Application of Gabor Wavelet in Quantum Holography for Image Recognition

Application of Gabor Wavelet in Quantum Holography for Image Recognition

Nuo Wi Tay (Multimedia University, Malaysia), Chu Kiong Loo (Multimedia University, Malaysia) and Mitja Perus (University of Ljubljana, Slovenia)
Copyright: © 2010 |Pages: 18
DOI: 10.4018/jnmc.2010010104
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Abstract

Gabor wavelet is considered the best mathematical descriptor for receptive fields in the striate cortex. As a basis function, it is suitable to sparsely represent natural scenes due to its property in maximizing information. It is argued that Gabor-like receptive fields emerged by the sparseness-enforcing or infomax method, with sparseness-enforcing being more biologically plausible. This paper incorporates Gabor over-complete representation into Quantum Holography for image recognition tasks. Correlations are performed using sampled result from all frequencies as well as the optimum frequency. Correlation is also performed using only those points of least activity, which shows improvements in recognition. Analysis on the use of conjugation in reconstruction is provided. The authors also suggest improvements through iterative methods for reconstruction.
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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 1st and 2nd convoluted with a Difference-of-Gaussian function and the 3rd with the Gabor wavelet. Since this paper focuses on the Gabor transform in image recognition, the 1st and 2nd stage of the visual pathway with not be touched upon.

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