Noise filtering with edge preservation in digital images
Claudio Rey · cIRcle (University of British Columbia) · 2010
The widespread use of the absolute gradient and the sample variance in present day local noise filters in digital image processing is pointed out. It is shown that the sample variance and the absolute gradient can be viewed as measures of the modelling error for a simple zeroth order local image model. This is shown to lead to a general formulation of local noise filtering applicable to the great majority of current local noise niters for digital images. This formulations describes local noise filtering as a two step process. In the first step a robust estimation of every pixel z[sub o] is obtained. In the second step a better estimate of z[sub o] is obtained by performing a weighted sum within a neighborhood of z[sub o]. The weights in the second step are related to some measure of modelling error of the above zeroth order model; namely, the absolute gradient or the sample variance. Of the above two measures of modelling error, the sample variance is shown to be the least sensitive to noise. Furthermore, the sample variance is also more sensitive to faint image edges. Therefore,the sample variance is the most desirable of the above two measures of modelling error. Unfortunately, its use until now has been hampered by its poor edge localization. To solve this problem a new measure of modelling error is introduced which achieves far superior edge localization than the sample variance (though still lower than the absolute gradient) but maintains the low noise sensitivity. A filter is designed based on this new measure of modelling error (of the zeroth order model described above) which is shown to perform better, in a least squares sense, than all other local noise filters for non-impulsive additive and multiplicative noise. A practical implementation of this original filter is also presented.