Dept. of Cognitive and Neural Systems
Boston University
Tues. 1-4 PM
677 Beacon Street, Basement Auditorium

Course Syllabus and Required Readings

Professor Eric Schwartz
Office: Room 310, 677 Beacon Street
Office hours: W 1-5
Phone: 353-6179

OVERVIEW: Computational neuroscience refers to the area of overlap between computer science, mathematics,engineering and neuroscience. On the one hand, methods of computer graphics, image processing, and numerical methods have provided basic tools for application in neuroscience. At the most basic level, the visualization and reconstruction of neuroanatomical material obtained from histology (serial sections) and tomographic studies (PETT, MRI, etc.) are dependent on relatively sophisticated computational techniques. At a higher level, models of the neuronal, columnar, and topographic brain structures of interest to experimental neuroscientists are being modeled, and increasingly, can only be understood in terms of, sophisticated computational models. Finally, at the functional level, the methods by which the nervous system achieves its powerful computational abilities are of increasing interest to engineers and computer scientists, who seek to learn from the brain, as well as neuroscientists and psychologists, who seek to learn about the brain.

These three levels of computational neuroscience will be explored in the context of a reading seminar for advanced graduate students in the Dept. of Cognitive and Neural Systems, the College of Engineering, and the School of Medicine. The goal of the course is exposure to the literature of computational neuroscience. Original papers in the areas of the structure, function and modeling of primate visual cortex will provide one major area of coverage. Special emphasis will be placed on the columnar and topographic structure of visual cortex, and the computational and functional models that have been developed in the context of visual cortex. A second major area of emphasis will be on technological applications in the areas of active (computer) vision.

This material is by nature multidisciplinary: students will be expected to have a strong background in at least one of neuroscience, computer science or computer technology. A mathematical background which includes a working knowledge of applied linear algebra, fourier analysis, and advanced calculus will be assumed. However, some attempt will be made to provide a self-contained presentation: a brief review of all advanced material will be provided.

REQUIREMENTS: All students must complete either a term paper or a computer project. Topics for these will be suggested during the seminar. There will be a mid-term exam, but the term paper assignment will be used instead of a final exam.

Problem sets, or brief literature reviews, will be assigned during class. The final grade will be weighted equally between the mid-term, the problem sets, and the term paper/project assignment.

E-MAIL An alias cn780 will be set up and used to broadcast information to students enrolled in cn780.

CLASS WEBSITE is at CN780 WIKI. There is a login and password which will be distributed during the first class meeting.

This web site is interactive (its a "wiki"), so two-way interchanges can occur between all of us. In addition, the syllabus, all important announcements, and electronic versions of the readings will be posted there, when available, and also additional information. Please consult the wiki each week for updates to the syllabus, readings, or other matters.

Reading Material Copies of all required reading will be placed on the wiki in electronic form. Supplementary material will be available, by e-mail appointment, at my office at 677 Beacon Street. Students will be responsible for reading material listed as required on the class wiki. Students are expected to have completed the required reading listed for a given week by the date of the lecture.


1 Introduction and Review

The first lecture will be a preview of the course, in order to allow a decision about the interest and appropriateness of background for each student, and a review of some basic material in pattern recognition and image processing.


1.1 Early history of computational neuroscience

1.2 Some basic facts of neuroscience

1.3 Dialectics of comp. neuroscience

1.4 Principle research areas of comp. neuroscience

1.4.1 Pattern recognition

1.4.2 Control

1.4.3 Neuronal pattern formation

1.4.4 Computer aided neuroanatomy

1.4.5 Data analysis and interpretation

1.4.6 VLSI

1.4.7 Applications

1.5 Resources

1.5.1 Journals, abstracting services

1.5.2 Trade, Computer, Electronics

1.5.3 Meetings

1.5.4 Books

1.6 Criteria for reading and evaluating the literature

1.7 Review

1.7.1 Review of statistical pattern recognition

[Duda et al., 2000a] [Duda et al., 2000b] [Duda et al., 2000c]

