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Connection Geometry, Color, and Stereo

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Computer Analysis of Images and Patterns (CAIP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4673))

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Abstract

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.

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References

  1. O’Neill, B.: Elementary Differential Geometry. Academic Press, San Diego (1966)

    MATH  Google Scholar 

  2. Parent, P., Zucker, S.W.: Trace inference, curvature consistency, and curve detection. IEEE Trans. Pattern Analysis and Machine Intelligence 11, 823–839 (1989)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

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  5. Ben-Shahar, O., Zucker, S.W.: Hue geometry and horizontal connections. Neural Networks 17(5-6), 753–771 (2004)

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  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)

    Article  Google Scholar 

  7. Li, G., Zucker, S.W.: Contextual Inference in Contour-Based Stereo Correspondence. Int. J. of Computer Vision 69(1), 59–75 (2006)

    Article  Google Scholar 

  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)

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  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)

    Article  Google Scholar 

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Walter G. Kropatsch Martin Kampel Allan Hanbury

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© 2007 Springer-Verlag Berlin Heidelberg

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Ben-Shahar, O., Li, G., Zucker, S.W. (2007). Connection Geometry, Color, and Stereo. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds) Computer Analysis of Images and Patterns. CAIP 2007. Lecture Notes in Computer Science, vol 4673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74272-2_2

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  • DOI: https://doi.org/10.1007/978-3-540-74272-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74271-5

  • Online ISBN: 978-3-540-74272-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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