Edge detection is a projection

A desirable property of any edge detector is that it be a projection in the mathematical sense, that is, that when it is applied to its own output it produces no further change. This report examines the behaviour of some conventional and some new operators when applied to line-drawings. The Marr-Hildreth and some gradient operators are among the conventional operators examined. Also a class of energy feature detectors is explored. It is shown that the energy feature detector is a true projection and does not proliferate edges when applied to a line-drawing, whereas several of the conventional operators do.