Measurement of the lengths of digitized curved lines

An examination is made of methods of measuring the lengths of arbitrarily shaped smooth curves from their quantized representations, both in the absence and in the presence of noise. For 4-way encoded curves in the absence of noise, the length of the underlying smooth curve can be accurately assessed as nπ/4 where n is the number of direction vectors in the curve, or as a function of n and the number of corners in the curve. Good measurements can also be obtained in the presence or absence of noise by means of an m-step polygon measure, or after direction or curvature smoothing. The methods are explained and their merits are compared.