Dependence structures in multidimensional arrays

Abstract

In the process of data acquisition the information obtained are more than often contaminated by noise. To purify the data smoothers are designed to remove the noise. The LULU operators are such smoothers, more speci cally, they are designed to remove impulsive noise. Carl Rohwer and his collaborators devel- oped the LULU operators in one dimension in the last four decades and, more recently, the operators have been extended to higher dimensions by Roumen Anguelov and Inger Fabris-Rotelli [2]. The prop- erties in shape preservation and total variation preservation are extended from one-dimensional LULU operators. This allows for smoothing with the operators in images. However, because their de nition uses a morphological concept of a connection, the question of how complex the connectivity should be therefore arises. Using the results from correlation analysis, we explore the extent at which the pixels of an image depend on its neighbours and establish the complexity of the connectivity for LULU operators in two-dimensions. In addition, as a measure of how e ective the LULU smoothers remove noise, we examine the noise extractions by the operators for images.