Multiscale and Directional Representations of High-Dimensional Information Content in Remotely Sensed Data

Although wavelets are optimal for decomposing functions in one dimension, they are unable to achieve the same success in two or more dimensions due to the presence of curves and surfaces of discontinuity. In order to optimally capture the behavior of a function at high-dimensional discontinuities, we must be able to incorporate directional information into our analyzing functions, in addition to location and scale.

Examples of such representations are contourlets, curvelets, ridgelets, bandelets, wedgelets, and shearlets. Using directional representations, in particular shearlets, we tackle several challenging problems in the processing of remotely sensed data. First, we detect roads and ditches in LIDAR data of rural scenes.