Geometry in Action

Medical Imaging

A key problem in medical computation is reconstruction of shapes (of organs, bones, tumors etc) from lower dimensional information such as CAT scans and sonograms. The CAT scan information is originally one-dimensional, but is transformed into two-dimensional slices by signal processing techniques. However the reconstruction of three-dimensional shapes from slices becomes a more geometric problem, which can be abstracted as that of finding a surface connecting a collection of contour lines or data points. A different problem relates to compression of medical images for transmission and storage; this differs from most other applications of image compression in that little or no loss of information can be tolerated.

Part of Geometry in Action, a collection of applications of computational geometry.
David Eppstein, Theory Group, ICS, UC Irvine.

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