In computer vision, one often wants to analyse oriented image structures, like edges under a certain angle. One could filter the image with a range of oriented kernels which cover the whole continuum of angles present in the image. However, this would demand a high computational cost. In literature, it is shown that one can restrict the computations to filter the image with a fixed set of basic kernels, and interpolate the image filtered with a kernel under an arbitrary direction from the results of the image filtered with the basic kernels [1, 2]. Such a set of kernels is called a steerable filter set.

- Steerable pyramid with odd filters
- Steerable pyramid with even filters
- Why quadrature sets of filters?
- Noise reduction
- Image restoration

My publications (with pdf's online) can be found here. Most of them use steerable pyramids.

in which you can find a Fourier-domain based implementation in C++ of the real and the complex steerable pyramid can be found here. This software is part of my larger image processing source code STIRA

[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. P. Simoncelli, W. T. Freeman, E. H. Adelson, and D. J. Heeger, "Shiftable multi-scale transforms," IEEE Trans. Informations Theory, vol. 38, no. 2, 1992.