Inhomogeneous spatial modelling of DPT pulses for marine images

Abstract

The Discrete Pulse Transform (DPT) is a nonlinear decomposition of a signal and extracts the structures in a signal at discrete scale levels. This study models the image structure extracted using the DPT as connected components. For this purpose, the Matérn cluster process is being used as it mimics the pulses of the DPT as clusters. In this paper it is applied to a marine image. Inhomogeneity of the pattern is dealt with by means of the fitted intensity. The model residuals exhibited the same pattern as the original image, and a refit resulted in residuals without pattern. The study concludes that the Matérn cluster model well fits the pulses obtained using the DPT and is well able to model the wave pulses of the ocean surface as clusters. This type of hierarchical cluster modelling presents interesting opportunities for simulations via conditioning.