Advanced modeling of visual information processing: A multi-resolution directional-oriented image transform based on Gaussian derivatives

Abstract

In this work, a multi-channel model for image representation is derived based on the scale-space theory. This model is inspired in biological insights and includes some important properties of human vision such as the Gaussian derivative model for early vision proposed by Young [The Gaussian derivative theory of spatial vision: analysis of cortical cell receptive field line-weighting profiles, General Motors Res. Labs. Rep. 4920, 1986]. The image transform that we propose in this work uses analysis operators similar to those of the Hermite transform at multiple scales, but the synthesis scheme of our approach integrates the responses of all channels at different scales. The advantages of this scheme are: (1) Both analysis and synthesis operators are Gaussian derivatives. This allows for simplicity during implementation. (2) The operator functions possess better space-frequency localization, and it is possible to separate adjacent scales one octave apart, according to Wilson's results on human vision channels. [H.R. Wilson, J.R. Bergen, A four mechanism model for spatial vision. Vision Res. 19 (1979) 19–32). (3) In the case of two-dimensional (2-D) signals, it is easy to analyze local orientations at different scales. A discrete approximation is also derived from an asymptotic relation between the Gaussian derivatives and the discrete binomial filters. We show in this work how the proposed transform can be applied to the problems of image coding, noise reduction and image fusion. Practical considerations are also of concern.