An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
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
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
Dynamic Bezier curves for variable rate-distortion
Pattern Recognition
Path planning based on dynamic multi-swarm particle swarm optimizer with crossover
ICIC'12 Proceedings of the 8th international conference on Intelligent Computing Theories and Applications
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Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods.