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.