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Shape Reconstruction of Symmetric Surfaces Using Photometric Stereo

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Innovations for Shape Analysis

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

Abstract

The reconstruction of a 3D surface through one gray scale digital image does not admit a unique solution in the orthographic Shape from Shading (SfS) framework. With the aim to make this type of problem well-posed it is possible to use the Photometric Stereo (PS) technique. It allows to add information about the surface introducing other images of the object taken from the same point of view but modifying, for each photo, the direction of the light source. The methods that use the PS technique with the orthographic model of SfS need of, at least, three images. However, even if three images are used, there is the possibility that the SfS-PS problem continues to be ill-posed. This is the case when the three images are taken using three coplanar light vectors. This work analyses this kind of ill-posedness in order to understand how it is possible to establish a connection among the images that do not guarantee uniqueness. A further result in this paper is given by a geometrical characterization of the surfaces for which it is possible to solve the classic SfS problem.

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Authors and Affiliations

  1. Dipartimento di Matematica “G. Castelnuovo”, Sapienza – University of Rome, Rome, Italy

    Roberto Mecca & Silvia Tozza

Authors
  1. Roberto Mecca
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  2. Silvia Tozza
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Correspondence to Roberto Mecca .

Editor information

Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Mecca, R., Tozza, S. (2013). Shape Reconstruction of Symmetric Surfaces Using Photometric Stereo. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_10

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