There were four samples of bone, and ten regions were mapped in each bone, yielding 40 spatial point patterns. The data can be regarded as replicated observations of a three-dimensional point process, nested within bone samples.
data(osteo)hyperframe with the following columns: id character string identifier of bone sample
shortid last numeral in id
brick serial number (1 to 10) of sampling volume within
this bone sample
pts three dimensional point pattern (class pp3)
depth the depth of the brick in microns
}
The parietal bones of three fully articulated adult Macaque monkey (Macaca fascicularis) skulls from the collection of University College London were used. The right parietal bone was examined, in each case, approximately 1 cm lateral to the sagittal suture and 2 cm posterior to the coronal suture. The skulls were mounted on plasticine on a moving stage placed beneath the TSRLM. Immersion oil was applied and a $\times 60$, NA 1.0 oil immersion objective lens (Lomo) was focussed at 10 microns below the cranial surface. The TV image was produced by a Panasonic WB 1850/B camera on a Sony PVM 90CE TV monitor.
A graduated rectangular counting frame $90 \times 110$ mm (representing $82 \times 100$ microns in real units) was marked on a Perspex overlay and fixed to the screen. The area of tissue seen within the frame defined a subfield: a guard area of 10 mm width was visible on all sides of the frame. Ten subfields were examined, arranged approximately in a rectangular grid pattern, with at least one field width separating each pair of fields. The initial field position was determined randomly by applying a randomly-generated coordinate shift to the moving stage. Subsequent fields were attained using the coarse controls of the microscope stage, in accordance with the rectangular grid pattern.
For each subfield, the focal plane was racked down from its initial 10 micron depth until all visible osteocyte lacunae had been examined. This depth $d$ was recorded. The 3-dimensional sampling volume was therefore a rectangular box of dimensions $82 \times 100 \times d$ microns, called a ``brick''. For each visible lacuna, the fine focus racking control was adjusted until maximum brightness was obtained. The depth of the focal plane was then recorded as the $z$ coordinate of the ``centre point'' of the lacuna. Without moving the focal plane, the $x$ and $y$ coordinates of the centre of the lacunar image were read off the graduated counting frame. This required a subjective judgement of the position of the centre of the 2-dimensional image. Profiles were approximately elliptical and the centre was considered to be well-defined. Accuracy of the recording procedure was tested by independent repetition (by the same operator and by different operators) and found to be reproducible to plus or minus 2 mm on the screen. A lacuna was counted only if its $(x, y)$ coordinates lay inside the $90 \times 110$ mm counting frame.
Each point pattern dataset gives the $(x,y,z)$ coordinates (in microns) of all points visible in a three-dimensional rectangular box (``brick'') of dimensions $81 \times 100 \times d$ microns, where $d$ varies. The $z$ coordinate is depth into the bone (depth of the focal plane of the confocal microscope); the $(x,y)$ plane is parallel to the exterior surface of the bone; the relative orientation of the $x$ and $y$ axes is not important. The bone samples were three intact skulls and one skull cap, all originally identified as belonging to the macaque monkey Macaca fascicularis, from the collection of the Department of Anatomy, University of London. Later analysis (Baddeley et al, 1993) suggested that the skull cap, given here as the first animal, was a different subspecies, and this was confirmed by anatomical inspection.
Baddeley, A.J., Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics 42 (1993) 641--668. Howard, C.V. and Reid, S. and Baddeley, A.J. and Boyde, A. (1985) Unbiased estimation of particle density in the tandem-scanning reflected light microscope. Journal of Microscopy 138 203--212.
data(osteo)
osteo
plot(osteo$pts[[1]], main="animal 1, brick 1")
ape1 <- osteo[osteo$shortid==4, ]
plot(ape1, tick.marks=FALSE)
with(osteo, summary(pts)$intensity)
plot(with(ape1, K3est(pts)))Run the code above in your browser using DataLab