Quadratic curve detection by sampling manner

Abstract

AbstractThis paper considers the “Segment Pairs Matching” (SPM) method which detects the quadratic curves (e.g., circles and ellipses, etc.) mingled in other patterns such as letters, symbols and straight lines. The SPM method determines the set of sample points lying on the quadratic curves by using the matching condition (named “SPM condition”) which is a restriction on the formation of the sample points. The SPM condition is derived from the algebraic necessary condition under which a quadratic curve can be formed so as to pass through more than five given points. Through theoretical discussions, we clarify the geometrical meaning of the SPM condition and give the generalized formula. The SPM condition plays a geometrical role in deciding whether or not a given curve has a diameter. Then some experimental results show that the SPM condition is approved by digital picture processing and the quadratic curves can be detected with high reliability. Comparison with the Hough Transform demonstrates that the SPM method has the following merits: (i) the processing is done in the picture space; (ii) the operations are very simple (i.e., arithmetical operations); and (iii) the process can be effectively performed from coarse to fine.