Area and perimeter measurement of blobs in discrete binary pictures

In picture processing one is often confronted with the problem of deriving some geometrical parameters (e.g., area, perimeter) of continuous figures (blobs, curves) from their digitizations. This paper concerns some particular aspects of this problem, namely, the construction of practical, simple, and computationally fast methods for measuring accurately the area and perimeter of blobs given as digital binary pictures. The analysis of some properties of digital pictures leads to two such methods. The first one uses only local, position-invariant parallel picture processing operations. The second one uses explicit polygonal approximations of the picture contour, with controlled degree of approximation, and can work on more noisy pictures. The methods were practically tested in a working program for shape factor measurement of fiber sections. In addition some useful properties of Freeman's digitization scheme are investigated and proved.