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.

Your browser is not Java enabled. Instead you can download and unzip the software and execute the applets locally through the provided batch scripts: click here. Note that this still requires a local Java installation.

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