Beta Ganglion Cells in Cat Retina
Point pattern of cells in the retina, each cell classified as `on' or `off'. A bivariate point pattern.
betacells is an object of class
representing the point pattern of cell locations.
x Cartesian $x$-coordinate of cell
y Cartesian $y$-coordinate of cell
marks factor with levels
indicating ``off'' and ``on'' cells
ppp.object for details of the format.
Cartesian coordinates are given in microns.
betacells.extra is a list with one component
which is the vector of areas (in square microns) of the cells
in the pattern.
W"assle et al (1981), Figure 6(a),
scanned and processed by Stephen Eglen
This is a new, corrected version of the old dataset
ganglia. See below.
These data represent a pattern of beta-type ganglion cells
in the retina of a cat recorded by W"assle et al. (1981).
Beta cells are associated
with the resolution of fine detail in the cat's visual system.
They can be classified anatomically as ``on'' or ``off''.
Statistical independence of the arrangement of the
``on''- and ``off''-components
would strengthen the evidence for Hering's (1878) `opponent theory'
that there are two separate channels for sensing
``brightness'' and ``darkness''.
See W"assle et al (1981). There is considerable current interest
in the arrangement of cell mosaics in the retina, see
Rockhill et al (2000).
The dataset is a multitype point pattern giving the locations and types (``on'' or ``off'') of beta cells observed in a rectangle of dimensions $750 \times 990$ microns. Coordinates are given in microns (thousandths of a millimetre). The original source is Figure 6 of W"assle et al (1981), which is a manual drawing of the beta mosaic observed in a microscope field-of-view of a whole mount of the retina. Thus, all beta cells in the retina were effectively projected onto the same two-dimensional plane. The data were scanned in 2004 by Stephen Eglen from Figure 6(a) of W"assle et al (1981). Image analysis software was used to identify the soma (cell body). The $x,y$ location of each cell was taken to be the centroid of the soma. The type of each cell (``on'' or `off'') was identified by referring to Figures 6(b) and 6(d).
The area of each soma (in square microns) was also computed,
and is provided in the dataset
Note that this is a corrected version of the
dataset provided in earlier versions of
The earlier data
ganglia were not faithful to the scale
in the original paper and contain some scanning errors.
Hering, E. (1878) Zur Lehre von Lichtsinn. Vienna.
Van Lieshout, M.N.M. and Baddeley, A.J. (1999) Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511--532.
Rockhill, R.L., Euler, T. and Masland, R.H. (2000) Spatial order within but not between types of retinal neurons. Proc. Nat. Acad. Sci. USA 97(5), 2303--2307.
W"assle, H., Boycott, B. B. & Illing, R.-B. (1981). Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc. Roy. Soc. London Ser. B 212, 177--195.
data(betacells) plot(betacells) plot(betacells$window, main="beta cells") symbols(betacells$x, betacells$y, circles=sqrt(betacells.extra$area/pi), inches=FALSE, add=TRUE)