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Direct Differential Photometric Stereo Shape Recovery of Diffuse and Specular Surfaces

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Abstract

Recovering the 3D shape of an object from shading is a challenging problem due to the complexity of modeling light propagation and surface reflections. Photometric Stereo (PS) is broadly considered a suitable approach for high-resolution shape recovery, but its functionality is restricted to a limited set of object surfaces and controlled lighting setup. In particular, PS models generally consider reflection from objects as purely diffuse, with specularities being regarded as a nuisance that breaks down shape reconstruction. This is a serious drawback for implementing PS approaches, since most common materials have prominent specular components. In this paper, we propose a PS model that solves the problem for both diffuse and specular components aimed at shape recovery of generic objects with the approach being independent of the albedo values thanks to the image ratio formulation used. Notably, we show that by including specularities, it is possible to solve the PS problem for a minimal number of three images using a setup with three calibrated lights and a standard industrial camera. Even if an initial separation of diffuse and specular components is still required for each input image, experimental results on synthetic and real objects demonstrate the feasibility of our approach for shape reconstruction of complex geometries.

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Acknowledgments

The first author acknowledges the support of INDAM under the GNCS research Project “Metodi numerici per la regolarizzazione nella ricostruzione feature-preserving di dati.”

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Authors and Affiliations

  1. Dipartimento di Matematica, Sapienza - Università di Roma, Piazzale Aldo Moro, 5, 00185, Rome, Italy

    S. Tozza

  2. Engineering Department, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

    R. Mecca

  3. Pattern Analysis & Computer Vision Department, Istituto Italiano di Tecnologia, Via Morego, 30, 16163, Genova, Italy

    A. Del Bue

  4. Nanoscopy, Istituto Italiano di Tecnologia, Via Morego, 30, 16163, Genova, Italy

    M. Duocastella

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  1. S. Tozza
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  2. R. Mecca
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  4. A. Del Bue
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Corresponding author

Correspondence to S. Tozza.

Additional information

R. Mecca: Marie Curie fellow of the Istituto Nazionale di Alta Matematica.

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Tozza, S., Mecca, R., Duocastella, M. et al. Direct Differential Photometric Stereo Shape Recovery of Diffuse and Specular Surfaces. J Math Imaging Vis 56, 57–76 (2016). https://doi.org/10.1007/s10851-016-0633-0

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