(Xi) -filters were introduced in the mid-1980s by the author and have been used in many applications, including industrial inspection, remote sensing, and medicine. This paper reviews some new developments in each of these areas. The (Xi) -filter is based on high- speed LUT (lookup table) operations wherein small-kernel, nonlinear convolutions are performed on three-dimensional data. In order to execute 3D transforms by LUT, it is necessary to utilize as compact a kernel as possible. This has led to the FCC (face-centered- cubic) tessellation where the kernel comprises only 13 binary data elements or voxels. (This is in contradistinction to the Cartesian tessellation where the kernel comprises 27 voxels.) Since each LUT contains at each of 8192 locations the transformed value of the voxel, the program word that defines a single (Xi) -filter transform is 8192 bits in length. There are, therefore, an essentially infinite number of program words and therefore an infinite number of transforms. In order to delimit the number of transforms to a set that are both useful and manageable, program works limited to the various ranking filters have been generated. In a kernel of 13 elements, there are, of course, only 13 ranks. By iterating (Xi) -filters based on these ranking transforms many interesting operations are possible as illustrated in this paper.