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Distance Images and the Enclosure Field: Applications in Intermediate-Level Computer and Biological Vision

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Innovations for Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Early computer vision is dominated by image patches or features derived from them; high-level vision is dominated by shape representation and recognition. However there is almost no work between these two levels, which creates a problem when trying to recognize complex categories such as “airports” for which natural feature clusters are ineffective. In contrast, the neurobiology of vision indicates a very rich interaction between low- and high-level constructs, because there is a rich system of feedback connections. Based on this, we argue that an intermediate-level representation is necessary for computer vision and that it should incorporate certain high-level notions of distance and geometric arrangement into a form derivable from images. We propose an algorithm based on a reaction-diffusion equation that meets these criteria; we prove that it reveals (global) aspects of the distance map locally; and illustrate its performance on airport and other imagery, including visual illusions. Finally, we conjecture that these ideas also can inform the neurobiology of vision, by providing a novel basis for neural computation.

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References

  1. Ambrosio, L., Tortorelli, V.: On the approximation of functionals depending on jumps by elliptic functionals via? γ-convergence. Commun. Pure Appl. Math. 43(8), 999–1036 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 6(15), 1373–1396 (2003)

    Article  Google Scholar 

  3. Ben-Shahar, O., Zucker, S.W.: Geometrical computations explain projection patterns of long-range horizontal connections in visual cortex. Neural Comput. 16(3), 445–4476 (2003)

    Article  Google Scholar 

  4. Borenstein, E., Ullman, S.: Combined top-down/bottom-up segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 30(12), 2109–2125 (2008)

    Article  Google Scholar 

  5. Coifman, R., Lafon, S., Lee, A., Maggioni, M., Nadler, B., Warner, F., Zucker, S.W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. Proc. Nat. Acad. Sci. USA 102, 7426–7431 (2005)

    Article  Google Scholar 

  6. Courant, R., Hilbert, D.: Methods of Mathematical Physics, vol. 2. Interscience, New York (1962)

    MATH  Google Scholar 

  7. Craft, E., Schutze, H., Niebur, E., von der Heydt, R.: A neural model of figure-ground organization. J Neurophysiol. 97(6), 4310–4326 (2007)

    Article  Google Scholar 

  8. Dimitrov, P., Zucker, S.W.: A constant production hypothesis that predicts the dynamics of leaf venation patterning. Proc. Nat. Acad. Sci. USA 13(24), 9363–9368 (2006)

    Article  Google Scholar 

  9. Dimitrov, P., Zucker, S.W.: Distance maps and plant development #1: Uniform production and proportional destruction. arXiv.org, arXiv:0905.4446v1 (q-bio.QM), 1–39 (2009)

    Google Scholar 

  10. Dimitrov, P., Zucker, S.W.: Distance maps and plant development #2: Facilitated transport and uniform gradient. arXiv.org, arXiv:0905.4662v1 (q-bio.QM)(24), 1–46 (2009)

    Google Scholar 

  11. Dimitrov, P., Lawlor, M., Zucker, S.W.: Distance images and intermediate-level vision. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.). Third International Conference on Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, vol. 1, pp. 653664. Springer (2011)

    Google Scholar 

  12. Dubuc, B., Zucker, S.W.: Complexity, confusion, and perceptual grouping. part i: the curve like representation. Int. J. Comput. Vis. 42(1), 55–82 (2001)

    Google Scholar 

  13. Elder, J., Zucker, S.W.: Contour closure and the perception of shape. Vis. Res. 33(7), 981–991 (1993)

    Article  Google Scholar 

  14. Ferrari, V., Jurie, F., Schmid, C.: From images to shape models for object detection. Int. J. Comput. Vis. 87(3), 284–303 (2010)

    Article  Google Scholar 

  15. Fidler, S., Leonardis, A.: Towards scalable representations of object categories: learning a hierarchy of parts. In: Proceedings of the 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2007), 1823 June 2007, Minneapolis, MN IEEE Computer Society (2007)

    Google Scholar 

  16. Florack, L.M.J., ter Haar Romeny, B.M., Viergever, M.A., Koenderink, J.J.: The Gaussian scale-space paradigm and the multiscale local jet. Int. J. Comput. Vis. 18(1), 61–75 (1996)

    Article  Google Scholar 

  17. Froyen, V., Feldman, J., Singh, M.: A bayesian framework for figure-ground interpretation. Adv. Neural Inf. Process. Syst. 23, 631–639 (2010).

