Image modeling with linear scale-invariant systems

Scaling or dilation is an integral part of the wavelet transform. The wavelet transform possesses certain scale-invariance properties. This paper explores scale invariance further in the construction of linear, two-dimensional, discrete-space, scale-invariant systems. Through a new definition of discrete-space, continuous-parameter dilation operation, deterministic and stochastic self-similarity in images is studied. It is shown that the dilation operation leads to the construction of linear scale-invariant systems for digital images. The paper provides methods for constructing such systems and shows application to the modeling of texture images.