spatstat (version 1.52-1)

betacells: Beta Ganglion Cells in Cat Retina


Point pattern of cells in the retina, each cell classified as `on' or `off' and labelled with the cell profile area.





betacells is an object of class "ppp" representing the point pattern of cell locations. Entries include

x Cartesian \(x\)-coordinate of cell
y Cartesian \(y\)-coordinate of cell

Cartesian coordinates are given in microns.

The data frame of marks has two columns:

type factor with levels off and on
indicating ``off'' and ``on'' cells
area numeric vector giving the

See ppp.object for details of the format.


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 marked point pattern giving the locations, types (``on'' or ``off''), and profile areas of beta cells observed in a rectangle of dimensions \(750 \times 990\) microns. Coordinates are given in microns (thousandths of a millimetre) and areas are given in square microns.

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.

Note that this is a corrected version of the ganglia dataset provided in earlier versions of spatstat. 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.


Run this code
   area <- marks(betacells)$area
   plot(betacells %mark% sqrt(area/pi), markscale=1)
# }

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