Proceedings PaperThree-dimensional mathematical morphology applications
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This paper reports on new results using three-dimensional binary ranking transforms. These transforms use the face-centered-cubic (FCC) tessellation which is the extension of the planar hexagonal transform in two dimensions. In this tessellation each voxel is surrounded by 12 equidistant neighbors. This leads to an interesting computational structure where any transform may be calculated by addressing a 8192-location lookup table. Thresholded medical images from CT or MR scanners have been processed to locate and measure volumes, both interior and exterior surface areas, surface convexity and concavity, tunnels, etc. Graylevel images may also be processed by column encoding where columns of voxels are erected at each x,y location whose height in the z-direction is proportional to the value of the graylevel image at that point. Using column-encoded graylevel images, three-dimensional mathem atical morphology transforms have been found which correspond to highpass, bandpass, and lowpass filters. These filters have the remarkable properties of sharp cutoffs (as steep as -60dB per octave) with no phase shifts. This paper presents several examples in military target detection, medical image analysis, and computer graphics.