Identification and Assessment of Selected Handwritten Function Graphs Using Least Square Approximation Combined with General Hough Transform

Abstract

Abstract The paper provides a comparison of three variants of algorithms for automatic assessment of some examination tasks involving sketching a function graph based on image processing. Three types of functions have been considered: linear, quadratic, and trigonometric. The assumption adopted in the design of the algorithm is to map the way the examiner assesses the solutions and to achieve the evaluation quality close to the one obtained in manual evaluation. In particular, the algorithm should not reject a partly correct solution and also extract the correct solution from other lines, deletions and corrections made by a student. Essential subproblems to solve in our scheme concern image segmentation, object identification and automatic understanding. We consider several techniques based on Hough Transform, least square fitting and nearest neighbor based classification. The most reliable solution is an algorithm combining least square fitting and Hough Transform.