Research And Development On The Recognition Of Topological Relations Of Graphs In Homework

The homework is an important teaching process in education. The reformation of homework technique is necessary due to the low efficiency of traditional methods. The distance homework system is a good trial to improve homework technique, which can solve the problems of automatic recognition and correction of mathematical expression. However,the distance homework system is still unable to correct the science and engineering courses' homework which contains graphics. This thesis concentrates on the automatic recognition and correction of graphics in homework.The graphics in homework are simple and informal, which are drawn by students in the process of doing their homework. This thesis analyses and summarizes the particularities of the technique of graphics' recognition: 1) The graphics in homework are blurry; 2) The technique of graphics' recognition is independent of the specific discipline's knowledge;3) The graphics in homework are relative to mathematical logic. Because of these particularities above and the graphics' specialties, no fixed starting point, no precise coordinates, and no unified proportion, the recognition of homework's graphics must use the similar recognition which base on the qualitative description of the graphics. The qualitative similar recognition of homework's graphics is studied in this paper and the results are as following:1) The paper proposes the GQD model as the model of the homework graphics' qualitative description. The GQD model describes the qualitative specialties completely and effectively by extracting graphics' type, attributes, position relations and topological relations.2) The paper establishes a kind of denoising mechanism to eliminate noise in the homework graphics. This noise existing in the graphics will disturb the later researches, such as the topology calculating and comprehensive recognition. So the denoising mechanism can effectively eliminate the noise interference,and ensure the following study.3) The paper presents the concept of "Generalization topological relations" and complete the classification and calculation of homework graphics' topological relations. The concept is presented in order to describe the topological relations of the homework graphics more accurate and detailed.