1.7.2 Review of image Processing

[Davies, 1990]

1.7.3 Review of Differential Geometry of Surfaces and Curves

2 Cortical Columns: experimental observation

2.1 Early ideas of V1 ``cortical column''

[Hubel, 1982]

2.2 The existence of local topographic structure in cat V1

[Das and Gilbert, 1997]

2.3 Optical dye observations: pinwheels

[Bonhoeffer and Grinvald, 1991,Blasdel, 1992a,Blasdel, 1992b]

2.4 Multi-column spatial relationships

[Bartfeld and Grinvald, 1992]

2.5 Spatial resolutions of single photon optical recording

[Polimeni et al., 2005]

2.6 Two photon optical recording

[Ohki et al., 2006]

3 Columns:Modeling

3.1 Local complex log

[Schwartz, 1977]

3.2 Swindale, competition-cooperation

[Swindale, 1980]

3.3 Rojer-Schwartz Band-pass filter

[Rojer and Schwartz, 1990a]

3.4 Rojer-Schwartz Topological singularity

[Schwartz and Rojer, 1991]

3.5 Protocolumn model

[Landau and Schwartz, 1994]

3.6 Dimension reduction models

[Erwin et al., 1993,Grossberg and Olson, 1994,Swindale, 1997,Durbin and Mitchison, 1990]

3.7 Continuum (mechanics) models

[Wood and Schwartz, 1999,Ringach, 2007]

4 Topography: Experimental

4.1 Brain anatomy and retrograde tracing methods

[Nauta and Feirtag, 1986]

4.2 Visual cortex topography

[Talbot and Marshall, 1941,Daniel and Whitteridge, 1961]

4.3 Metabolic mapping: Cytochrome oxidase and 2DG

[Kennedy et al., 1976,Wong-Riley, 1979]

4.4 Imaging Visual Cortex topography with fMRI

[Engel et al., 1997,Brewer et al., 2002]

5 Models of Topography and Psychophysical Scaling

5.1 Modeling magnification factor and mapping

[Schwartz, 1994,Rojer and Schwartz, 1990b]

5.2 Modeling psychophysical scaling laws

[Wilson et al., 1990]

5.3 Modeling retino-cortical relationship

[Fischer, 1973,Wassle et al., 1989]

5.4 Conformal and quasi-Conformal mapping models

[Symm, 1966,Guillermo A et al., 1995,Frederick and Schwartz, 1990b]

5.5 Develomental Modeling of Map Formation

[Goodhill, 2007]

6 Columns and maps: models of computational function

6.1 Cepstral stereo

[Yeshurun and Schwartz, 1989]

6.2 Ocular dominance columns and stereo vision

[Yeshurun and Schwartz, 1999]

6.3 Curvature features in V-4 and IT cortex

[Wilkinson et al., 1998,Gallant et al., 1996]

6.4 Form analysis and Glass patterns

[Wilson et al., 1997]

6.5 Mellin Transform and Invariance

[Casasent and Psaltis, 1976,Cavanagh, 1978]

6.6 Object tracking

[Weiman, 1989,Weiman, 1990a]

6.7 Video compression

[Weiman, 1990b]

6.8 Hough and Radon transforms

[Schwartz et al., 1983]

6.9 Foveal Vision on Pyramids

[Burt et al., 1989]

6.10 Active Vision

[Bajcsy, 1988]

6.11 Space-variant active vision

[Sandini and Dario, 1989] [Bederson et al., 1992] [Wallace et al., 1993] [Bonmassar and Schwartz, 1997]

7 Spatial Representation: Neurons as feature extractors

7.1 Early statements of the concept of feature extraction

[Barlow, 1972]

7.2 IT Cortex and Feature representation

[Gross et al., 1972,Schwartz et al., 1983,Tanaka, 1996,Logothetis et al., 1994,Logothetis and Sheinberg, 1996]

7.3 Interpolation between exemplars: Son of Grandmother

[Edleman, 1998]

8 Spatial Frequency, Scale, and Multi-resolution

8.1 Spatial frequency and multiple resolution

[Burt and Adelson, 1981]

