Wavelet transforms on vector spaces as a method of multispectral image characterisation

A new form of wavelet-based feature extraction has been developed for the multiresolution analysis of multispectral imagery. The wavelet components are vector-valued and can be used to characterise multispectral phenomena such as colour, in addition to brightness, position, scale and orientation. The authors show that various types of multispectral natural background have colour scale invariance, leading to an extension of the concept of selfsimilarity and enabling fractal models to characterise this type of data. Background selfsimilarity leads to a wavelet transformation which for many types of multispectral background is statistically invariant with respect to its parameters of position, scale and orientation. A norm, related to the background distribution, has been defined on the wavelet vector space and is used to identify objects of unusual brightness and colour. Wavelet-based feature extraction has been used to identify and characterise artefacts such as vehicles, roads and ship tracks in strongly electro-optical and infrared multispectral images.