Progressive Texture Synthesis on Geometric Surfaces Parametrised by Bi-quadratic Rational Bézier Patches

Progressive texture synthesis can provide an added functional advantage to existing texture synthesis algorithms, which are time consuming and fail to deliver in some application areas. To provide practical solutions to this challenge we have previously proposed a Discrete Wavelet Transform (DWT) based texture synthesis algorithm for 2D surfaces. In this paper we propose the extension of this approach to 3D progressive-texture synthesis. The proposed 3D progressivetexture synthesis algorithm makes use of the EZW (Embedded Zero-tree Wavelet) idea proposed by Shapiro, which is capable of prioritising the coefficients of a DWT decomposed image according to their visual significance. We demonstrate the use of the proposed algorithm on progressive texturing geometric surfaces such as Ring Dupin Cyclides, Toruses, Spheres, parametrised by rational Bézier patches. We provide experimental results to prove the effectiveness of the proposed approach, when synthesising textures of regular, irregular and stochastic nature. Further experimental results are provided to illustrate the practical use of the proposed progressive texture synthesis algorithm in resource constrained application domains.