Symmetry Axis Research And Application For Closed Graph

Currently, researchers have done a lot of work on digital protection of tangiblecultural heritage. But for intangible cultural heritage, the protection is just beginning,especially in China with a long traditional culture. Paper-cut is a national intangiblecultural heritage and an oldest folk art of our nation. Symmetry is an importantcriterion in visual aesthetic and a main feature of paper-cut pattern. The symmetryaxis research of paper-cut pattern is to study carving skills of paper-cut. It plays animportant role to protect paper-cut culture by keeping production techniques indigital form.This paper elaborates the relation between paper-cut crease and symmetry axisof non-circular closed graph. It uses classical image boundary detection method toget the boundary of original image and the closed graph. Extracting feature pointsfrom closed graph which does not include the circular, closed curve segments madeup with two neighboring feature points in closed graph are classified to let closedcurve segments of the same property together as a class. Any closed graph whichdoes not include the circular is basically processed on the basis of class-set. Pascaltheorem is an effective method to determine crossover points of pair ofcorresponding points is on one line. As its shortcoming is the limitation to aquadratic curve, the paper improves the theorem and expands the prerequisite todetermine whether crossover points of three pairs of corresponding points which arenot in quadratic curve are on a line. The innovation is the achievement to determinewhether any single closed graph in plane are symmetrical and find out all symmetryaxes by taking advantage of classified thought and classical Pascal theorem. With the help of theoretical data and software programs, correctness of the improved theoremis verified. It lays the foundation for study symmetry of several closed graphs.Moreover, based on the study of single closed graph and in virtue of optimalcorner points found PNF normalization method, axis symmetry judgment methodand symmetry axis seeking way are proposed for two closed graphs. First, wecalculate the number of corresponding closed curve segment of two closed curves,and judge whether elements of ordered class-set are same. Corresponding featurepoint sequence is obtained. Secondly, whether the feature points are in the sameorder is ascertained by using improved Pascal theorem and best corner points.Thirdly, two closed curves are determined whether or not to have axis-symmetricproperty. The symmetry axis of closed graphs are invariant including translation,rotation, scaling.In the end, the proposed theorems and methods are summarized. Potentialapplication value is showed and prospect for future work is leaded.