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IMA Annual Program Year Workshop
New Mathematics and Algorithms for 3-D Image Analysis
January 9-12, 2006

Les G. Butler Department of Chemistry, Louisiana State University
Gestur Olafsson Department of Mathematics, Louisiana State University
Eric Todd Quinto Department of Mathematics, Tufts University

New mathematics and algorithms are needed for 3-D image acquisition and analysis. The 3-D images come from many disciplines: biomedicine, geology, chemistry, and microfabrication. The mathematics is wide-ranging and includes at least tomography and inverse problems, wavelets, PDE, and conformal mapping. The depth of the problem and the extent of the mathematics argue for developing long-term collaborations between mathematicians and scientists. This workshops is a step toward that end.

This workshop will focus on two topics: the combination of multiple 3-D images into a reduced set of images; and the analysis of images with simple geometric shapes.

A goal in the first area is to use multiple reconstructions of the raw data to better perform image segmentation. For example, edge images (e.g., using ?-tomography) can be combined with composition images to derive a set of final images of much greater value to the experimentalists.

The analysis of simple geometric shapes has received little attention and yet could illuminate entirely new strategies in 3-D image analysis. Many non-medical problems involve high-quality images of objects with simple shapes, and this is an excellent starting point for new mathematics and algorithms.