A large part of my work in motion estimation is on warping motion estimation and its variants, also known as mesh-based estimation. The simplest motion estimation method is the block-matching algorithm (BMA), where the pixel values in blocks of each frame are estimated by a displaced block of similar shape and size in the past frame. Warping motion estimation allows these block shapes and sizes to change as they move from one frame to another, therefore allowing a more flexible (and hence more powerful) estimation.
In mesh-based motion, unlike BMA, the computation of a motion vector is affected by the neighboring vectors. This interdependence necessitates a costly iterative approach to the computation of motion. The computational cost of mesh-based motion has been a main drawback of this otherwise powerful technique. In  we find a method by which cheaply computed BMA motion vectors can be used in mesh-based systems. This is not a trivial task, since a straight forward insertion of BMA motion vectors in the mesh model leads to unpredictable and erratic results. Our approach is based on a careful analysis of the role of interpolation kernels in mesh models. In particular, we present a methodology to compute optimal motion interpolation kernels for any set of motion vectors (e.g., BMA motion vectors). We find a generalized orthogonality condition for these kernels. Experiments show that optimal kernels are often very different from the traditional bilinear kernels, and exhibit interesting variations. The new kernels benefit a variety of applications, including motion estimated interpolation, denoising, and compression.
Some of my work attempts to unify the framework of warping motion estimation, and overlapped block motion estimation .