Computational Models of Visual Hyperacuity

The process of visual hyperacuity is described and analyzed in the terms of informative theory. It is shown that in principle, the detection and representation of both luminance and edge features can be performed with a precision commensurate with human abilities. Algorithms are formulated in accord with the different representational methods, and are implemented as distinct computer models, which are tested with vernier acuity tasks. The results indicate that edge information, encoded either in the manner proposed by Marr and his col1eagucs (as zero-crossings in the Laplacian of a Gaussian convolved with the image) or when encoded as a simple filtered difference allows finer spatial localization than does the centroid of the intensity distribution. In particular it is shown that to judge changes of relative positions with a precision of 0.1 sec arc in two and three dimensions, it is sufficient to represent the displacement of an edge by the difference of two LaplacianGaussian filters rather than by the difference between interpolated zero-crossings in them. This method entails no loss of relative position information (sign), allows recovery of the magnitude of the change, and provides significant economies of computation. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-84-43. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/726 COMPUTATIONAL MODELS OF VISUAL HYPERACUITY Eric Paul Krotkov MS-CIS-84-43 GRASP LAB 15 Department Of Computer and Information Science Moore School University of Pennsylvania Philadelphia, PA 19104 May 1984 Acknowledgements: This research was supported in part by DARPA grants NO001 4-85-K-0018 and N00014-85-K-0807, NSF grants MCS8219196-CER, MCS-82-07294,l R01-HL-29985-01, U.S. Army grants DAA6-29-84-K-0061, DAAB07-84-K-F077, U.S. Air Force grant 82-NM-299, Al Center grants NSF-MCS-83-05221, U.S. Army Research office grant ARO-DAA29-84-9-0027, Lord Corporation, RCA and Digital Equipment Corporation. i~;irvE!LSITil C j E ' PENNSYLVANIA TEE MCCiFtZ SCHC3L CF 51,IiCTXICAL ENGMEERMG SCIIOOL 8F 2NGMEHRLNG AND APPLLED SCIENCE COn/ZPUThTIOFJAL FdBDELS OF VISUAL HYPERACUITY

[1]  D Marr,et al.  Bandpass channels, zero-crossings, and early visual information processing. , 1979, Journal of the Optical Society of America.

[2]  G. Westheimer.  Diffraction Theory and Visual Hyperacuity* , 1976, American journal of optometry and physiological optics.

[3]  T. Poggio,et al.  Zero-Crossings and Spatiotemporal Interpolation in Vision: Aliasing and Electrical Coupling between Sensors. , 1982 .

[4]  K. Oatley,et al.  Vernier acuity as affected by target length and separation , 1972 .

[5]  S. Ullman.  Visual routines , 1984, Cognition.

[6]  H. B. Barlow,et al.  Reconstructing the visual image in space and time , 1979, Nature.

[7]  D. Marr,et al.  Smallest channel in early human vision. , 1980, Journal of the Optical Society of America.

[8]  S. McKee,et al.  Exposure duration affects the sensitivity of vernier acuity to target motion , 1983, Vision Research.

[9]  E. Andersen,et al.  VISUAL PERCEPTION AND THE RETINAL MOSAIC , 1923 .

[10]  Gerald Westheimer,et al.  Temporal and spatial interference with vernier acuity , 1975, Vision Research.

[11]  R. N. Berry.  Quantitative relations among vernier, real depth, and stereoscopic depth acuities. , 1948, Journal of experimental psychology.

[12]  D. Marr,et al.  An Information Processing Approach to Understanding the Visual Cortex , 1980 .

[13]  W. H. Miller,et al.  Photoreceptor diameter and spacing for highest resolving power. , 1977, Journal of the Optical Society of America.

[14]  D. P. Andrews,et al.  Contour curvature analysis: Hyperacuities in the discrimination of detailed shape , 1982, Vision Research.

[15]  Ellen C. Hildreth,et al.  Implementation Of A Theory Of Edge Detection , 1980 .

[16]  D. P. Andrews,et al.  Acuities for spatial arrangement in line figures: human and ideal observers compared. , 1973, Vision research.

[17]  M C FLOM,et al.  VISUAL RESOLUTION AND CONTOUR INTERACTION. , 1963, Journal of the Optical Society of America.

[18]  R. J. Watt,et al.  Mechanisms responsible for the assessment of visual location: Theory and evidence , 1983, Vision Research.

[19]  R. Gubisch,et al.  Optical Performance of the Human Eye , 1967 .

[20]  Kenneth W. Ford.  Classical and Modern Physics , 1973 .

[21]  S. McKee,et al.  Visual acuity in the presence of retinal-image motion. , 1975, Journal of the Optical Society of America.

[22]  R. J. Watt,et al.  Mechanisms of interpolation in human spatial vision , 1982, Nature.