Analysis of the digitized boundaries of planar objects

Abstract The digitized boundary of an object can be expressed as a chain of points or of directions or of curvatures, all of which, however, are subject to contamination by spatial noise. The curvature chain is used to detect indentations in the boundary and it can be freed of noise (smoothed) by convolving it with a rectangular filter, once (the Freeman operation), twice (the Gallus operation) or more times. An analysis is made of the spatial frequencies passed by these operations. The analysis provides criteria for determining the optimal values of the width of the filter and the number of times it should be applied. The smoothing procedure is applied to the boundaries of conjugated objects consisting of two or more juxtaposed elementary objects (muscle fibres seen in transverse section). It is then possible to pick out indentations (nodes) in a boundary. The nodes are classified and matched and lines of segmentation are drawn between matched pairs. Criteria of acceptable matching of node pairs are described and examples of segmentation are illustrated.