Page 137 - Contributed Paper Session (CPS) - Volume 3

CPS1972 Livio Corain et al.
robust bases for objective tissue screening. In this view, cell shape analysis is
a powerful proxy of cellular function (Lobo et al., 2016).
Cell-oriented shape analysis differs from classical shape analysis
supporting traditional bio-medical morphometric studies in one important
issue: because of their relatively small sizes (at most a few tens of microns),
cell shapes are generally much more regular than traditional anatomical
shapes (objects of size usually in the scale of centimetre, such as bones,
anatomical regions, etc.). As a result, instead of focusing on spatial landmarks,
the endpoints of interest in cell shape analysis are cytomorphometric
descriptors such as area, perimeter, axis length, etc. In this view, there is no
need for pre-processing morphometric data by translation, scaling or rotation
methods such as procrustes superimposition.
As about the statistical hypothesis testing methods for geometric shape
analysis, it turns out that traditional testing approaches refer to quadratic-like
statistics (Rohlf, 2000), so that they are not suitable to handle multivariate
directional alternatives. This is a central issue in cell shape analysis because
formalizing the departure from the null hypothesis by one specific direction
allows us to draw conclusions on whether some populations have smaller vs.
larger or more regular vs. irregular cells, or finally denser vs. sparser cell
density. According to the so-called multi-aspect permutation paradigm
(Brombin and Salmaso 2009), in this paper we face the cell shape testing
problem by focusing the attention into two different aspects: the location-
aspect, based on the comparison of location-related statistics, and the scatter-
aspect, based on the comparison of variability-related statistics.

2. Methodology
Let us assume that we are facing a comparative neuroanatomy problem
involving a number of ≥ 2 populations that are defined according to the
levels of one factor of interest such as sex, age, specie, etc. In order to formalize
the comparison between the C populations, we assume a two-way
experimental cytomorphometric data representation model where we
represent as Y a dataset of size = Σ , where morphometric features

(belonging to a given morphometric domain such as size, regularity and
density) have been measured on the i-th cell, located in the l-th brain region
layer, and belonging to the j-th population. Let us assume that the p-variate
response variable the can be modelled as

where are i.i.d. possibly non-Gaussian error terms with null mean and
population/region-dependent scale coefficients and unknown
2

distribution P , is a population-invariant constant, coefficients represent

ε
the main population effects, and () refer to location effects due to the

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