A parametrized family of nonlinear image smoothing filters

A parameterized family of nonlinear image smoothers is developed which provides a range of tradeoffs between noise smoothing and edge retention. The presentation unifies many approaches to the problem of image smoothing where the estimate of the gray level of a pixel is taken as a nonlinear data-dependent weighted sum of the gray levels of the pixel´s neighborhood. Local confidence measures are defined, and it is shown how filters based on the sample median, the absolute gradient, and the sample variance incorporate these confidence measures in their nonlinear weights. The notion of localized sample variance is then introduced and shown to constitute a more appropriate confidence measure. Using the localized sample variances, a family of filters termed LV_n is derived. Smaller values of n provide better noise removal, whereas higher values of n provide better edge preservation. Experiments indicate that the LV ₂ member of the family is very efficient for noise removal, while the extreme member LV_∞ is nearly perfect for edge retention. A good tradeoff is achieved using n=4, 5, or 6. These values give the most aesthetically appealing results and yield lower RMS error than those of other filters discussed