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How Optimal Depth Cue Integration Depends on the Task

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Abstract

Bayesian parameter estimation can be used to generate statistically optimal solutions to the problem of cue integration. However, the complexity and dimensionality of these solutions is frequently prohibitive. In this paper, we show how the complexity and performance characteristics of the optimal estimator for a task depend strongly on the detailed formulation of the task, including the choice of representation for the scene variables. In particular, some representations lead to simpler inference algorithms than others. We illustrate the problem of cue integration for the perception of depth from two highly disparate cues, cast shadow position and image size, and show how the complexity and performance of the depth estimators depends on the specific representation (choice) of depth parameter. From the analysis we predict human performance on a simple depth discrimination task from the optimal cue integration in each depth representation. We find that the cue-integration strategy used by human subjects can be described as near-optimal using a particular choice of depth representation.

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References

  • Blake, A., Bulthoff, H.H., and Sheinberg, D. 1996. Shape from texture: Ideal observers and human psychophysics. In Perception as Bayesian Inference, D.C. Knill and W. Richards (Eds.). Cambridge University Press: New York, pp. 287–321.

    Google Scholar 

  • Brainard, D.H. and Freeman, W.T. 1997. Bayesian color constancy. J. Opt. Soc. Am. A, 14(7):1393–1411.

    Google Scholar 

  • Clark, J.J. and Yuille, A.L. 1990. Data Fusion for Sensory Information Processing Systems. Kluwer Academic Publishers: Boston.

    Google Scholar 

  • Cutting, J.E. and Vishton, P.M. 1996. Perceiving layout and knowing distances: The integration, relative potency, and contextual use of different information about depth. In Perception of Space and Motion, W. Epstein and S. Rogers (Eds.). Academic Press: San Diego, pp. 69–117.

    Google Scholar 

  • Edwards, A.W.F. 1992. Likelihood. Johns Hopkins University Press: Baltimore.

    Google Scholar 

  • Freeman, W.T. 1994. The generic viewpoint assumption in a framework for visual perception. Nature, 368:542–545.

    Google Scholar 

  • Goodale, M.A., Meenan, J.P., Bulthoff, H.H., Nicolle, D.A., Murphy, K.J., and Racicot, C.I. 1994. Separate neural pathways for the visual analysis of object shape in perception and prehension. Current Biology, 4(7):604–610.

    Google Scholar 

  • Jensen, F.V. 1996. An Introduction to Bayesian Networks. Springer: New York.

    Google Scholar 

  • Kersten, D., Knill, D., Mamassian, P., and Buelthoff, I. 1996. Illusory motion from shadows. Nature, 379(6560):31.

    Google Scholar 

  • Kersten, D., Mamassian, P., and Knill, D.C. 1997. Moving cast shadows induce apparent motion in depth. Perception, 26:171–192.

    Google Scholar 

  • Knill, D.C. and Kersten, D. 1991. Apparent surface curvature affects lightness perception. Nature, 351:228–230.

    Google Scholar 

  • Landy, M.S., Maloney, L.T., Johnson, E.B., and Young, M. 1995. Measurement and modeling of depth cue combination: In defense of weak fusion. Vision Research, 35:389–412.

    Google Scholar 

  • Lawson, S., Madison, C., and Kersten, D. 1998. Depth from cast shadows and size-change: Predictions from statistical decision theory. Investigative Opthamology and Visual Sciences (ARVO), 39(5):827.

    Google Scholar 

  • Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann: San Mateo, CA.

    Google Scholar 

  • Rao, C. 1973. Linear Statistical Inference and Its Applications. John Wiley and Sons: New York.

    Google Scholar 

  • Stevens, S.S. 1957. On the psychophysical law. The Psychological Review, 64(3):153–181.

    Google Scholar 

  • Tanner, M.A. 1996. Tools for Statistical Inference. Springer: New York.

    Google Scholar 

  • Yuille, A.L. and Bulthoff, H.H. 1996. Bayesian decision theory and psychophysics. In Perception as Bayesian Inference, D.C. Knill and W. Richards (Eds.). Cambridge University Press: New York, pp. 123–161.

    Google Scholar 

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Schrater, P.R., Kersten, D. How Optimal Depth Cue Integration Depends on the Task. International Journal of Computer Vision 40, 71–89 (2000). https://doi.org/10.1023/A:1026557704054

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  • DOI: https://doi.org/10.1023/A:1026557704054

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