Applied computational geometry in fundamentals of bio-imaging and analysis

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As a computer scientist working in the discipline of biosystems engineering, my long term research program focuses on the application of computational geometry to the fundamental physical sciences of imaging and analyzing food and biological materials.  In the analysis of materials, traditional spectroscopic techniques provide the spectral signature of a chemical sample, modern spectroscopic imaging provides entire spectra at each pixel of a sample.  While each technology and manufacturer has equipment with differing spatial resolutions many devices offer hundreds of thousand of pixels per sample.  Similarly spectral resolution varies from the multispectral (tens of spectra per pixel) to hyperspectral (hundreds to tens of thousands per pixel).Computational geometry typically analyzes structure within a geometric abstraction of a data set.  As an example of geometric structure, a particular substance's spectra can be considered geometric data by considering individual peaks in the spectra and their magnitude as separate mathematical values (features) of that data point.  Sets of substances (i.e., data points) can be analyzed to find clusters/structures of chemicals with similar chemical bonds (e.g. chemical sub-groups).   The long term goal of the proposed research is to establish computational geometry as a key component in the analysis and acquisition of spectral signals and their use in the determination of quality of food and biological materials.  My short term goals focus on two areas:  the use of nearest neighbour methods to perform cluster and classification analysis of spectral data and the use of polygonal simplification and estimation techniques to improve data acquisition in nuclear magnetic resonance spectroscopy.