Research On Line Detection And Circle Detection For The Diagram Of Plane Geometry Problems

With the rapid development of modern educational technology and artificial intelligence,re-search on the machine solver for the primary subject problems once again becomes popular.Compared to other subjects,mathematics is an subject based on quantities and relationships,it is a good starting point to explore the machine solving of mathematical problems to guide the developments of the general machine solver techniques.In the field of machine solution of mathematical problems,in view of the variety and complexity of the field of mathematics,the solution of primary mathematical problems is still a big difficulty,and plane geometry problems occupy a large part in the field of primary mathematics.Through the investigation and analysis of literature,at present,the main work in the research of plane geometry prob-lem solving focuses on the research of geometric reasoning and geometric proving.Most of plane geometry problems not only contain detailed text description,but also contain di-agrams with richer and more intuitive information expression.Therefore,in the field of geometric reasoning and geometric proving,the automatic understanding of plane geometry is a important part.However,in the literature reading of automatic understanding of plane geometry,it can be found that most of the research is based on existing image detection methods,such as circle detection method based on Hough transform,line detection method based on RAN SAC,etc.However,these methods are applicable to both images and dia-grams,but they also have many defects in the detection of diagrams.It can be found clearly that on the diagrams the speed of existing line detection algorithm is fast enough,but the ac-curacy is not very satisfactory,so the results of standard Hough transform line detection are proposed to be further process to obtain more accurate and complete results.And because the time-consuming of line detection algorithm is negligible compared to circle detection algorithm,a new circle detection algorithm for plane geometry diagrams which removed all the lines before detecting circle is proposed to solve problems of existing image detection methods such as slow detection speed or low detection accuracy.In the end,these detected information can be directly displayed to help students understand and independently explore the solution to the problem,or it can be induct the positional relationships between geo-metric primitives to integrate with text information or other geometric entity information to obtain more complete information about the problem and help achieve machine solution to the plane geometry problems.The research content of this thesis mainly includes two parts.The first part is the line de-tection and line segment pixel removal for the diagrams of plane geometry,which mainly includes the four stages:image preprocessing,line detection,optimization of line detec-tion result and line segment pixel removal.In the beginning,after reading the literature and analysis,this thesis chose the Cannny edge detection algorithm to extract the edge points,which retaining the original image attributes while significantly reduced the calculation of next step.For the line detection process,after experiments and analysis,this thesis chose the Standard Hough transform line detection algorithm and proposed a method to improve the detection result.And after the removal of these line segment pixels,this stage can weaken the influence of the line on the subsequent detection process while retaining as many pixels as possible of the circle entity.The second part is the algorithm to detect the incomplete circle entities by using the charac-teristics of circle.The algorithm mainly includes four stages:sampling edge points,extract candidate circles,evaluate the candidate circles,and verifying the candidate circles.After obtaining the edge points after canny edge detection,this thesis samples the collected edge point set for the purpose of speeding up the calculation,which saves approximately 24 times the time before sampling.Based on the property that the perpendicular line between two points on the circle must pass through the center of the circle,this algorithm will repeat the process that randomly select two points from the sampled edge points to calculate the center and radius of the candidate circle until all edge points are traversed,and add these candidates to a set to remove duplicate candidate circles.Finally,the candidate circles are evaluated us-ing the coverage rate and deviation distance sum of the circle entities in the original image,then the similar candidate circles are be verified according to the coverage rate and deviation distance sum.Finally,the circle entities with the highest coverage and the smallest deviation distance will be output.And in order to show the practical value of these information,this thesis summarized 16 kinds of basic positional relations between the line segment and the circle based on these information.In the end,a robust circle detection framework for plane geometry image is formed in this thesis,and a large number of experiments are performed on the collected image data sets to verify the rationality and robustness of the framework.