In this paper we propose a new algorithm for extracting dominant points from the real contour of a digital shape. A polygonal approximation of the shape can be obtained by the set of dominant points. In the proposed algorithm, in the first step before searching for dominant points, the real contour is made sparse using a geometric concept, named convex deficiency tree. This helps to select a set of candidate points from real contour. In comparison with break points (which are initial points in many algorithms), the set of candidate points is more heuristic and the ratio of them to the all points of the contour is lower. In the second step of the proposed algorithm, the less informative candidate points are removed in an iterative manner. After removing one candidate point, its adjacent positions are searched to find more stable position for its neighbors. The comparative result of the proposed algorithm with others shows its efficiency. The algorithm finds an effective polygonal approximation for digital shapes especially for the real contours, which makes the method more practical.
Dominant point Polygonal approximation Digital planner curve Shape representation Convex deficiency tree
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We want to thank A. A. Carmona-Poyato for kindly providing us the results of his method via mail to be compared with our proposed method.
Ruberto DC, Morgera A (2009) A new iterative approach for dominant points extraction in planar curves Source. WSEAS Trans Comput 8(3):482–493Google Scholar
Sarkar D (1993) A simple algorithm for detection of significant vertices for polygonal approximation of chain-coded curves. Pattern Recognit Lett 14:959–964CrossRefGoogle Scholar
Rosin PL (1997) Techniques for assessing polygonal approximation of curves. IEEE Trans Pattern Anal Mach Intell 19(6):659–666CrossRefGoogle Scholar
Batchelor BG (1980) Hierarchical shape description based upon convex hulls of concavities. J Cybern 10:205–210CrossRefGoogle Scholar
Carmona-Poyato A, Madrid-Cuevas FJ, Medina Carnicer R, Munoz-Salinas R (2010) Polygonal approximation of digital planar curves through break point suppression. Pattern Recognit 43(1):14–25CrossRefMATHMathSciNetGoogle Scholar
Carmona-Poyato A, Medina-Carnicer R, Muñoz-Salinas R, Yeguas-Bolivar E (2012) On stop conditions about methods to obtain polygonal approximations relied on breakpoint suppression. Image Vis Comput 30(8):513–523CrossRefGoogle Scholar
Hao S, Jiang J, Guo Y, Zhan S (2012) ϵ-Isometry based shape approximation for image content representation. Signal Process (in press)Google Scholar
Latecki LJ, Lakamper R (1999) Convexity rule for shape decomposition based on discrete contour evolution. Comput Vis Image Underst 73:441–454CrossRefGoogle Scholar
Cronin TM (1999) A boundary concavity code to support dominant points detection. Pattern Recognit Lett 20:617–634CrossRefGoogle Scholar
Dobkin D, Guibas L, Hershberger J, Snoeyink J (1988) An efficient algorithm for finding the CSG representation of a simple polygon. Comput Graph 22(4):31–40CrossRefGoogle Scholar
Shapiro V (2001) A convex deficiency tree algorithm for curved polygons. Int J Comput Geom Appl 11(2):215–238CrossRefMATHGoogle Scholar
Parvez MT, Mahmoud SA (2010) Polygonal approximation of digital planar curves through adaptive optimizations. Pattern Recognit Lett 31:1997–2005CrossRefGoogle Scholar
Nguyen TP, Rennesson ID (2011) A discrete geometry approach for dominant point detection. Pattern Recognit 44:32–44CrossRefMATHGoogle Scholar