Polygonal approximation of digital planar curves through break point suppression

Methods for Ellipse Detection from Edge Maps of Real Images

“…The hybrid ellipse detection methods use one or more of the above approaches as just an intermediate step in the ellipse detection algorithm. Other steps like sophisticated digital curve pre-processing techniques (Bhowmick and Bhattacharya, 2007;Carmona-Poyato et al, 2010;Masood, 2008;Prasad and Leung, 2010d;Prasad et al, 2011b;Prasad et al, 2012), curvature estimation and correction techniques (Anderson and Bezdek, 1984;Cazals and Pouget, 2005;Heikkila, 1998;Matas et al, 1995;Prasad et al, 2011a;Worring and Smeulders, 1993;Zhong et al, 2009), partial retrieval of ellipses' parameters using some geometric properties of ellipses (Guil and Zapata, 1997;Ho and Chen, 1995;Yuen et al, 1989;Zhang and Liu, 2005) are usually added before the actual ellipse detection method. Further, most hybrid methods include some or other form of grouping mechanism to group the edges that possibly belong to the same ellipse (Chia et al, 2011;Hahn et al, 2008;Kawaguchi and Nagata, 1998b;Kim et al, 2002;Mai et al, 2008).…”

A new thresholding approach for automatic generation of polygonal approximations

“…A parameterized version W E n = ISE (CR) n has also been proposed [5,20,25,26] to balance the contribution of ISE and CR, where n = 1, 2, 3. Carmona [4] demonstrated that the value n = 2 obtains the best performance.…”

“…The computational complexity of the Carmona algorithm is O((m − n d )n), where n is the number of the contour points, m is the number of initial break points, and n d is the number of final dominant points [5]. The computational complexity of the Masood method can be given as O((m − n d )n 2 ) owing to its optimization process [23].…”

“…• Heuristic approach: these methods construct the approximating polygon using some reasonable geometric or perceptual features of the contours [10] -Parametric approach: these methods take into account a parameter to generate the polygonal approximations [2,4,5,7,18,21,22,23].…”

Polygonal Representation of Digital Curves

“…This is a maximization metric, i.e., larger value of FOM is preferred over a lower value. However, it is well known that FOM is biased towards ISE [Carmona-Poyato, et al, 2010]. For example, if the break points of a digital curve [Masood, 2008] are considered as the dominant points, the ISE is zero and inconsequent of the CR, FOM is infinity.…”