4.4 Phase Spectrum of the Quaternion Fourier Transform Approach

In the case of multiple channels, PFT can be easily extended to a phase quaternion Fourier transform (PQFT) approach if multidimensional data at each pixel can be represented as a quaternion [5, 6]. The quaternion is a mathematical tool in multidimensional signal processing [28]. In later discussion, we will see that the use of the quaternion in the visual attention model has somewhat biological reason.

4.4.1 Biological Plausibility for Multichannel Representation

Most of the spatial domain models consider several low-level features as different feature maps or channels, which are coincident with physiological results. Let us recall the cells in the low-level visual cortex. Several simple cells that are close together share a receptive field in the input scene. These simple cells extract different features in the receptive field such as intensity, colour, orientations and so on, which can be simulated by a neural network [29]. Figure 4.7 gives a sketch of receptive fields and their related simple cells, where visual input is regarded as the input image or retina of the eye, and the ellipses on the visual input are these overlapped receptive fields that cover the whole visual input. Each receptive field is related to a cell set in a row-dashed block or to same location (one pixel) of many feature images. In Figure 4.7 we only draw the receptive fields on one side of the visual input. In each row-dashed block of this ...

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