1. A method of filtering an image to remove minor parts thereof without degrading major image identifying edges, comprising the steps of: determining the value of at least one visible characteristic for each pixel of the image; ascertaining the same characteristic values of neighboring pixels for each pixel, the spatial extent of neighboring pixels for each pixel being governed by a single scale parameter; calculating a solution of a nonlinear equation based upon weighted average pixel characteristic values from neighboring image pixels for each given pixel; and reconstructing an image representation displaying the calculated solution of neighboring nonlinearly weighted average characteristic values in place of each original pixel.