    Google Scholar 

  18. Gregory, R.L.: Eye and Brain. McGraw Hill, New York (1966)

    Google Scholar 

  19. Hubel, D.H., Wiesel, T.N.: Functional architecture of macaque monkey visual cortex. Proc. R. Soc. Lond. B 198, 1–59 (1977)

    Article  Google Scholar 

  20. Koenderink, J.J.: The structure of images. Biol. Cybern. 50, 363–370 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  21. Koffka, K.: Principles of Gestalt Psychology. Harcourt, Brace & World, New York (1935)

    Google Scholar 

  22. Lamme, V.A.F.: The neurophysiology of figure ground segregation in primary visual cortex. J. Neurosci. 15, 1605–1615 (1995)

    Google Scholar 

  23. Lee, T.S., Mumford, D., Romeo, R., Lamme, V.A.F.: The role of the primary visual cortex in higher level vision. Vis. Res. 38, 2429–2454 (1998)

    Article  Google Scholar 

  24. Lowe, D.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60, 91–110 (2004)

    Article  Google Scholar 

  25. McKeown, D.M., Harvey, W.A., McDermott, J.: Rule-based interpretation of aerial imagery. IEEE Trans. Pattern Anal. Mach. Intell. 7(5), 570–585 (1985)

    Article  Google Scholar 

  26. Montemurro, M.A., Rasch, M.J., Murayama, Y., Logothetis, N.K., Panzeri, S.: Phase-of-firing coding of natural visual stimuli in primary visual cortex. Curr. Biol. 18(5), 375–380 (2008)

    Article  Google Scholar 

  27. Opelt, A., Pinz, A., Zisserman, A.: A boundary-fragment-model for object detection. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV (2). Lecture Notes in Computer Science, vol. 3952, pp. 575–588. Springer, Berlin/Heidelberg (2006)

    Google Scholar 

  28. Opelt, A., Pinz, A., Zisserman, A.: Learning an alphabet of shape and appearance for multi-class object detection. Int. J. Comput. Vis. 80(1), 16–44 (2008)

    Article  Google Scholar 

  29. Orban, G.A.: Higher order visual processing in macaque extrastriate cortex. Physiol. Rev. 88(1), 59–89 (2008)

    Article  MathSciNet  Google Scholar 

  30. Plonsey, R.: Bioelectric Phenomena. McGraw-Hill, New York (1969)

    Google Scholar 

  31. Qiu, F., von der Heydt, R.: Figure and ground in the visual cortex: V2 combines stereoscopic cues with gestalt rules. Neuron 47, 155–166 (2005)

    Article  Google Scholar 

  32. Rubin, E.: Synsoplevede Figurer. Gyldendalske Boghandel, Nordisk Forlag, Denmark (1915)

    Google Scholar 

  33. Sajda, P., Finkel, L.: Intermediate-level visual representations and the construction of surface perception. J. Cognit. Neurosci. 7, 267–291 (1995)

    Article  Google Scholar 

  34. Sakai, K., Nishimura, H.: Determination of border ownership based on the surround context of contrast. Neurocomputing 58, 843–848 (2004)

    Article  Google Scholar 

  35. Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock graphs and shape matching. Int. J. Comput. Vis. 35(1), 13–32 (1999)

    Article  Google Scholar 

  36. Tari, S., Genctav, M.: From a modified ambrosio-tortorelli to a randomized part hierarchy tree. In: Third International Conference on Scale Space and Variational Methods in Computer Vision, vol. 1. Springer, Berlin/Heidelberg (2011)

    Google Scholar 

  37. Treisman, A., Gelade, G.: A feature-integration theory of attention. Cognit. Psychol. 12(1), 97–136 (1980)

    Article  Google Scholar 

  38. Ullman, S.: Visual routines. In: Fischler, M.A., Firschein, O. (eds.) Readings in Computer Vision: Issues, Problems, Principles, and Paradigms, pp. 298–328. Morgan Kaufmann, San Francisco (1987)

    Google Scholar 

  39. Ullman, S., Epshtein, B.: Visual classification by a hierarchy of extended fragments. In: Ponce, J., Hebert, M., Schmid, C., Zisserman, A. (eds.) Toward Category-Level Object Recognition. Lecture Notes in Computer Science, vol. 4170, pp. 321–344. Springer, Berlin/New York (2006)

    Chapter  Google Scholar 

  40. Ward, L.M., Coren, S.: The effect of optically induced blur on the magnitude of the mueller-lyer illusion. Bull. Psychon. Soc. 7(5), 483–484 (1976)

    Google Scholar 

  41. Zhaoping, L.: Border ownership from intracortical interactions in visual area v2. Neuron 47, 143–153 (2005)

    Article  Google Scholar 

  42. Zhou, H., Friedman, H.S., von der Heydt, R.: Coding of border ownership in monkey visual cortex. J. Neurosci. 20, 6594–6611 (2000)

    Google Scholar 

  43. Zipser, K., Lamme, V.A.F., Schiller, P.H.: Contextual modulation in primary visual cortex. J. Neurosci. 16(22), 7376–7389 (1996)

    Google Scholar 

  44. Zucker, S.W.: Local field potentials and border ownership: a conjecture about computation in visual cortex. J. Physiol. (Paris) 106, 297–315 (2012)

    Article  Google Scholar 

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Acknowledgements

The computer vision content in this paper was in [11]; I thank P. Dimitrov and M. Lawlor for permission to reuse that material here. S. Tari pointed out the possible connection to Ambrosio-Tortorelli. Research supported by AFOSR, ARO, NIH/NIAAA and NSF.

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  1. Computer Science, Biomedical Engineering and Applied Mathematics, Yale University, New Haven, CT, USA

    Steven W. Zucker

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  1. Steven W. Zucker
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Correspondence to Steven W. Zucker .

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  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Zucker, S.W. (2013). Distance Images and the Enclosure Field: Applications in Intermediate-Level Computer and Biological Vision. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_14

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