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A Comparison of Non-Lambertian Models for the Shape-from-Shading Problem

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Perspectives in Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

In this paper we present in a unified approach Shape-from-Shading models under orthographic projection for non-Lambertian surfaces and compare them with the classical Lambertian model. Those non-Lambertian models have been proposed in the literature by various authors in order to take into account more realistic surfaces such as rough and specular surfaces. The advantage of our unified mathematical model is the possibility to easily modify a single differential model to various situations just changing some control parameters. Moreover, the numerical approximation we propose is valid for that general model and can be easily adapted to the real situation. Finally, we compare the models on some benchmarks including real and synthetic images.

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Acknowledgements

The first author wishes to acknowledge the support obtained by Gruppo Nazionale per il Calcolo Scientifico (GNCS-INdAM).

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Authors and Affiliations

  1. Dipartimento di Matematica “G. Castelnuovo”, Sapienza – Università di Roma, Roma, Italy

    Silvia Tozza & Maurizio Falcone

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  1. Silvia Tozza
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  2. Maurizio Falcone
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Correspondence to Silvia Tozza .

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Editors and Affiliations

  1. Institute for Applied Mathematics and Scientific Computing, Brandenburg University of Technology, Cottbus, Germany

    Michael Breuß

  2. Israel Institute of Technology Technion, Haifa, Israel

    Alfred Bruckstein

  3. School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece

    Petros Maragos

  4. INRIA, Grenoble Rhône-Alpes, Saint Ismier, France

    Stefanie Wuhrer

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Tozza, S., Falcone, M. (2016). A Comparison of Non-Lambertian Models for the Shape-from-Shading Problem. In: Breuß, M., Bruckstein, A., Maragos, P., Wuhrer, S. (eds) Perspectives in Shape Analysis. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-24726-7_2

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