Application of Gabor Wavelet in Quantum Holography for Image Recognition

Introduction

The purpose of this paper is to combine Gabor transform with Quantum Associative memory (Peruš, 2005) on facial recognition. Gabor wavelet is considered the best mathematical descriptor for striate cortex receptive fields (Palmer, 1999; Buser & Imbert, 1992), which is selective to a particular orientation and spatial frequency. Careful comparison is done by (Jones & Palmer 1987) which supported this claim. It can be used to describe the orientation and spatial-frequency tuned receptive fields of simple cells in V1 (Marcelja, 1980). The design of biological cells fits the two 90 degree phase difference representations of Gabor wavelet (Pollen, 1981). Gabor wavelets representation is nearly affine invariant by manipulating its parameters (Kyrki et al., 2004). Although non-orthogonal, (Lee, 1996) derives conditions under which Gabor wavelets, which are generally non-orthogonal, behave as if they are orthogonal. Oversampling in primate’s visual system achieves this almost tight-frame condition, enabling reconstruction of high-resolution images from the wavelets. This, of course, is a lot more convenient than finding biorthogonal function which is quite difficult (Bastiaan, 1980). According to (Grossman, 1989), this overcompleteness provides a robust representation that is able to be stored by low precision neurons through redundancy. Besides, it provides a good medium for tasks like image segmentation. (Daugman, 1988; Lee, 1996)

Normal images are generally highly self-correlated due to internal morphological consistency, which should be utilized and exploited in image recognition (Daugman, 1988). Field (1993) shows that wavelet is the most suitable descriptor for natural images, which is relatively sparse compared to total spectral or spatial domain representation. Under the general cases, Gabor wavelet function can extract maximum information from an input image (Okajima, 1998). As shown by (Linsker, 1988), 1993, the RF of neurons employ an information-theoretic method by maximizing mutual information. He showed that mutual-information maximization is related to Hebbian learning rule for neural network connectivity (Linsker, 1988). Gabor-like receptive fields can emerge by sparseness-enforcing (Olshausen & Field, 1996, 1997) or by an Infomax method (Bell & Sejnowski, 1995, 1997). Both methods produce Gabor-like outputs as statistically independent scene-components. (Peruš, 2001a, 2005) have argued that the Olshausen-Field method is more biologically plausible than Bell-Sejnowski approach.

According to (Pribram, 1991), there is a triple convolution for preliminary visual pathway from retina to lateral geniculate nucleus (LGN) to the striate cortex (V1), with the 1^st and 2^nd convoluted with a Difference-of-Gaussian function and the 3^rd with the Gabor wavelet. Since this paper focuses on the Gabor transform in image recognition, the 1^st and 2^nd stage of the visual pathway with not be touched upon.