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Due to their biological relevance (Daugman, 1980; Marcelja, 1980) and computational properties Gabor wavelets were introduced to image analysis. As a feature generator Gabor filters are widely used in face recognition. .
Since the kernels of Gabor wavelets are similar to the 2D receptive field profiles of the mammalian cortical simple cells, they exhibit desirable characteristics of spatial locality and orientation selectivity. Also they are optimally localized in the space and frequency domains. The Gabor wavelets (kernels / filters) can be defined as following, (Lades, et al., 1993)
(1) where
and
define the scale and orientation of the Gabor kernel,
denotes the pixel, i.e.,
;
denotes the Euclidean norm operator, and the wave vector
is defined as:
(2) where
is the orientation parameter and
, here
is the spacing factor between filters in the frequency domain.
Usually, Gabor filters at five scales (
in Equation (1), and eight orientations (
ranging between 
to 
in Equation (2) are applied on each preprocessed facial image. These 40 filters are shown in Figure 1.
Figure 1. Real part of Gabor kernels: 8 orientations (
) and 5 scales (
)
Key Terms in this Chapter
Primary Visual Cortex: The part of the cerebral cortex responsible for processing visual information.
Face Authentication: Concerned with validating a claimed identity based on the image of a face.
Principal Component Analysis (PCA): An orthogonal linear transformation that transforms the data to a new coordinate system preferably lower dimensional than original.
Local Gabor Binary Pattern Histogram Sequence (LGBPHS): A non-statistics based face representation approach in which training procedure is unnecessary to construct the face model.
Support Vector Machine (SVM): A supervised learning model with associated learning algorithms that analyze data and recognize patterns.
Gabor Wavelet: A set of linear filters used to extract features from multidimensional signal.
Face Recognition: Biometric identification by scanning a person's face and matching it against a library of known faces.