| In this dissertation a new class of nonlinear filters is introduced and analyzed. These filters are rank order based and will be referred to as lower-upper-middle (LUM) filters since their output is determined by comparing lower and upper order statistics to the middle sample in the filter window. With an appropriate choice of parameters, LUM filters can be designed for outlier rejection, smoothing, and sharpening. This class of filters is extraordinarily versatile without sacrificing simplicity and has many advantages over existing filtering techniques.;The smoothing characteristics of the LUM filter are controlled by one of two filter parameters. Varying this parameter changes the level of smoothing from no smoothing to that of the median. Having such control allows one to best balance the tradeoffs between noise smoothing and signal detail preservation. If this parameter is selected such that a small amount of smoothing is performed then the filter functions as an outlier rejector. It will remove outliers while leaving most "normal" samples unmodified.;LUM filters can also be designed to enhance edge gradients. The amount of enhancement done by the LUM filter is controlled by the second filter parameter. It is demonstrated that LUM filters avoid many of the shortcomings of conventional 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 type noise while simultaneously enhancing edges. Furthermore, LUM filters do not cause any overshoot or undershoot.;Many statistical and deterministic properties of the LUM filters are developed. Filter design techniques are discussed and a number of experimental results are presented in order illustrate the performance of these filters. The experiments include applying the new filters to one-dimensional signals, grey scale images and color images. A quantitative comparison between the LUM and other techniques is presented and many filtered signals and images are shown for subjective evaluation. Applications of the filters to edge detection are also considered. Furthermore, both the hardware and software implementation issues are addressed and a VLSI chip design for implementing the LUM filter is discussed. |
