A method of finding critical (or corner) points and describing a two-dimensional closed boundary is presented. The method uses a split-and-merge technique. It first splits a closed boundary in half until the boundary is approximated by a line within a given error bound to find critical points and all the control points are linked by lines, that is, linearly approximated. Next, by finding some breaking points which have sharp angles between three critical points, a closed boundary is divided by some intervals. Within each interval, a merging technique based on an LMS (least-mean-square) error is used to reduce the number of critical points and segments. Then, each shape is represented by an ordered sequence of line segments and circular arc segments with control points as vertex points. The resulting description is a good approximation of the original in the sense that it makes interesting points explicit and achieves significant data compression.