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Highlights: [•] New minimal bounds are derived for the magnitudes of the derivatives of rational Bézier paths and surfaces. [•] The derived minimal bounds are for a generic and well-known type of pointwise bound. [•] Simple, explicit closed-form expressions are obtained for the minimal bounds. [ABSTRACT FROM AUTHOR]

Abstract: New derivative bounds for the rational quadratic Bézier paths are obtained, both for particular weight vectors and for classes of equivalent parametrisations. A comprehensive analysis of our bounds against existing bounds is made. [Copyright &y& Elsevier]

A generalization of Patterson's work on the invariants of the rational Bezier curves, to the case of weight vectors of mixed-sign is presented. It is shown that an additional invariant is required in the general case. The results are viewed from the perspective of the Fundamental Theorem on invariants for Lie groups. [ABSTRACT FROM AUTHOR]

Abstract: A generalisation of Patterson''s work, on the invariants of the rational Bézier paths, to the case of surface patches is presented. An equation for the determination of the invariants for patches of degree is derived and solved for the bi-quadratics – for which it is shown that seven independent, invariant functions exist. Explicit forms of the invariants are derived and a number of applications are presented. [Copyright &y& Elsevier]

Dupin cyclides, their applications in geometric modelling and their parametrization using bi-quadratic patches bounded by lines of curvature, have been investigated in recent years by a number of authors such as Martin, de Pont and Sharrock in 1986, Boehm in 1990, Pratt in 1990, and Degen in 1994. However, no completely reliable and general algorithm for the determination of bi-quadratic cyclide patches has appeared in the literature. This paper presents a new approach that produces any required bi-quadratic patch, bounded by lines of curvature, without non-intrinsic geometric constraints or restrictions. Specifically, if a bi-quadratic parametrization exists for the specified region of the cyclide, then it is correctly determined. Explicit formulae are given for the Bernstein weights and vectors of the parametrizations. The method is neither cyclide specific nor specific to the construction of bi-quadratic rational parametrizations - it may therefore be applied to other surfaces and to higher degree rational constructions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a fast DWT-based multi-resolution texture synthesis algorithm in which coefficient blocks of the spatio-frequency components of the input texture are efficiently stitched together to form the corresponding components of the synthesised output texture. We propose the use of an automatically generated threshold to determine the visually significant coefficients, which act as elements of a matching template used in the texture quilting process. We show that the use of a limited set of visually significant coefficients, regardless of their level of resolution, not only reduces the computational cost, but also results in more realistic texture synthesis. A transform domain texture blending strategy is used to remove the remaining artefacts across edges, improving the synthesised texture quality further. We use popular test textures to compare our results with that of the state-of-the-art techniques. Some application scenarios of the proposed algorithm are also discussed. [Copyright &y& Elsevier]

In this paper, we propose a novel, discrete wavelet transform (DWT) domain implementation of our previously proposed, pioneering block-based disparity compensated predictive coding algorithm for stereo image compression. Under the present research context we perform predictive coding in the form of pioneering block search in the sub-band domain. The resulting transform domain predictive error image is subsequently converted to a so-called wavelet-block representation, before being quantized and entropy coded by a JPEG-like CODEC. We show that the proposed novel implementation is able to effectively transfer the inherent advantages of DWT-based image coding technology to efficient stereo image pair compression. At equivalent bit rates, the proposed algorithm achieves peak signal to noise ratio gains of up to 5.5 dB, for reconstructed predicted images, as compared to traditional and state of the art DCT and DWT-based predictive coding algorithms. [Copyright &y& Elsevier]