LUM filters: a class of rank-order-based filters for smoothing and sharpening

In this paper, we present a new class of rank-order-based filters, lower-upper-middle (LUM) filters. The output of these filters is determined by comparing a lowerand upper-order statistic to the middle sample in the filter window. These filters can be designed for smoothing, sharpening, and outlier rejection. This wide range of characteristics can be obtained from a single filter structure by simply varying the filter parameters. Thus, this class of filters is extraordinarily versatile. When used as smoothers, LUM filters can take on a range of smoothing characteristics. The level of smoothing done by the filter can range from no smoothing to that of the median. This flexibility allows the LUM filter to be designed to best balance the tradeoffs between noise smoothing and signal detail preservation. LUM filters can be designed to enhance edge gradients, We demonstrate that they avoid many of the shortcomings of linear edge-enhancing filters. Namely, LUM filters can be designed to be insensitive to low levels of additive noise and can be designed to remove impulsive noise while enhancing edges. Furthermore, LUM filters do not cause overshoot or undershoot. We develop some statistical and deterministic properties of the LUM filters and present a number of experimental results to illustrate the performance of these filters. These experiments include applying the new filters to 1-D signals and images.