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Steering the Steerable Pyramid Transform filters

One of the primary advantages of the Steerable Pyramid transform (see [1]) is that the filter response in an arbitrary direction can be obtained as a linear sum of the filter responses computed for a *fixed* number of orientations. Equivalently, by taking linear sums of the basis elements, an arbitrary rotated version of the main basis element can be obtained. This property is usually called *steerability*. Below, a visual illustration is given.

By using steerable filters for different scales and orientations, a multi-scale and multi-directional transform is obtained. This transform is called the Steerable Pyramid Transform and is presented in [2].

Brief explanation of the parameters:

*Scale*: the dyadic scale index of the basis function (1=finest scale, 4=coarsest scale).
*Orientations*: the number of steering filters being used (more filters=finer angular resolution).
*Angle*: the steering angle used for computing the synthesized filter.
*Fourier space*: show the filters in frequency space.

#### References

- [1] W. T. Freeman and E. H. Adelson, "The design and use of steerable filters", IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 9, pp. 891--906, 1991.
- [2] E. Simoncelli, W. T. Freeman, E. H. Adelson, D. J. Heeger,
"Shiftable Multi-scale Transforms," IEEE Trans. Information Theory,
38(2):587–607, 1992