Modelling of Learning and Perception

Centre of Excellence in Computational Complex Systems Research


Steerability Properties of Gabor Filters

Researchers: Ilkka Kalliomäki and Jouko Lampinen

Gabor filters are information-theoretically optimal oriented bandpass filters which have been traditionally used in pattern recognition as a generic framework for the representation of visual images. Gabor-based features are widely used in face recognition, for example. Neurological studies have found Gabor-type structures on the visual cortex of mammals. This fact suggests that the Gabor representation is an efficient one in pattern recognition tasks.

Steerable filters are another variety of 2D oriented filters. They have applications in a wide variety of early vision tasks including edge detection, orientation analysis, texture analysis and stereo vision. While non-optimal in terms of joint space-frequency uncertainty principle, steerable filters have other desirable properties as oriented feature detectors. The most notable of these is the ability to compute filter responses in arbitrary orientation by weighting the responses of a fixed filter bank with a handful of different orientations. This property is known as 'steerability'.

We have derived analytical steering equations for Gabor filters, which enable Gabor filters to be used as steerable filters. Some families of steerable filters are quite close to Gabor filters in terms of impulse responses, and the steering performance of Gabor filters can be understood via this connection. However, the steerability of Gabor filters is only approximate, and the accuracy depends heavily on the parameters and the number of different orientations in the bank.

We intend to apply the results to pose-invariant face recognition, where the variability of features due to orientation is a central problem. Using steerability, a simple and computationally efficient measure of feature similarity which is invariant to rotations in the image plane may be developed.

Figure 1

Figure 1. Steering Gabor filter bank into arbitrary orientations. First and second row portray Gabor filters in the spatial domain, and third and fourth row show the same filters in the frequency domain. Leftmost and rightmost columns correspond to known orientations in a bank of five different orientations. The four intermediate filters have been computed via analytical steering, and they approximate exact Gabor filters in the corresponding orientations very well both in spatial and frequency domains.