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Shape from shading: Level set propagation and viscosity solutions

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Abstract

We present a new implementation of an algorithm aimed at recovering a 3D shape from its 2D gray-level picture. In order to reconstruct the shape of the object, an almost arbitrarily initialized 3D function is propagated on a rectangular grid, so that a level set of this function tracks the height contours of the shape. The method imports techniques from differential geometry, fluid dynamics, and numerical analysis and provides an accurate shape from shading algorithm. The method solves some topological problems and gracefully handles cases of non-smooth surfaces that give rise to shocks in the propagating contours. Real and synthetic images of 3D profiles were submitted to the algorithm and the reconstructed surfaces are presented, demonstrating the effectiveness of the proposed method.

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Authors and Affiliations

  1. Electrical Engineering Dept. Technion, 32000, Haifa, Israel

    Ron Kimmel

  2. Laboratory for Man/Machine Systems, Brown University, USA

    Kaleem Siddiqi & Benjamin B. Kimia

  3. Computer Science Dept. Technion, 32000, Haifa, Israel

    Alfred M. Bruckstein

Authors
  1. Ron Kimmel
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  2. Kaleem Siddiqi
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  3. Benjamin B. Kimia
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  4. Alfred M. Bruckstein
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Additional information

R. Kimmel's work was partly supported by the Ollendorf Fund.

B.B. Kimia's work was supported by the Sun Microsystems Academic Equipment Grant.

A.M. Bruckstein's work was supported in part by the Fund for the Promotion of Research at the Technion.

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Kimmel, R., Siddiqi, K., Kimia, B.B. et al. Shape from shading: Level set propagation and viscosity solutions. Int J Comput Vision 16, 107–133 (1995). https://doi.org/10.1007/BF01539551

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