8.2 Gabor functions and wavelets

[Marcelja, 1980]

8.3 Convolution, Energy, Cepstrum, Delta Functions, Uncertainty

[Bracewell, 1978,Gabor, 1946,Stork and Wilson, 9899,Klein and Beutter, 1992]

8.4 Computational uses of spatial frequency

[Ben-Aries and Wang, 1998,Ben-Arie and Nandy, 1998]

9 Non Linear Diffusion

9.1 Lateral inhibition, the Laplacian and the D.O.G.

9.2 Koenderink-Hummel: The Heat (Diffusion) Equation

[Hummel, 1986,Koenderink, 1984]

9.3 Mingolla-Grossberg: Anisotropic diffusion and neural nets

[Cohen and Grossberg, 1984,Grossberg and Mingolla, 1985]

9.4 Malik-Perona: anisotropic diffusion and PDE's

[Perona, 1990]

9.5 Fischl-Schwartz: Diffusionless diffusion

[Fischl and Schwartz, 1997,Fischl and Schwartz, 1999]

9.6 Medial axis and long range interactions in V1

[Lamme, 1995,Spillmand and Werner, 1996]

10 Computer aided neuroanatomy of visual cortex

10.1 Alignment

[Merickel, 1988]

10.2 Segmentation

[Schwartz et al., 1988]

10.3 Flattening

[Schwartz et al., 1989,Olavarria and Sluyters, 1985,vanand Maunsell, 1980,Khaneja et al., 1998]

10.4 Brain Peeling

[Frederick and Schwartz, 1990a]

10.5 Triangulation

[Fuchs et al., 1977,Shaw and Schwartz, 1989]

11 Olfaction: Sensation and spatial mapping

[Turin, 2006]



Bajcsy, 1988
Bajcsy, R. (1988).
Active perception.
IEEE Proceedings, 76(8):996-1005.

Barlow, 1972
Barlow, H. B. (1972).
Single units and sensation: a neuron doctrine for perceptual psychology.
Perception, 1:371-380.

Bartfeld and Grinvald, 1992
Bartfeld, E. and Grinvald, A. (1992).
Relationships bwtween orientation-preference pinwheels, cytochrome oxidase blobs , and ocular dominance columns.
Proc. Nat. Acd. Sci., 89:11905-11909.

Bederson et al., 1992
Bederson, B., Wallace, R. S., and Schwartz, E. L. (1992).
A miniaturized active vision system.
In 11th IAPR International Conference on Pattern Recognition, volume B of Specialty Conference on Pattern Recognition Hardware Architecture, pages 58-62, The Hague, Netherlands.

Ben-Arie and Nandy, 1998
Ben-Arie, J. and Nandy, D. (1998).
A volumetric iconic frequency domain representation for objects with application for pose invariant face recognition.

Ben-Aries and Wang, 1998
Ben-Aries, J. and Wang, Z. (1998).
Pictorial recogntion of objects employing affine invariance in the frequency domain.

Blasdel, 1992a
Blasdel, G. G. (1992a).
Differential imaging of ocular dominance and orientation selectivity in monkey striate cortex.
Journal of Neuroscience, 12(8):3115-3138.

Blasdel, 1992b
Blasdel, G. G. (1992b).
Orientation selectivity, preference, and continuity in monkey striate cortex.
Journal of Neuroscience, 12(8):3139-3161.

Bonhoeffer and Grinvald, 1991
Bonhoeffer, T. and Grinvald, A. (1991).
Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns.
Nature, 353:429-431.

Bonmassar and Schwartz, 1997
Bonmassar, G. and Schwartz, E. L. (1997).
Space-variant fourier analysis: the exponential chirp.
IEEE Pattern Analysis and Machine Vision, 19:1080-1089.
Download Postscript.

Bracewell, 1978
Bracewell, R. N. (1978).
The Fourier Transform and Its Applications.
McGraw Hill.

