3d steerable filters

Example of a three-dimensional steerable filter. Surfaces of constant value are shown for the six basis filters of a second derivative of a three-dimensional Gaussian. Linear combinations of these six filters can synthesize the filter rotated to any orientation in three-space. Such three-dimensional steerable filters are useful for analysis and enhancement of motion sequences or volumetric image data, such as MRI or CT data. For discussions of steerable filters in three or more dimensions, see references below. (Martin Friedmann rendered this image with the Thingworld program).

References

W. T. Freeman, Steerable Filters and Local Analysis of Image Structure, Ph.D. Thesis, Massachusetts Institute of Technology, 1992.

W. T. Freeman and E. H. Adelson, The design and use of steerable filters, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 13, no. 9, pp. 891 - 906, September, 1991. MIT Vision and Modeling Group TR 126.

H. Knutsson, L. Haglund and H. Barman, A tensor based approach to structure analysis and enhancement in 2D, 3D, and 4D, IEEE Signal Processing Society, Proc. 7th Workshop on Multidimensional Signal Processing, Lake Placid, New York, page 9.10, 1991.

H. Knutsson, L. Haglund and G. H. Granlund, Tensor field controlled image sequence enhancement, SSAB Symposium on Image Analysis, March 1990, Linkoping, Sweden.

P. Perona, Deformable kernels for early vision, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp. 488-499, May, 1995.