ALGEBRAIC DESCRIPTION OF CURVE STRUCTURE

We propose a compact and concise description method of curves in terms of the quasi-topological features and the structure of each singular point. By quasi-topological features, we mean the convexity, loop, and connectivity. The quasi-topological structure is analyzed in a hierarchical way, and algebraic structure is presented explicitly on each representation level. The lower level representations are integrated into the higher level one in the 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.