Brewer et al., 2002
Brewer, A. A., Press, W. A., Logothetis, N. K., and Wandell, B. A. (2002).
Visual areas in macaque cortex measured using functional magnetic resonance imaging.
Journal of Neuroscience, pages 10416-10426.

Burt and Adelson, 1981
Burt, P. and Adelson, T. (1981).
A laplacian pyramid for data compression.
IEEE Transactions on Communications, 8:1230-1245.

Burt et al., 1989
Burt, P. J., Bergen, J. R., Hingorani, R., Kolczynski, R., Lee, W. A., Leung, A., Lubin, J., and Shvaytser, H. (1989).
Object tracking with a moving camera.
Proc. Work. on Visual Motion, pages 2-12.

Casasent and Psaltis, 1976
Casasent, D. and Psaltis, D. (1976).
Position, rotation and scale-invariant optical correlation.
Applied Optics, 15:1793-1799.

Cavanagh, 1978
Cavanagh, P. (1978).
Size and position invariance in the visual system.
Perception, 7:167-177.

Cohen and Grossberg, 1984
Cohen, M. A. and Grossberg, S. (1984).
Neural dynamics of brightness perception: Features, boundaries, diffusion, and resonance.
Perception and Psychophysics, 36:428-456.

Daniel and Whitteridge, 1961
Daniel, M. and Whitteridge, D. (1961).
The representation of the visual field on the cerebral cortex in monkeys.
J. Physiol., 159:203-221.

Das and Gilbert, 1997
Das, A. and Gilbert, C. D. (1997).
Distortions of visuotopic map match orientation singularities in primary visual cortex.
Nature, 387(6633):594-598.

Davies, 1990
Davies, E. R. (1990).
Machine Vision.
Academic Press.

Duda et al., 2000a
Duda, R. O., Hart, P. E., and Stork, D. G. (2000a).
Pattern Classification.
Wiley Intersicnece, second edition.
Download Postscript.

Duda et al., 2000b
Duda, R. O., Hart, P. E., and Stork, D. G. (2000b).
Pattern Classification.
Wiley Intersicnece, second edition.
Download Postscript.

Duda et al., 2000c
Duda, R. O., Hart, P. E., and Stork, D. G. (2000c).
Pattern Classification.
Wiley Intersicnece, second edition.
Download Postscript.

Durbin and Mitchison, 1990
Durbin, R. and Mitchison, G. (1990).
A dimension reduction framework for understanding cortical maps.
Nature, 343:644.

Edleman, 1998
Edleman, S. (1998).
Representation is representation of similarities.
Behavioural and Brain Sciences.

Engel et al., 1997
Engel, S. A., Glover, G. H., and Wandell, B. (1997).
Retinotopic organization in human visual cortex and the spatial rpecision of functional mri.
Cerebral Cortex.

Erwin et al., 1993
Erwin, E., Obermeyer, K., and Schulten, K. (1993).
A comparison of models of visual cortical map formation.
In Eeeckman, F. and Bower, J., editors, Computation and Neural Systems, pages 137-150. Kluwer Academic Press.

Fischer, 1973
Fischer, B. (1973).
Overlap of receptive field centers and representation of the visual field in the cat's optic tract.
Vision Res., 13:2113-2120.

Fischl and Schwartz, 1997
Fischl, B. and Schwartz, E. L. (1997).
Learning an integral equation approximation toanisotropic diffusion in image processing.
IEEE Pattern Analysis and Machine Vision, 19:342-351.
Download Postscript.

Fischl and Schwartz, 1999
Fischl, B. and Schwartz, E. L. (1999).
Adaptive non-local filtering: A fast alternative to anisotropic diffusion for image segmentation.
IEEE Patt. Anal. and Mach. Intell., 22:42-48.
Download Postscript.

Frederick and Schwartz, 1990a
Frederick, C. and Schwartz, E. L. (1990a).
The brain peeler: viewing the inside of a three dimensional shell.
Visual Computer, 6(1):37-49.

Frederick and Schwartz, 1990b
Frederick, C. and Schwartz, E. L. (1990b).
Conformal image warping.
IEEE Computer Graphics and Applications, March:54-61.

