<title>Multiresolution directional-oriented image transform based on Gaussian derivatives</title>

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 it includes some important properties of human vision such as the Gaussian derivative model for early vision proposed by Young. The image transform that we propose in this work uses similar analysis operators as 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. 3) In the case of 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 problem of image coding. Practical considerations are also of concern.