Nicola Cross and R.G. Wilson, Object Representation Using Circular Harmonics (June 1, 1994).
The system presented here is one that can be used to project information describing the corners of an object from some storage area, down onto a network. The idea is to reinforce the detection of object boundaries performed by a Hopfield network. These networks are efficient in terms of detecting edges, but are less efficient at detecting corners. This is because the Hopfield network works by assuming that an edge will continue in a more or less straight line. A ripple filter is used; this projects ripples of vectors onto the areas where corners are expected. Each vector consists of: a magnitude that indicates a level of certainty about the position of the corner, and a direction which indicates the expected orientation of the corner. The vectors are used by the Hopfield network to override existing straight links with curved links, so helping it to detect corners. We describe a method for projecting sectors of the ripples using circular harmonics. Possible extensions and improvements to the work are considered.