We introduce new transforms for efficient compression of image blocks with directional preferences. Each transform, which is an orthogonal basis for a specific direction, is constructed from an eigen-decomposition of a discrete directional Laplacian system matrix. The method is a natural extension of the DCT, expressing the Laplacian in Cartesian coordinates rotated to some predetermined angles. Symmetry properties of the transforms over square domains lead to efficient computation and compact storage of the directional transforms. A version of the directional transforms was implemented within the beyond HEVC software and demonstrated significant improvement for intra block coding.

We examine the shape from shading problem without boundary conditions as a polynomial system. This view allows, in generic cases, a complete solution for ideal polyhedral objects. For the general case we propose a semidefinite programming relaxation procedure, and an exact line search iterative procedure with a new smoothness term that favors folds at edges. We use this numerical technique to inspect shading ambiguities.

We revisit the problem of recovering 3D shape from the projection of planar curves on a surface. This problem is strongly motivated by perception studies. Applications include single-view modeling and fully uncalibrated structured light. When the curves intersect, the problem leads to a linear system for which a direct least-squares method is sensitive to noise. We derive a more stable solution and show examples where the same method produces plausible surfaces from the projection of parallel (non-intersecting) planar cross sections.