Value-and-Criterion Filters: A new filter structure based upon morphological opening and closing

In this paper, we introduce the value-and-criterion filter structure and give an example of a filter with the structure. The value-and-criterion filter structure is based on morphological opening (or closing), which is actually two filters applied sequentially: the first assigns values based on the original image values, and the second assigns values based on the results of the first. The value-and-criterion structure is similar, but includes an additional step in parallel to the first that computes a different set of values to use as criteria for selecting a final value. Value-and-criterion filters have a “value” function (V) and a “criterion” function (C), each operating separately on the original image, and a “selection” operator (S) acting on the output of C. The selection operator chooses a location from the output of C, and the output of V at that point is the output of the overall filter. The value-andcriterion structure allows the use of different linear and nonlinear elements in a single filter, but also provides the shape control of morphological filters. An example of a value-and-criterion filter is the Mean of Least Variance (MLV) filter, which we define to have V = mean, C = variance, and S = minimum. The MLV filter resembles several earlier edge-preserving smoothing filters, but performs better and is more flexible and more efficient. The MLV filter smooths homogeneous regions and enhances edges, and is therefore useful in segmentation algorithms. We illustrate its response to various image features and compare it to the median filter on different biomedical images.