GOAL

1. A DYNAMIC BEZIER CURVE MODELFerdous A. Sohel, Laurence S. Dooley, and Gour C. KarmakarGippsland School of Information TechnologyMonash University, Victoria – 3842, AUSTRALIA.{Ferdous.Sohel, Laurence.Dooley, Gour.Karmakar}@infotech.monash.edu.au Global Information EXPERIMENTAL RESULTS Low Degree Curves BC How? Low Distortion GOAL Low Bit-Rate DBC Local Information Lip Shape Arabic Character Kettle Table 1: Summary of results for different shape description methods (distortions are measured using [1]). is the GAP that occurs in Bezier for and C is the curve point. Test Shape (Admissible Dmax) Peak distortion (pel) Mean-squared distortion (pel2) Whether the control pts lie on the shape Max distance between consecutivecontrol pts (pel) BC DBC BC DBC BC DBC BC DBC Kettle (1) 3.5 1 3.1 0.8 Yes Yes 18 18 Lip (0.5) 1.0 0.5 0.7 0.12 No Yes 28.3 15 Arabic (1) 2 1 0.1 0.04 No Yes 30 27 ABSTRACT Bezier curves (BC) are fundamental to a wide range of applications from computer-aided design through to object shape descriptions and surface mapping. Since BC only consider global information with respect to their control points, this can lead to erroneous shape representations, though integrating local control point information minimises this error. This paper presents a new Dynamic Bezier Curve (DBC) model whichcombines both localised and global shape information by making a parametric shift of the BC points in the gap between the curve and its control polygon. The value of the shifting parameter is dynamically determined for a prescribed maximum distortion. DBC retains the kernel properties of the BC without increasing computational complexity order. The model’s performance has been empirically evaluated on a number of arbitrary-shaped objects from geometric modelling to shape coding. Both qualitative and quantitative results confirm the improvement achieved compared with the classical BC representation. • MOTIVATION • Classical Bezier only considers global control point information which can lead to large gaps. • Bezier variants – degree elevation, composite and subdivision and refinements reduce this gap, BUT also increase the number of control points. RESEARCH CHALLENGE Reduce the gap without increasing the number of control points. CONTRIBUTION Incorporate local information into the global Bezier framework by shifting the Bezier point towards the control polygon with the Dynamic Bezier Curve (DBC) model. • CONCLUSIONS • New Bezier framework incorporating local geometric information for superior shape approximations. • Admissible shape distortion can be maintained. • Lower distortion than Bezier as well as smaller descriptor length. • DBC retains the core properties of Bezier. • Same computational complexity as Bezier. Where P(x1,y1)Q(x2,y2) is the closest control polygon edge from BC point for a particular t and (J,K) is the closest point on PQ, E=x1-x2, F=y1-y2, X and Y refer either (x1,y1) or (x2,y2) pair. m is the shifting parameter and deduced by Lagrangian multiplier method for a prescribed distortion. REFERENCE [1] F.A. Sohel, L.S. Dooley, G.C. Karmakar, “Accurate distortion measurement for generic shape coding,” Pattern Recognition Letters, in press.