The area and the perimeter of a planar object are two useful features to describe the shape of the object, and again the motion of it. This paper deals with the estimation of the two features from a discrete binary image. The area can often be accurately estimated by counting the number of pixels inside the object. However, the estimation of the perimeter is a problem, since many possible contours, all having different lengths, correspond to a specific discrete realization. Thus, to develop a practical length estimator, some reasonable assumption about the original contour should be made. We assume that the boundary of a blob-like object consists of chains of circular arcs, and therefore evaluate the precision of several area and length estimators applied to circles. The problem of efficient computation is also discussed.