This chapter presents a lattice algebra approach to hyperspectral image unmixing and to color image segmentation. The chapter consists of four main sections, with the first three sections being devoted to hyperspectral image unmixing and the last section covering color image segmentation. The first section introduces the reader to the concepts of hyperspectral imaging, end- members, image segmentation. and image unmixing. What may surprise is the fact that the mathematical basis of the image segmentation process is directly linked to the two associative memories W and M discussed in Chapter 5, and therefore called the WM-method.

The WM-method was first validated based on a hyperspectral image remotely acquired with the Airborne Visible and Infrared Imaging Spectrometer (AVIRIS) of NASA's Jet Propulsion Laboratory. The AVIRIS hyperspectral image is of the mining site of Cuprite, Nevada. It is one of the most studied hyperspectral images for the segmentation of various mineralogical and chemical compositions. A second validation was based on a hyperspectral image of Moffett Field, which is a remote sensing test site on the bay of San Francisco, a few kilometers north of Mountain View, California. The site includes the Naval Air Station Moffett Field, agriculture fields, water ponds, salt banks, and man-made constructions including several airplane hangars. A third validation was based on a hyperspectral image of the biological preserve at Jasper Ridge. All three validations were excellent when compared to other methods. Tables comparing the performance of the WM-method with other methods bear this out. The segmentation process based on the selection of the endmembers is called the

The final section is dedicated to color image segmentation. Here the reader is introduced to the meaning and uses of color image segmentation. Here again the W and M associative memories play an important role in the segmentation process. The chapter concludes with segmentation results and comparison with other methods.