Contents
How are 1D Gabor functions used in face recognition?
The report is organized as follows: In section 2, the definition of 1D Gabor functions and 2D Gabor wavelets are introduced, and important mathematical properties and derivations are included. Applications on face recognition are presented in section 3, followed by texture features and classification in section 4.
Which is the optimal basis for the Gabor wavelet transform?
Among various wavelet bases, Gabor functions provide the optimal resolution in both the time (spatial) and frequency domains, and the Gabor wavelet transform seems to be the optimal basis to extract local features for several reasons [2]:
How is frequency resolution related to window size?
This is the effect of the Heisenberg–Gabor uncertainty principle 9 or the Gabor limit 10, i.e., one cannot simultaneously localize precisely a signal in both time and frequency 11. Frequency resolution is proportional to window size, as defined by the Rayleigh frequency 12, 13.
How is super resolution achieved in time frequency?
Time-frequency super-resolution is achieved by combining short, large-bandwidth wavelets, with longer, narrow-bandwidth wavelets.
Is the 2-D Gabor function a self similar wavelet?
The 2-D Gabor function defined in Eq.6 meets this form and could be seen as a set of self-similar Gabor wavelets. The spatial shifting terms are missing in Eq.6 while these could be compensated by the convolution operation between this equation and the input image.
Which is the shift of the Gabor filter?
A pictorial description of the fourier transform in (28) is given by fig 6-b, which is expectedly a gaussian shifted by (f1cos(θ), f1sin(θ)). Note the black dot, which is deliberately added at (f1cos(θ), f1sin(θ)), to verify the correctness of the shift. Also please note that, since lambda = 0.5, the transform is elliptical.
How is the Gabor wavelet transform used in image processing?
Among kinds of wavelet transforms, the Gabor wavelet transform has some impressive mathematical and biological properties and has been used frequently on researches of image processing. 1. Introduction