Connection Geometry, Color, and Stereo

  • Ohad Ben-Shahar
  • Gang Li
  • Steven W. Zucker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4673)


The visual systems in primates are organized around orientation with a rich set of long-range horizontal connections. We abstract this from a differential-geometric perspective, and introduce the covariant derivative of frame fields as a general framework for early vision. This paper overviews our research showing how curve detection, texture, shading, color (hue), and stereo can be unified within this framework.


Early Vision Curve Detection Stereo Correspondence Tangent Estimate Frenet Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O’Neill, B.: Elementary Differential Geometry. Academic Press, San Diego (1966)zbMATHGoogle Scholar
  2. 2.
    Parent, P., Zucker, S.W.: Trace inference, curvature consistency, and curve detection. IEEE Trans. Pattern Analysis and Machine Intelligence 11, 823–839 (1989)CrossRefGoogle Scholar
  3. 3.
    Hummel, R.A., Zucker, S.W.: On the foundations of relaxation labeling processes. IEEE Trans. Pattern Analysis and Machine Intelligence PAMI-5, 267–287 (1983)CrossRefGoogle Scholar
  4. 4.
    Ben-Shahar, O., Zucker, S.W.: Hue fields and color curvatures: A perceptual organization approach to color image denoising. In: CVPR 2003. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Madison, WI (2003)Google Scholar
  5. 5.
    Ben-Shahar, O., Zucker, S.W.: Hue geometry and horizontal connections. Neural Networks 17(5-6), 753–771 (2004)CrossRefGoogle Scholar
  6. 6.
    Ben-Shahar, O., Zucker, S.W.: The Perceptual Organization of Texture Flow: A Contextual Inference Approach. IEEE Trans. Pattern Analysis and Machine Intelligence 25(4), 401–417 (2003)CrossRefGoogle Scholar
  7. 7.
    Li, G., Zucker, S.W.: Contextual Inference in Contour-Based Stereo Correspondence. Int. J. of Computer Vision 69(1), 59–75 (2006)CrossRefGoogle Scholar
  8. 8.
    Li, G., Zucker, S.W.: Differential Geometric Consistency Extends Stereo to Curved Surfaces. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3954, pp. 7–13. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Ben-Shahar, O., Zucker, S.W.: Geometrical computations explain projection patterns of long-range horizontal connections in visual cortex. Neural Computation 16(3), 445–476 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ohad Ben-Shahar
    • 1
  • Gang Li
    • 2
  • Steven W. Zucker
    • 3
  1. 1.Computer Science, Ben Gurion UniversityIsrael
  2. 2.Real-Time Vision and Modeling Dept., Siemens Corp. Research, Princeton, NJ 
  3. 3.Computer Science, Yale University, New Haven, CT 

Personalised recommendations