2000
DOI: 10.1364/oe.7.000155
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A geometric framework for nonlinear visual coding

Abstract: It is argued that important aspects of early and middle level visual coding may be understood as resulting from basic geometric processing of the visual input. The input is treated as a hypersurface defined by image intensity as a function of two spatial coordinates and time. Analytical results show how the Riemann curvature tensor R of this hypersurface represents speed and direction of motion. Moreover, the results can predict the selectivity of MT neurons for multiple motions and for motion in a direction a… Show more

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Cited by 21 publications
(13 citation statements)
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References 30 publications
(38 reference statements)
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“…have Gaussian curvature. In case of n = 3 (here movie surfaces), we still have mean and Gaussian curvature but here the "true" curvature is measured by the Riemann tensor -see Barth and Watson (2000).…”
Section: Curvature and Uniqueness Of 2d Regionsmentioning
confidence: 99%
“…have Gaussian curvature. In case of n = 3 (here movie surfaces), we still have mean and Gaussian curvature but here the "true" curvature is measured by the Riemann tensor -see Barth and Watson (2000).…”
Section: Curvature and Uniqueness Of 2d Regionsmentioning
confidence: 99%
“…However, the straightforward hypothesis that during visual processing signals with lower intrinsic dimension are suppressed renders also our model biologically plausible as well. Indeed, previous work has shown that this simple hypothesis can already explain the occurrence of lateral inhibition (i0D signals are suppressed), end-stopping (i1D signals are suppressed) [35], and motion selectivity [50].…”
Section: Discussionmentioning
confidence: 88%
“…they fully specify the image [8]. The evaluation of the intrinsic dimension is possible within a geometric approach that is plausible for biological vision [9] and is implemented here by using the structure tensor J, which is well known in the computer-vision literature [10]. The structure tensor is defined in terms of the spatio-temporal gradient ∇f of the image intensity function…”
Section: Eye Movement Predictionsmentioning
confidence: 99%