manifold embedding

In this paper we show how surface height recovery from the field of surface normals can be posed as one of low dimensional embedding. To do this, we make use of the surface normals to compute the surface height increments corresponding to each location on the pixel lattice. With the height increments to hand, we can estimate the surface height difference between each pair of pixel-locations. We pose the problem of surface height recovery as that of embedding the surface normals on a manifold in a 3D space that preserves both the pattern of surface height differences and the lattice footprint of the field of surface normals. We present a sensitivity study on synthetic imagery and perform experiments on a variety of real world image data, where it produces qualitatively good reconstructed surfaces.