<title>LUM filters for smoothing and sharpening</title>

Abstract

We introduce the LUM filter for both smoothing and sharpening. The LUM filter is a moving window estimator that does the following: it finds the order statistics by sorting the samples in the window, and it compares a lower order statistic, an upper order statistic, and the middle sample. The two order statistics define a range of 'normal' values. If smoothing is desired, the LUM filter outputs the middle sample if it is between the two order statistics; otherwise, it outputs the closest of the two order statistics. If sharpening is desired, the roles are reversed. The LUM sharpener outputs the middle sample if it is outside the two order statistics; otherwise it outputs the closest of the two order statistics. Furthermore, both characteristics can be achieved at the same time. We compare the LUM filter against common alternatives such as linear smoothers and sharpeners, moving medians, and sharpeners such as the CS filter. In summary, we believe the LUM filter is widely applicable and has good performance in a wide range of applications.