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Bidirectional Texture Function Modeling

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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Abstract

An authentic material’s surface reflectance function is a complex function of over 16 physical variables, which are unfeasible both to measure and to mathematically model. The best simplified measurable material texture representation and approximation of this general surface reflectance function is the seven-dimensional bidirectional texture function (BTF). BTF can be simultaneously measured and modeled using state-of-the-art measurement devices and computers and the most advanced mathematical models of visual data. However, such an enormous amount of visual BTF data, measured on the single material sample, inevitably requires state-of-the-art storage, compression, modeling, visualization, and quality verification. Storage technology is still the weak part of computer technology, which lags behind recent data sensing technologies; thus, even for virtual reality correct materials modeling, it is infeasible to use BTF measurements directly. Hence, for visual texture synthesis or analysis applications, efficient mathematical BTF models cannot be avoided. The probabilistic BTF models allow unlimited seamless material texture enlargement, texture restoration, tremendous unbeatable appearance data compression (up to 1:1000 000), and even editing or creating new material appearance data. Simultaneously, they require neither storing actual measurements nor any pixel-wise parametric representation. Unfortunately, there is no single universal BTF model applicable for physically correct modeling of visual properties of all possible BTF textures. Every presented model is better suited for some subspace of possible BTF textures, either natural or artificial. In this contribution, we intend to survey existing mathematical BTF models which allow physically correct modeling and enlargement measured texture under any illumination and viewing conditions while simultaneously offering huge compression ratio relative to natural surface materials optical measurements. Exceptional 3D Markovian or mixture models, which can be either solved analytically or iteratively and quickly synthesized, are presented. Illumination invariants can be derived from some of its recursive statistics and exploited in content-based image retrieval, supervised or unsupervised image recognition. Although our primary goal is physically correct texture synthesis of any unlimited size, the presented models are equally helpful for various texture analytical applications. Their modeling efficiency is demonstrated in several analytical and modeling image applications, in particular, on a (un)supervised image segmentation, bidirectional texture function (BTF) synthesis and compression, and adaptive multispectral and multi-channel image and video restoration.

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Acknowledgements

The Czech Science Foundation Project GAČR 19-12340S supported this research.

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Authors and Affiliations

  1. Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czechia

    Michal Haindl

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  1. Michal Haindl
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Correspondence to Michal Haindl .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Dept Appl Math & Theoretical Phys, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xue-Cheng Tai

  4. Department of Applied Mathematics & Stat, Johns Hopkins University, Baltimore, MD, USA

    Laurent Younces

Section Editor information

  1. Department of Mathematical Sciences, University of Liverpool Mathematical Sciences Building, Liverpool, UK

    Ke Chen Ph.D

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Xuecheng Tai Ph.D

  3. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Carola Schönlieb Ph.D

  4. Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD, USA

    Laurent Younes

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Haindl, M. (2022). Bidirectional Texture Function Modeling. In: Chen, K., Schönlieb, CB., Tai, XC., Younces, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-03009-4_103-1

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  • DOI: https://doi.org/10.1007/978-3-030-03009-4_103-1

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  • Online ISBN: 978-3-030-03009-4

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