Statistical properties of the contours of random surfaces

A random surface is a sample function of a random process
\{f(x, y)\}
depending on two real parameters. Examples of random surfaces would be: photographs or television pictures; topographic maps; atmospheric pressure charts; and the like. A number of statistical properties of the contours of such surfaces are derived. An application of the results to the problem of obtaining bounds on the information content of quantized random surfaces is outlined.