Digital Signal Processing Reference
In-Depth Information
additional three-dimensional information was available to the experts
for confirmation of the cell/non cell status. Figure 13.11(a) shows the
resulting numbers; clearly the experts differ considerably, with the first
expert typically counting more than the second one. The standard
deviation
σ
i
:=
√
var
X
i
in each counting result
X
i
ranges from 14
.
1
to 171
.
8. We normalize the deviation by dividing by the estimated mean
μ
i
:=
E
(
X
i
) of each experiment, and get a total relative deviation of
E
(
σ
i
/μ
i
)=0
.
1494. Hence the mean deviation between the two experts
lies at 15%.
Finally, even though the problem of differences in the number of
counted cells is well known, a possible solution such as deliberate slight
overcounting in order not to miss important features is not feasible. This
is because over- and undercounting are equally bad. The former results
in a too high variability, whereas the latter does not allow for sucient
differentiation.
ZANE counting
When training the cell classifier in practice, we use perceptron learning
after preprocessing with both and ICA in order to increase the per-
formance of the learning algorithm with linearly separated data. Using
prior knowledge about the sizes of cells and the zoom factor of the im-
ages, the patch size is chosen to be 20
20. Optimal values for threshold
and cut out radii have been obtained using optimization on the training
images. A thresholding of 0
.
8 is applied in the confidence map, and the
cut out radius for cell detection in the confidence map is chosen to be
18 pixels. In figure 13.1, an automatically segmented picture is shown.
Figure 13.10 presents the segmentation of the stitched image from fig-
ure 13.3. ZANE counted 281 cells, versus 267 counted cells by an expert
using focusing in the full three-dimensional slice; this confirms the good
performance of the counting algorithm.
A more detailed analysis of the ZANE cell counting algorithm is
shown in figure 13.11. In (c), five stitched brain section images of a
single mouse are counted using ZANE, manual counting, and two other
segmentation algorithms, based on clustering [30] and the watershed
transform [68] respectively. Note that manual counting can be performed
either by using the digital image only or by directly using the microscope
(this is usually done in experiments). Then the counting person can
change the focus plane, and hence detect and count cells that lie below or
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