Scanning Microscopy


Scanning electron microscopes, and transmission instruments equipped for EELS, generate a host of signals and hence of images from each pixel of the specimen. Numerous ingenious ways of coping with this multiplicity of information, which may be very different in character, have been devised, but no detailed study has yet been made of the appropriate mathematical structure, with the aid of which all this information could be manipulated reasonably easily.

One such structure falls within the subject that has come to be known as Image Algebra, the principal attraction of which is that we deal directly with entire images and not with individual pixels; the operations involved do of course ultimately take effect at pixel level. Despite its forbidding name, image algebra is intrinsically very simple and has the merit that the notion of "image" is very general. Images can in particular be multi-valued, that is, a set of values can be associated with every pixel. Indeed, a whole image is associated with each pixel, in the case of the very important class of images known as templates. Image algebra has proved to be an extremely fertile subject, generating many new ideas and especially, revealing several unsuspected relationships between different branches of image and signal processing.

The value of this approach will be examined, after a very simple introduction to the basic ideas. The application to image-spectra will be considered as a tangible example. We conclude with some speculations concerning the future of this rich new way of "picturing" images.

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