Shape from shading is known to be an ill-posed problem. We show in this paper that if we model the problem in a different way than it is usually done, more precisely by taking into account the 1/r/sup 2/ attenuation term of the illumination, shape from shading becomes completely well-posed. Thus the shading allows to recover (almost) any surface from only one image (of this surface) without any additional data (in particular, without the knowledge of the heights of the solution at the local intensity "minima", contrary to [P. Dupuis et al. (1994), E. Prados et al. (2004), B. Horn (1986), E. Rouy et al. (1992), R. Kimmel et al. (2001)]) and without regularity assumptions (contrary to [J. Oliensis et al. (1993), R. Kimmel et al. (1995)], for example). More precisely, we formulate the problem as that of solving a new partial differential equation (PDE), we develop a complete mathematical study of this equation and we design a new provably convergent numerical method. Finally, we present results of our new shape from shading method on various synthetic and real images.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Shape from shading: a well-posed problem?


    Contributors:
    Prados, E. (author) / Faugeras, O. (author)


    Publication date :

    2005-01-01


    Size :

    489094 byte





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Interactive shape from shading

    Gang Zeng, / Matsushita, Y. / Long Quan, et al. | IEEE | 2005


    Global Shape from Shading

    Shimshoni, I. / Kimmel, R. / Bruckstein, A. M. | British Library Online Contents | 1996


    Robust shape from shading

    Jones, A. G. / Taylor, C. J. | British Library Online Contents | 1994


    Global Shape from Shading

    Kimmel, R. / Bruckstein, A. M. | British Library Online Contents | 1995