Advantages And Disadvantages Of Gabor Filter

Earlier than 1946, the Fourier system was the futuristic in signal analysis. The premise of the Fourier analysis is representation of random signal with trigonometric functions called Fourier series. The purpose of Fourier transform is to convert a time-domain signal into the frequency-domain, and to measure the frequency components of the signal. The frequency components at specific locations of an image are used to represent the texture features of that image. Texture features calculated from high frequency elements are the main separating factors between images that are used in CBIR. Therefore, frequency information at particular locations is required to differentiate images in CBIR. However, the disadvantage of Fourier transform is that

It is ideal as far as minimizing the joint uncertainty in space and frequency, and is often utilized as an orientation and scale tunable edge and line (bar) detector. There have been various approaches suggested to characterize textures of images based on Gabor filters. Gabor wavelet transform is a suitable multiresolution technique that represents the texture of an image in an effective way using multiple orientations and scales. This technique has a spatial property that is indistinguishable to mammalian perceptual vision, thereby giving researchers a better chance to utilize it in image processing. Gabor filters are develops to perform superior than wavelet transform and other multiresolution approaches in constituting to textures and retrieving images due to its multiple orientation approach

Figure 3.2: Gabor Filter Composition for 1-D Signals.
The 2-D Gabor function can be identified by the frequency of the sinusoid W and the standard deviation σx and σy, of the Gaussian envelope as: g(x,y)=1/(2πσ_x σ_y ) exp(-1/2 (x^2/(σ_x^2 )+y^2/(σ_y^2 ))+2πjWx) (3.3) where W denotes the radial frequency of the Gabor function. The space constants σx and σy define the Gaussian envelope along the x and y axes. Furthermore can be defined that σu =1/(2πσx) and σv=1/(2πσy). A group of self-similar functions, referred to as Gabor wavelets, which have been utilized for image retrieval [11]. Gabor functions kind a complete but non-orthogonal basis set. Expanding a signal using this premise provides a localized frequency description.
3.3.3 Generation of Gabor Wavelets
Wavelets are families of basis functions developed by dilations (scaling) and translations of a elementary wavelet called the mother wavelet. The basis functions are themselves elementary functional building block of any wavelet family. A group of self-similar functions regarded as Gabor wavelets, is presently considered. Let g(x,y) be the mother Gabor wavelet, then this self-similar filter dictionary can be acquired by suitable dilations and rotations of g(x,y) through the generating function