Closed Principle Curves Learning and Algorithm for Topological Recognition of Bounded Domains in Plane
平面有界闭区域图形的拓扑分类识别

By applying closed principal curve learning algorithm,we can obtain a simple polydragon as an approach for every simple closed curve in plane.So we can extract the boundary of every connect closed domain (?) in plane by simple polydragons.Thus we only need to consider the case of all domain which boundaries are simple polydragons.In this case,by topological degree theory,we can define conjunction index L_(i.j)=ind(P_i,P_j)for two un-joint simple closed curves P_i,P_j in plane,and conjunction matrix I((?))=(I_(i,j))for every bounded closed domain (?) in lane.Then we in- troduce the conception of F-homeomorphism for any two pictures in plane,and apply this conception to image recogni- tion.In5],combining the algebraic topology method,we have proven that conjunction matrix is complete topological invariant of bounded closed domain (?) in plane under F-homeomorphism.so,for any two bounded closed domain in plane (?)_1 and (?)_2,we design several algorithms to pick-up their boundaries ,computer their conjunction matrixes,and compare their conjunction matrixes when they will be the same.after all,we have satisfactorily resolved the problem of topological recognition of bounded closed domain in plane under F-homeomorphism.