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A single-lobe photometric stereo approach for heterogeneous material

Published version
Peer-reviewed

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Authors

Mecca, R 
Quéau, Y 
Logothetis, F 

Abstract

Shape from shading with multiple light sources is an active research area, and a diverse range of approaches have been proposed in recent decades. However, devising a robust reconstruction technique still remains a challenging goal, as the image acquisition process is highly nonlinear. Recent Photometric Stereo variants rely on simplifying assumptions in order to make the problem solvable: light propagation is still commonly assumed to be uniform, and the Bidirectional Reflectance Distribution Function is assumed to be diffuse, with limited interest for specular materials. In this work, we introduce a well-posed formulation based on partial differential equations (PDEs) for a unified reflectance function that can model both diffuse and specular reflections. We base our derivation on ratio of images, which makes the model independent from photometric invariants and yields a well-posed differential problem based on a system of quasi-linear PDEs with discontinuous coefficients. In addition, we directly solve a differential problem for the unknown depth, thus avoiding the intermediate step of approximating the normal field. A variational approach is presented ensuring robustness to noise and outliers (such as black shadows), and this is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art.

Description

Keywords

Photometric Stereo, quasi-linear PDEs, single-lobe BRDF, specular reflection, diffuse reflection, variational method

Journal Title

SIAM Journal on Imaging Sciences

Conference Name

Journal ISSN

1936-4954
1936-4954

Volume Title

9

Publisher

Society for Industrial and Applied Mathematics
Sponsorship
Roberto Mecca is a Marie Curie fellow of the “Istituto Nazionale di Alta Matematica” (Italy) for a project shared with University of Cambridge, Department of Engineering and the Department of Mathematics, University of Bologna.