Fuchs et al., 1977
Fuchs, H., Kedem, Z. M., and Uselton, S. P. (1977).
Optimal surface reconstruction from planar contours.
Communications of the ACM, 20:693-702.

Gabor, 1946
Gabor, D. (1946).
Theory of communication.
Proc. of Institute of Electrical Engineers, 93(3):429-457.

Gallant et al., 1996
Gallant, J. L., Connor, C. E., Bakshit, S., Lewis, J. W., and van Essen, D. C. (1996).
Neural responses to polar, hyhperbolic and cartesian gratings in area v4 of the macaque monkey.
Journal of Neurophysiology, 76(4):2718-2739.

Goodhill, 2007
Goodhill, G. (2007).
Contributions of theoretical modeling to the understanding of neural map development.
Neuron, 56:301.

Gross et al., 1972
Gross, C. G., Rocha-Mirand, C. E., and Bender, D. (1972).
Visual properties of neurons in infero-temporal cortex.
J. Neurophysiology, 235:96-111.

Grossberg and Mingolla, 1985
Grossberg, S. and Mingolla, E. (1985).
Neural dynamics of perceptual grouping: Textures, boundaries and emergent segmentation.
Perception and Psychophysics, 38:148-171.

Grossberg and Olson, 1994
Grossberg, S. and Olson, S. J. (1994).
Rules for the cortical map of ocular dominance and orientation columns.
Neural Networks, pages 883-894.

Guillermo A et al., 1995
Guillermo A, B., Olivero, A. M., Rodriguez, E. J., Safar, F. G., and Sanz, J. L. C. (1995).
Conformal mapping based image processing: theory and applications.
Journal of Visual Communication and Image Representation, 6:35-51.

Hubel, 1982
Hubel, D. (1982).
Exploration of the primary visual cortex:1955-1978.
Nature, 299:515.

Hummel, 1986
Hummel, R. (1986).
Representations based on zero-crossings in scale-space.
In Fischler, M. and Firscheim, O., editors, Readings in Computer Vision: Issues, Problems, Principles and Paradigms. Morgan Kaufmann.

Kennedy et al., 1976
Kennedy, C., des Roches, H., Sakurada, O., Shinohara, M., Reivitch, M., and Jehle, J. (1976).
Metabolic mapping of the primary visual system of the monkey by means of the autoradiographic c14 dexoglucose techniqe.
Proc. Nat. Acad. Sciences, 73:420-4234.

Khaneja et al., 1998
Khaneja, N., Miller, M. I., and Grenander, U. (1998).
Dynamic programming generation of curves on brain surfaces.
IEEE PAMI, 20:1260-1265.

Klein and Beutter, 1992
Klein, S. A. and Beutter, B. (1992).
Minimizing and maximizing the joint space-spatial frequency uncertainty of gabor-like functions: comment.
J. Opt. Soc. America.

Koenderink, 1984
Koenderink, J. (1984).
The structure of images.
Biol. Cybernetics, 50:363-370.

Lamme, 1995
Lamme, V. A. F. (1995).
The neurophysiology of figure-ground separation in primary visual cortex.
Journal of Neuroscience, 15(2):1605-1615.

Landau and Schwartz, 1994
Landau, P. and Schwartz, E. L. (1994).
Subset warping: Rubber sheeting with cuts.
Computer Vision , Graphics and Image Processing, 56:247-266.
Download Postscript.

Logothetis et al., 1994
Logothetis, N. K., Pauls, J., Bulthoff, H. H., and Poggio, T. (1994).
View-independent object recognition by monkey.
Current Biology, 4(5):410-414.

Logothetis and Sheinberg, 1996
Logothetis, N. K. and Sheinberg, D. L. (1996).
Visual object recognition.
Ann. Rev. Neurosci.

Marcelja, 1980
Marcelja, S. (1980).
Mathematical description of the responses of simple cortical cells.
J. Opt. Soc. America, 70(11):1297-1300.

