Topological Data Analysis and Wide Area Detection of Chemical and Biological Contamination

Topological data analysis is a new mathematical method used to study these massive data sets that arise in a variety of situations including military operations and national security. The use of passive infrared sensors for a wide area detection system involving chemical and biological contaminants produces massive amounts of hyperspectral image data. Recent research in this area include fast algorithms for computing homology dimension, the extension of homology from sets to distributions and functions, and a smart convolution filter that interprets local topological features that span between user defined geometric boundaries. Together these innovations give a new morphology grammar implemented through the geometry of the filter, its density distribution values, and iteration with other statistical procedures that extracts and manipulates the desired information in the most effective and efficient manner possible. The Phase I results have demonstrated that the use of homology could change the very nature of data analyses for a variety of national security and military situations where the current statistical methods are not capable of detecting qualitative structures. Procedures for combining the classical image tools with the topological tools are being developed including how the topological method could be best developed in Matlab and linked with CHomP.