Representation, Optimization and Compression of High Dimensional Data

The exponential growth of available computing power opens the door for new capabilities in modeling the objects in the high dimensional real world that we live in. Traditionally we have manipulated data defined on simple entities such as the real line (e.g. audio), a rectangle in the plane (e.g. images) or a three-dimensional open-ended box (e.g. video sequence of planar images). Today graphics cards and accelerators, powerful processors and cheap memory allows us to interact with complex 3D and higher dimensional objects. We need to build mathematical representations, algorithms and software that will allow us to easily represent, compress and manipulate such objects. In this paper we will summarize some algorithms designed to that goal and used in the areas of robotics, computer graphics, 3D haptics (touch interaction with the environment) and data compression,. Those algorithms use novel methods in evolutionary computation, motion planning and geometric modeling, wavelets and embedded signal coding.