It is widely recognized that effective image processing and machine vision must involve the use of information at multiple scales, and that models of human vision must be multi-scale as well. The most commonly used image representations are linear transforms, in which an image is decomposed into a sum of elementary basis functions. Besides being well understood, linear transformations which can be expressed in terms of convolutions provide a useful model of early processing in the human visual system. In this presentation, we describe a new family of orthogonal multi-scale representations that have useful properties for image processing and vision modelling.