Merickel, 1988
Merickel, M. (1988).
3D reconstruction: The registration problem.
Computer vision, graphics, and image processing, 42:206-219.

Nauta and Feirtag, 1986
Nauta, W. J. H. and Feirtag, M. (1986).
Fundamental Neuroanatomy.
W.H. Freeman and Company.

Ohki et al., 2006
Ohki, K., Chung, S., Kara, P., Hübener, M., Bonhoeffer, T., and Reid, C. R. (2006).
Highly ordered arrangement of single neurons in orientation pinwheels.
Nature, 442(7105):925-928.

Olavarria and Sluyters, 1985
Olavarria, J. and Sluyters, R. C. V. (1985).
Unfolding and flattening the cortex of gyrencephalic brains.
Journal, of Neuroscience Methods, 15:191-202.

Perona, 1990
Perona, P. (1990).
Scale-space and edge detection using anistropic diffusion.
IEEE PAMI, 12(7):629-639.

Polimeni et al., 2005
Polimeni, J. R., Granquist-Fraser, D., Wood, R. J., and Schwartz, E. L. (2005).
Physical limits to spatial resolution of optical recording: Clarifying the spatial structure of cortical hypercolumns.
Proceedings of the National Academy of Sciences of the United States of America, 102(11):4158-4163.

Ringach, 2007
Ringach, D. (2007).
On the origin of the functional architecture of thje cortex.
Plos One, 2(2).

Rojer and Schwartz, 1990a
Rojer, A. and Schwartz, E. L. (1990a).
Cat and monkey cortical columnar patterns modeled by bandpass-filtered 2D white noise.
Biological Cybernetics, 62:381-391.

Rojer and Schwartz, 1990b
Rojer, A. S. and Schwartz, E. L. (1990b).
Design considerations for a space-variant visual sensor with complex-logarithmic geometry.
10th International Conference on Pattern Recognition, Vol. 2, pages 278-285.

Sandini and Dario, 1989
Sandini, G. and Dario, P. (1989).
Active vision based on space-variant sensing.
Intl. Symp. on Robotics Research.

Schwartz, 1977
Schwartz, E. L. (1977).
Afferent geometry in the primate visual cortex and the generation of neuronal trigger features.
Biological Cybernetics, 28:1-24.

Schwartz, 1994
Schwartz, E. L. (1994).
Computational studies of the spatial architecture of primate visual cortex:columns, maps, and protomaps.
In Peters, A. and Rocklund, K., editors, Primary Visual Cortex in Primates, volume 10 of Cerebral Cortex. Plenum Press.
Download Postscript.

Schwartz et al., 1983
Schwartz, E. L., Desimone, R., Albright, T., and Gross, C. G. (1983).
Shape recognition and inferior temporal neurons.
Proceedings of the National Academy of Sciences, 80:5776-5778.

Schwartz et al., 1988
Schwartz, E. L., Merker, B., Wolfson, E., and Shaw, A. (1988).
Computational neuroscience: Applications of computer graphics and image processing to two and three dimensional modeling of the functional architecture of visual cortex.
IEEE Computer Graphics and Applications, 8(4):13-28 (July).

Schwartz and Rojer, 1991
Schwartz, E. L. and Rojer, A. S. (1991).
Cortical hypercolumns and the topology of random orientation maps.
Technical Report 593, Courant Institute of Mathematical Sciences, 251 Mercer Street.

Schwartz et al., 1989
Schwartz, E. L., Shaw, A., and Wolfson, E. (1989).
A numerical solution to the generalized mapmaker's problem.
IEEE Trans. Pattern Analysis and Machine Intelligence, 11:1005-1008.
Download Postscript.

Shaw and Schwartz, 1989
Shaw, A. and Schwartz, E. L. (1989).
Construction of polyhedral surfaces from serial sections: exact and heuristic solutions.
SPIE Medical Imaging III: Image Capture and Display, 1091:221-233.

Spillmand and Werner, 1996
Spillmand, L. and Werner, J. S. (1996).
Long-range interactions in visual perception.
Trends in the Neurosciences, 19(10):428-434.

