Algebraic description of curve structure

The authors propose a compact and concise method of describing curves in terms of the quasi-topological features and the structure of each singular point. The quasi-topological features are the convexity, loop, and connectivity. The quasi-topological structure is analyzed in a hierarchical way, and algebraic structure is presented explicitly for each representation level. The lower-level representations are integrated into the higher-level one in a systematic way. When a curve has singular points (branch points), the curve is decomposed into components, where each is a simple arc or a simple closed curve, by decomposing each singular point. The description scheme is applied to character recognition