The Earth Mover's Distance (EMD) is a distance measure between distributions with applications in image retrieval and matching. We consider the problem of computing a transformation of one distribution which minimizes its EMD to another. The applications discussed here include estimation of the size at which a color pattern occurs in an image, lighting-invariant object recognition, and point feature matching in stereo image pairs. We present a monotonically convergent iteration which can be applied to a large class of EMD under transformation problems, although the iteration may converge to only a locally optimal transformation. We also provide algorithms that are guaranteed to compute a globally optimal transformation for a few specific problems, including some EMD under translation problems.

Line integral convolution (LIC), introduced by Cabral and Leedom (1993) is a powerful technique for imaging and animating vector fields. We extend the LIC technique in three ways. Firstly the existing algorithm is limited to vector fields over a regular Cartesian grid. We extend the algorithm and the animation techniques possible with it to vector fields over curvilinear surfaces, such as those found in computational fluid dynamics simulations. Secondly we introduce a technique to visualize vector magnitude as well as vector direction, i.e., variable-speed flow animation. Thirdly we show how to modify LIC to visualize unsteady (time dependent) flows. Our implementation utilizes texture-mapping hardware to run in real time, which allows our algorithms to be included in interactive applications.>