A new version of Blum's medial axial function (MAF) for visual patterns is presented. The new version is incorporated in the chord space analysis framework developed by the authors and has the advantage that, unlike the original version, it is defined for grey level pictures and is a much more ``robust'' definition. Computer generated examples are shown, and it is indicated how the technique is being applied by the authors in the development of a character recognition system.

A new type of nonlinear filter, called theE-filter, is introduced that involves a transformation of the independent variable of the input function. It is shown how anE-filter can be designed to filter out superimposed "noise" on a signal, leaving the large peaks of the signal unattenuated. Unlike a Iow-pass linear filter, the low-passE-filter is almost frequency independent and so does not affect the amplitudes of large sharp peaks of the signal. It is shown that theE-filter can be realized in real time and that a wide class ofE-filters have a filtering action which is independent of the dc level of the input signal.

A conceptual framework for an analytic theory of form or shape is presented. It is demonstrated that by using various statistics on the chords of a pattern objective measures of pattern features can be obtained. The autocorrelation function of the patterns is one such statistic, and it is shown how the autocorrelation function can be exploited to enhance and/or extract pattern features. One of the interesting facets of the theory is that it can be implemented using a parallel processing type of computer.

One aspect of a new theory of feature perception is considered. An algorithm is presented which can perceive and locate various features of a pattern by analyzing a statistic of the "chords" of the pattern. The procedure is illustrated by applying the algorithm to a pattern containing the Muller-Lyer figures. In measuring the length of the figures it is found that the algorithm has a visual illusion. A machine capable of executing the algorithm is described.