Geometric measure theory is the study of geometric properties of sets and measures by measure theoretical means. Geometric analysis permits the construction of precise, discriminating metrics that can be tuned to ignore the unimportant. Geometric measure theory (GMT) is just beginning to be exploited for the analysis of data in all its diversity. DDMA work in this area includes:

• Our recent research results connect the L1TV image functional and the flat norm from GMT, introducing a flat norm with scale. The flat norm is a particularly appropriate metric for distinguishing between different shapes, so our work enables the identification of shape at any scale. This nonlinear multiscale decomposition and metric opens up a great number of practical applications, including automated identification of astronomical objects.
• Kevin Vixie is teaching a course in Geometric Measure Theory in the Spring of 2007 at LANL and UCLA. See link for background and bibliography on Geometric Measure Theory.
• Currently, Kevin Vixie is a Senior Fellow at the IPAM Random Shapes program at the University of California, Los Angeles.