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 Λ-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.