Shape from Shading

Shape from Shading (SfS) means recovering a three-dimensional surface from the shading information contained in exactl one two-dimensional image under known illumination conditions and reflectance properties of the surface.

Classic SfS research, which has been started in 1970 by Horn, dealt with images obtained using orthographic camera model and a light source at infinity, mostly for Lambertian surfaces.

In the last years, SfS models based on perspective camera models and point light sources close to the photographed became more and more popular. These models are much closer to reality and have been proven to be much closer to reality than orthographic models.

These images show a real-world input image, three pieces from a chess set and the reconstruction using one of our most advanced SfS methods.

Research in our group deals with advanced perspective SfS models, which also consider non-Lambertian reflectance models. In addition to that, our goal is to design efficient numerical schemes for actually computing 3-D shapes from shading.

• Direct variational orthographic SfS with non-linear regularisation
  In the early years of SfS research, the standard for (orthographic) SfS was to compute the gradient of a surface from shading, and then apply a depth-from-gradient technique. We showed how to avoid this additional step and directly compute the depth using a variational framework. In addition to that, we introduced non-linear regularisation to this variational framework, which significantly improved the reconstruction quality of orthographic SfS [1].
  
  
• Efficient numerics for perspective SfS
  While the first numerical schemes for advanced perspective SfS models have been quite complex, we introduced a novel numerical method for recovering shapes using these models. The algorithm we suggested proved to be significantly easier to implement than other numerical methods and up to ten times faster. [2] [3].
  
  
• Non-Lambertian reflectance models for perspective SfS
  SfS in general, but in particular perspective SfS models almost exclusively dealt with Lambertian, i.e. purely diffuse, reflectance only. In reality, however, all surfaces also reflect light specularly, which results in highlights. We extended previous SfS models by this component, proposing a model that both includes Lambertian reflectance and specular highlight. Results show that this model is another step towards a realistic model, as it improves the reconstruction quality on real-world images significantly. [4] [5].
  
  
• Fast marching methods for advanced perspective SfS models
  For orthographic SfS models and early perspective SfS models, it has been suggested to use a fast marching method as numerical solver. These methods, however, depend on certain points on the surface to be known, and are not compatible with new, advanced, models. We suggested an alternative fast marching method, which is compatible to both the models developed in the recent years and our non-Lambertian model. In addition to that, this method does not require any depth information or boundary information to be provided. It is significantly faster than other numerical methods. [6]

1. O. Vogel, A. Bruhn, J. Weickert, S. Didas:
   Direct Shape-from-Shading with Adaptive Higher Order Regularisation.
   In F. Sgallari, A. Murli, N. Paragios (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Vol. 4485, 871 - 882, Springer, Berlin, 2007.
   © Springer-Verlag Berlin Heidelberg 2007.
2. O. Vogel, M. Breuß, J. Weickert:
   A Direct Numerical Approach to Perspective Shape-from-Shading
   In H. Lensch, B. Rosenhahn, H.-P. Seidel, P. Slusallek, J. Weickert (Eds.): Vision, Modeling, and Visualization 2007. Saarbrücken, Germany, 91-100, November 2007.
3. M. Breuß, O. Vogel, J. Weickert:
   Efficient numerical techniques for perspective shape from shading.
   In A. Handlovicova, P. Frolkovic, K. Mikula, D. Sevcovic (Eds.): Algoritmy 2009 (Podbanske, Slovakia, March 2009), pp. 11-20, Slovak University of Technology, Bratislava, 2009.
4. O. Vogel, M. Breuß, J. Weickert:
   Perspective shape from shading with non-Lambertian reflectance.
   In G. Rigoll (Ed.): Pattern Recognition, Lecture Notes in Computer Science, Vol. 5096, 517-526, Springer, Berlin, 2008.

5. M. Breuß, O. Vogel, J. Weickert:
   Perspective shape from shading for Phong-type non-Lambertian surfaces.
   Technical Report No. 216, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany, August 2008.
6. O. Vogel, M. Breuß, T. Leichtweis, J. Weickert:
   Fast shape from shading for Phong-type surfaces.
   To appear in Proc. Second International Conference on Scale-Space and Variational Methods (SSVM 2009, Voss, Norway, June 2009).

MIA Group
©2001-2012
The author is not
responsible for
the content of
external pages.