This Article 
 Bibliographic References 
 Add to: 
Computer-Aided Neuroanatomy: Differential Geometry of Cortical Surfaces and an Optimal Flattening Algorithm
March 1986 (vol. 6 no. 3)
pp. 36-44
Eric Schwartz, New York University Medical Center, NSK Institute, and Courant Institute of Mathematical Sciences
Bjorn Merker, New York University Medical Center
In a variety of species including monkeys and humans, the surface of the retina is mapped in an accurate manner to the surface of primary visual cortex. In a real sense there is an image, expressed in the firing density of neurons, impressed on the surface of the brain. The various images found in the brain have complicated natures: They are ``distorted'' by nonlinear map functions, and contain submodality information expressed spatially in the form of columnar systems representing stereo, orientation, motion, and other forms of data. The detailed study of such maps represents a difficult series of problems in the areas of computer graphics, image processing, numerical analysis, and neuroanatomy. This article describes some intial steps in the field of computer-aided neuroanatomy. An algorithm for unfolding and flattening cortical surfaces and a measurement of the differential geometric aspects of these surfaces are presented. Models of the structure of images as they would appear mapped to the surface of primate striate cortex are also shown.

1. B.Merker and E.L.Schwartz, "Computer-Aided Anatomy: Reconstruction and Characterization of the Opercular Surface of Macaque Striate Cortex," Investigative Opthalmology Supplemment (AVRO) Vol. 26, pp. 164 1985
2. Carmo, Differential Geometry of Curves of Surfaces , John Wiley and Sons 1975
3. D.H.Hubel and T.N.Wiesel, "Sequence Regularity and Geometry of Orientation Columns in Monkey Striate Cortex," J. Comparative Neurology Vol. 158, pp. 267-293 1974
4. E.L.Schwartz, "Spatial Mapping in the Primate Sensory System: Analytic Structure and Relevance to Perception," Biological Cybermetics Vol. 25, pp. 181-194 1977
5. D.C.Van Essen, W.T.Newsome, and J.H.R.Maunsell, "The Visual Representation in Striate Cortex of the Macaque Monkey: Assymetries, Anisotropies, and Individual Variability," Vision Research Vol. 24, pp. 429-448 1984
6. B.Dow, R.G.Vautin, and R.Bauer, "The Mapping of Visual Space onto Foveal Striate Cortex in the Macaque Monkey," J. Neuroscience Vol. 5, pp. 890-902 1985
7. R.Tootel, M.S.Silverman, E.Switkes, and R.DeValois, "Deoxyglucose Retinotopic Maps and the Complex Log Model in Macaque Striate Cortex," Science Vol. 227, pp. 1066 1985
8. E.L.Schwartz, "Image Processing Simulations of the Functional Architecture of Macaque Striate Cortex," Investigative Opthalmology Supplement (AVRO) Vol. 26, pp. 164 1985
9. M.Livingstone and D.H.Hubel, "Anatomy and Physiology of a Color System in the Primate Visual Cortex," J. Neuroscience Vol. 4, pp. 309-356 1984
10. R.Tootel, M.S.Silverman, E.Switkes, and R.DeVois, "Deoxyglucose Analysis of Retinotopic Organization in Primate Striate Cortex," Science Vol. 218, pp. 902-904 1982
11. E.L.Schwartz, D.R.Christman, and A.P.Wolf, "An Application of PETT Scanning to the Observation of Human Visual Cortex Topographic Mapping," Neuro. Soc. Abstracts Vol. 7, pp. 351 1981
12. E.L.Schwartz, D.R.Christman, and A.P.Wolf, "Human Primary Visual Cortex Topography Imaged Via Positron Tomography," Brain Research Vol. 294, pp. 225-230 1984
13. J.W.Sammon, "A Nonlinear Mapping for Data Structure Analysis," IEEE Trans. Computers Vol. C-18, pp. 401-408 1969
14. M.Sharir, "Distance Calculations in Polygonal Spaces," , Courant Institute of Math Sciences 1985 Robotics Research Technical Reports
15. E.Wolfson and E.L.Schwartz, "An Algorithm for Calculating Distances in Polyhedral Spaces," , Courant Institute of Mathematical Sciences Robotics Research Technical Reports (in preparation)
16. E.L.Schwartz, "Analytic Structure of the Retinotopic Maping of Striate Cortex and Relevance to Perception," Neuroscience Abstracts Vol. 6, pp. 1636 1976
17. E.L.Schwartz, "Anatomical and Physiological Correlates of Visual Computation from Striate to Infro-Temporal Cortex," IEEE SMC Vol. 14, pp. 257-269 1984
18. S.D.Levay, D.H.Hubel, and T.N.Wiesel, "The Pattern Ocular Dominance Columns in Macaque Visual Cortex Revealed by a Reduced Silver Stain," J. Comparative Neurology Vol. 159, pp. 559-576 1975

Eric Schwartz, Bjorn Merker, "Computer-Aided Neuroanatomy: Differential Geometry of Cortical Surfaces and an Optimal Flattening Algorithm," IEEE Computer Graphics and Applications, vol. 6, no. 3, pp. 36-44, March 1986, doi:10.1109/MCG.1986.276630
Usage of this product signifies your acceptance of the Terms of Use.