Achieving Minimum Length Scale in Heaviside-based Morphological Filters

Minimum length scale can fulfil the requirements for manufacturing and provide the extended robustness of design performance. This paper proposes a method to impose the minimum length scale in Heaviside-based morphological filters. With the method, the physical filter radius is first utilized to construct the element neighbourhood in density filter. Then, the density filter is embedded in the Heaviside filter and modified Heaviside filter. Finally, the morphological filters are constructed based on the principles of morphology-based restriction schemes, in which the Heaviside filter plays the role of dilation filter and the modified Heaviside filter acts as the erosion filter. Test results show that the minimum structural sizes in the final design are larger than the specified filter radius size. The characteristics of the basic filters and the embedded filters are discussed.