Some researchers used less than 40 Gabor Filters but very rarely. Why are 40 Gabor Filters more often used? Please answer in detail with justification.
It really depends on the application at hand, and the trade-off between computational speed and the desired accuracy. Gabor filters are typically used for detecting certain aspects of an image, such as edges and textures, or for analysing the image with respect to larger structures, such as object detection and character recognition.
A Gabor filter is essentially a sinusoid modulated by a Gaussian. One can think of the frequency and orientation of the sinusoid, and the scale of the Gaussian as the parameters which characterise each of the Gabor filters within the bank. Just how many combinations of these parameters are used is something which the practitioner needs to consider with care, to come up with a suitable compromise for a given application.
Typical orientations are 0, 45, 90, and 135 degrees. The frequencies of the sinusoid depend on the width of the processing kernel. Typically, for a PxP kernel, 4Log2(P/2) filters are constructed.
Why 40? Well, here is one possible explanation. For a typical 5x5 pixel kernel, 4Log2(P/2) rounds up to 10. Combined with the four typical orientations of 0, 45, 90, and 135 degrees gives 40. As to the scale of the Gaussian, one value is typically chosen, and applied to all the filters in the bank.
As is normally the case with good filter design, there are no hard and fast rules on how to pick the scales, orientations, or frequencies. A practitioner may experiment with these parameters to find a good combination for solving a given problem. Some researchers have proposed guidelines on how to select these parameters, in way of rules of thumb, for specific applications. Others have proposed recursive filtering where the scale and resolution is stepped up or down (typically in octaves) in each recursion. While others have employed machine learning methods combined with human expert input, in the form of supervised learning techniques.
These are but a few examples of how this problem has been approached. One finds in the literature a great many other approaches, just as diverse as their target applications. Hope the above sheds some light on this topic, and goes some way to answering your question.
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