An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Shape description using cubic polynomial Bezier curves
Pattern Recognition Letters
Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Rate-Distortion Based Video Compression: Optimal Video Frame Compression and Object Boundary Encoding
Computer Graphics
Automatic outline capture of Arabic fonts
Information Sciences—Informatics and Computer Science: An International Journal - Special issue: Software engineering: Systems and tools
Accurate distortion measurement for generic shape coding
Pattern Recognition Letters
Quasi-Bezier curves integrating localised information
Pattern Recognition
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatial shape error concealment for object-based image and video coding
IEEE Transactions on Image Processing
MPEG-4 standardized methods for the compression of arbitrarily shaped video objects
IEEE Transactions on Circuits and Systems for Video Technology
Joint optimal object shape estimation and encoding
IEEE Transactions on Circuits and Systems for Video Technology
New Dynamic Enhancements to the Vertex-Based Rate-Distortion Optimal Shape Coding Framework
IEEE Transactions on Circuits and Systems for Video Technology
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Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer-aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortion in shape representation. While BC variants like degree elevation, composite BC and refinement and subdivision narrow this gap, they increase the number of CP and thereby both the required bit-rate and computational complexity. In addition, while quasi-Bezier curves (QBC) close the gap without increasing the number of CP, they reduce the underlying distortion by only a fixed amount. This paper presents a novel contribution to BC theory, with the introduction of a dynamic Bezier curve (DBC) model, which embeds variable localised CP information into the inherently global Bezier framework, by strategically moving BC points towards the CtrlPoly. A shifting parameter (SP) is defined that enables curves lying within the region between the BC and CtrlPoly to be generated, with no commensurate increase in CP. DBC provides a flexible rate-distortion (RD) criterion for shape coding applications, with a theoretical model for determining the optimal SP value for any admissible distortion being formulated. Crucially DBC retains core properties of the classical BC, including the convex hull and affine invariance, and can be seamlessly integrated into both the vertex-based shape coding and shape descriptor frameworks to improve their RD performance. DBC has been empirically tested upon a number of natural and synthetically shaped objects, with qualitative and quantitative results confirming its consistently superior shape approximation performance, compared with the classical BC, QBC and other established BC-based shape descriptor techniques.