**Gabor T. Herman**

Graduate Center, City University of New York

Department of Computer Science

New York

USA

e-mail: gherman@gc.cuny.edu |
http://www.cs.gc.cuny.edu/~gherman |

**Abstract**:

A three-dimensional (3D) object can be represented as a linear
combination of "blobs" (these are spherically-symmetric
smooth functions) each attached to one of an efficiently-arranged
grid of points in space. The representation problem becomes that
of calculating how much weight to give to each of the individual
blobs based on some given data. Surfaces defined by such a
representation are inherently smooth, allowing superior 3D
displays based on such representations to those obtained from the
traditional voxel-based representations. Volume visualization can
be achieved by efficient footprint algorithms and associated
hardware mappings.

**Recommended readings**:

- R. M. Lewitt. Multidimensional digital image representations using generalized Kaiser-Bessel window functions. Journal of the Optical Society of America, Optics and Image Science, 7:1834-1846, 1990.
- R. Marabini, G. T. Herman, and J. M. Carazo. 3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). Ultramicroscopy, 72:53-65, 1997.
- S. Matej and R. M. Lewitt. Efficient 3D grids for image-reconstruction using spherically-symmetrical volume elements. IEEE Transactions on Nuclear Science, 42:1361-1370, 1996.
- S. Muraki. Volumetric shape description of range data using "Blobby Model". Computer Graphics, 25:227-235, 1991.