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).
W. T. Freeman, Steerable Filters and Local Analysis of Image Structure,
Massachusetts Institute of Technology,
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,
H. Knutsson, L. Haglund and G. H. Granlund,
Tensor field controlled image sequence enhancement,
SSAB Symposium on Image Analysis, March
P. Perona, Deformable kernels for early vision, IEEE Trans. on
Pattern Analysis and Machine Intelligence, vol. 17, no. 5,
pp. 488-499, May, 1995.