Stork and Wilson, 9899
Stork, D. G. and Wilson, H. R. (19899).
Do gabor functions provide appropriate descriptions of visual cortical fields.
J. Opt. Soc. America.

Swindale, 1980
Swindale, N. V. (1980).
A model for the formation of ocular dominance column stripes.
Proc. Roy. Soc. Lond. B, 208:243-264.

Swindale, 1997
Swindale, N. V. (1997).
The development of topography in the visual cortex: a review of models.
Network, 7:161-247.

Symm, 1966
Symm, G. T. (1966).
An integral equation method in conformal mapping.
Numerische Mathematik, 9:250-258.

Talbot and Marshall, 1941
Talbot, S. A. and Marshall, W. H. (1941).
Physiological studies on neural mechanisms of visual localization and discrimination.
Amer. J. Opthal., 24:1255-1263.

Tanaka, 1996
Tanaka, K. (1996).
Inferotemporal cortex and object vision.
Ann. Rev. Neurosci.

Turin, 2006
Turin, L. (2006).
The Secret of Scent.
Harper Collins.

vanand Maunsell, 1980
van, D. C. and Maunsell, J. (1980).
Two dimensional maps of the cerebral cortex.
Journal of Comparitive Neurology, 191:255-281.

Wallace et al., 1993
Wallace, R., Ong, P.-W., Bederson, B., and Schwartz, E. (1993).
Space variant image processing.
International Journal of Machine Vision, page In press.

Wassle et al., 1989
Wassle, H., Grunert, U., Rohrenbeck, J., and Boycott, B. B. (1989).
Cortical magnification factor and the ganglion cell density of the primate retina.
Nature, 341:643-646.

Weiman, 1989
Weiman, C. F. R. (1989).
Tracking algorithms using log-polar mapped image coordinates.
SPIE Proceedings on Intelligent Robots and Computer Vision VIII, 1192.

Weiman, 1990a
Weiman, C. F. R. (1990a).
Polar exponential sensor arrays unify iconic and hough space representation.
SPIE Proceedings on Intelligent Robots and Computer Vision VIII, 1192.

Weiman, 1990b
Weiman, C. F. R. (1990b).
Video compression via log polar mapping.
SPIE Symposium on OE/Areospace Sensing, pages 1-12.

Wilkinson et al., 1998
Wilkinson, F., Wilson, H., and Habak, C. (1998).
Detection and recogntion of radial frequency patterns.
Vision Research, 38:3555-3568.

Wilson et al., 1990
Wilson, H., Levi, D., Maffei, L., Rovamo, J., and DeValois, R. (1990).
The perception of form.
In Visual Perception: The Neurophysiological Foundations. Academic Press, New York.

Wilson et al., 1997
Wilson, H. R., Wilkinson, F., and Assad, W. (1997).
Concentric orientation summation in human form vision.
Vision Research, 37:2325-2330.

Wong-Riley, 1979
Wong-Riley, M. (1979).
Changes in the visual system of monocularly sutured or enucleated cats demonstrable with cytochrome oxidase histochemistry.
Brain Research, 171:11-28.

Wood and Schwartz, 1999
Wood, R. and Schwartz, E. L. (1999).
Topographic shear and the relationship of ocular dominance columns to orientation columns in monkey and cat visual cortex.
Neural Networks, 12:205-210.
Download Postscript.

Yeshurun and Schwartz, 1989
Yeshurun, Y. and Schwartz, E. L. (1989).
Cepstral filtering on a columnar image architecture: a fast algorithm for binocular stereo segmentation.
IEEE Trans. Pattern Analysis and Machine Intelligence, 11(7):759-767.

Yeshurun and Schwartz, 1999
Yeshurun, Y. and Schwartz, E. L. (1999).
Cortical hypercolumn size determines stereo fusion limits.
Bio. Cybernetics, 80(2):117-131.
Download Postscript.

copyright Prof. Eric L. Schwartz
Dept. of Cognitive and Neural Systems