Limits of stereopsis explained by local cross-correlation.

Human stereopsis has two well-known constraints: the disparity-gradient limit, which is the inability to perceive depth when the change in disparity within a region is too large, and the limit of stereoresolution, which is the inability to perceive spatial variations in disparity that occur at too fine a spatial scale. We propose that both limitations can be understood as byproducts of estimating disparity by cross-correlating the two eyes' images, the fundamental computation underlying the disparity-energy model. To test this proposal, we constructed a local cross-correlation model with biologically motivated properties. We then compared model and human behaviors in the same psychophysical tasks. The model and humans behaved quite similarly: they both exhibited a disparity-gradient limit and had similar stereoresolution thresholds. Performance was affected similarly by changes in a variety of stimulus parameters. By modeling the effects of stimulus blur and of using different sizes of image patches, we found evidence that the smallest neural mechanism humans use to estimate disparity is 3-6 arcmin in diameter. We conclude that the disparity-gradient limit and stereoresolution are indeed byproducts of using local cross-correlation to estimate disparity.

[1]  A. Parker,et al.  Receptive Field Size in V1 Neurons Limits Acuity for Perceiving Disparity Modulation , 2004, The Journal of Neuroscience.

[2]  David Williams,et al.  A visual nonlinearity fed by single cones , 1992, Vision Research.

[3]  S J Anderson,et al.  Peripheral spatial vision: limits imposed by optics, photoreceptors, and receptor pooling. , 1991, Journal of the Optical Society of America. A, Optics and image science.

[4]  M. Landy,et al.  Why Is Spatial Stereoresolution So Low? , 2004, The Journal of Neuroscience.

[5]  L. Cormack,et al.  Interocular correlation, luminance contrast and cyclopean processing , 1991, Vision Research.

[6]  C. Blakemore.  The range and scope of binocular depth discrimination in man , 1970, The Journal of physiology.

[7]  C. WILLIAM TYLER,et al.  Depth perception in disparity gratings , 1974, Nature.

[8]  K. N. Ogle.  Precision and validity of stereoscopic depth perception from double images. , 1953, Journal of the Optical Society of America.

[9]  James M. Hillis,et al.  Slant from texture and disparity cues: optimal cue combination. , 2004, Journal of vision.

[10]  David J. Fleet,et al.  Neural encoding of binocular disparity: Energy models, position shifts and phase shifts , 1996, Vision Research.

[11]  Martin S. Banks,et al.  Misperceptions in stereoscopic displays: a vision science perspective , 2008, APGV '08.

[12]  Richard A Eagle,et al.  Stereo correspondence in one-dimensional Gabor stimuli , 2000, Vision Research.

[13]  H. Sakata,et al.  Selectivity of the parietal visual neurones in 3D orientation of surface of stereoscopic stimuli. , 1996, Neuroreport.

[14]  Izumi Ohzawa,et al.  Mechanisms of stereoscopic vision: the disparity energy model , 1998, Current Opinion in Neurobiology.

[15]  J T Todd,et al.  The perception of stereoscopic transparency , 1988, Perception & psychophysics.

[16]  P. Panum.  Physiologische Untersuchungen über das Sehen mit zwei Augen , 1858 .

[17]  J P Frisby,et al.  PMF: A Stereo Correspondence Algorithm Using a Disparity Gradient Limit , 1985, Perception.

[18]  J. Robson,et al.  Application of fourier analysis to the visibility of gratings , 1968, The Journal of physiology.

[19]  I. Ohzawa,et al.  Stereoscopic depth discrimination in the visual cortex: neurons ideally suited as disparity detectors. , 1990, Science.

[20]  Lawrence K. Cormack,et al.  Disparity tuning in mechanisms of human stereopsis , 1992, Vision Research.

[21]  Wilson S. Geisler,et al.  The physical limits of grating visibility , 1987, Vision Research.

[22]  M F Bradshaw,et al.  Disparity Scaling and the Perception of Frontoparallel Surfaces , 1995, Perception.

[23]  Preeti Verghese,et al.  Stereo transparency and the disparity gradient limit , 2002, Vision Research.

[24]  Martin S. Banks,et al.  Are corresponding points fixed? , 2001, Vision Research.

[25]  Robert F Hess,et al.  Global factors that determine the maximum disparity for seeing cyclopean surface shape , 2000, Vision Research.

[26]  H. B. Barlow,et al.  What does the eye see best? , 1983, Nature.

[27]  D Marr,et al.  Cooperative computation of stereo disparity. , 1976, Science.

[28]  K. Prazdny.  Detection of binocular disparities , 2004, Biological cybernetics.

[29]  M F Bradshaw,et al.  Vertical disparities, differential perspective and binocular stereopsis , 1993, Nature.

[30]  Ze-Nian Li,et al.  Analysis of disparity gradient based cooperative stereo , 1996, IEEE Trans. Image Process..

[31]  Mark F. Bradshaw,et al.  Sensitivity to horizontal and vertical corrugations defined by binocular disparity , 1999, Vision Research.

[32]  T. O. Binford,et al.  Geometric Constraints In Stereo Vision , 1980, Optics & Photonics.

[33]  B. Julesz,et al.  A disparity gradient limit for binocular fusion. , 1980, Science.

[34]  C. Tyler.  Spatial organization of binocular disparity sensitivity , 1975, Vision Research.

[35]  F A Wichmann,et al.  Ning for Helpful Comments and Suggestions. This Paper Benefited Con- Siderably from Conscientious Peer Review, and We Thank Our Reviewers the Psychometric Function: I. Fitting, Sampling, and Goodness of Fit , 2001 .

[36]  G C DeAngelis,et al.  The physiology of stereopsis. , 2001, Annual review of neuroscience.

[37]  Takeo Kanade,et al.  A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[38]  Dennis M. Levi,et al.  Vernier acuity, crowding and amblyopia , 1985, Vision Research.

[39]  S. A. Lloyd,et al.  The Role of Disparity Gradient in Stereo Vision , 1985, Perception.

[40]  Jerry D. Nguyenkim,et al.  Disparity-Based Coding of Three-Dimensional Surface Orientation by Macaque Middle Temporal Neurons , 2003, The Journal of Neuroscience.

[41]  C. Tyler.  Stereoscopic Vision: Cortical Limitations and a Disparity Scaling Effect , 1973, Science.

[42]  Julie M. Harris,et al.  Fine-scale processing in human binocular stereopsis. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.

[43]  Stéphane Mallat,et al.  The Texture Gradient Equation for Recovering Shape from Texture , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[44]  James A. Crowell,et al.  Horizontal and vertical disparity, eye position, and stereoscopic slant perception , 1999, Vision Research.

[45]  I. Ohzawa,et al.  Neural mechanisms for processing binocular information I. Simple cells. , 1999, Journal of neurophysiology.

[46]  W. Geisler,et al.  Ideal discriminators in spatial vision: two-point stimuli. , 1985, Journal of the Optical Society of America. A, Optics and image science.