Detection of Trigonometric Diagrams from Handwritten Mathematical Answer Sheets Using Deep Learning Techniques

Hand-drawn trigonometric diagrams are crucial for many individuals seeking solutions to complex problems. They also aid in understanding geometric concepts in educational environments. Mathematicians apply them to illustrate the proofs, investigate theorems, and study mathematical phenomena further to come up with discoveries. Beyond mathematics, these flexible diagrams are applicable in various fields, from construction and engineering to navigation, to provide real-world, intuitive solutions to problems. Hand-drawn trigonometric diagrams mainly help in learning and enabling problem-solving and investigative studies in various diversified streams of study. Though the trigonometric diagrams are helpful in enhancing learning, there is less study related to the detection of such hand-drawn elements from mathematics answer scripts that students write. In this paper, we address this void by providing a new dataset called JUDVLP-MATHANSWERSHEET.v1, containing 197 handwritten answer sheets of students between classes V and XII. Our dataset is used in the training up and evaluation of several object identification models, including YOLOv3, YOLOv5, SSD, DSSD, and RetinaNet. YOLOv5 has been shown to outperform other models in evaluations, attaining a precision of 90.6%, recall of 79.7%, and mAP50 of 87.3% on the validation dataset, and a precision of 72.6%, recall of 91.9%, and mAP50 of 83.4% on the test dataset. The successively proven performance and robustness in processing novel data of the YOLOv5 architecture make it the most effective framework for finding trigonometric diagrams in handwritten mathematical answer sheets.