Fuzzy and rule-based image convolution

An image can be sharpened by high pass filtering of its discrete Fourier transform or by an equivalent convolution processing in the spatial domain. Edge detection is a form of drastic sharpening with conversion to black and white. The approach taken here to sharpening and edge detection, as well as smoothing and other processing is to use a ‘smart’ convolution mask that makes rule-based decisions. Upon employing gains in the rule consequents, we achieve a type of fuzzy convolution of the output pixels. We also enlarge images using our new type of fuzzy interpolation to obtain higher resolution, detect edges with the rules and then reduce to the original size to obtain better edges than by merely applying the edge detection rules to the original image. We provide examples of sharpening directly with our rules. We also provide examples of edge detection both with and without the enlargement–reduction process.