Coordinator: Alessandra Micheletti (Universita’ degli Studi di Milano)
Shape analysis deals with the geometrical information on objects that is
left after location, scale and rotation effects are removed. If scale
effects are not removed, then we are led to form (size and shape). In
applications, bodies rarely have exactly the same shape within measurement
error; hence randomness of shapes needs to be taken into account. Thanks to
the development of information technologies, the last decade has seen a
considerable growth of interest in the statistical theory of shape and its
application to many and diverse scientific areas. Often the diagnosis of a
pathology, or the description of a biological process mainly depend on the
shapes present in images of cells, organs, biological systems, etc., and
mathematical models which relate the main features of these shapes with the
correct outcome of the diagnosis, or with the main kinetic parameters of a
biological system are still not present. In materials science optimisation
for quality control require methods of statistical shape analysis. From the
mathematical point of view, shape analysis uses a variety of mathematical
tools from differential geometry, geometric measure theory, stochastic
geometry, etc. Quite recently, instruments from algebraic topology have
been introduced for shape description, giving rise to a new field of
research called Topological Data Analysis. As far as applications are
concerned, the members of the SIG emphasize here topics which are relevant
in medicine, biotechnology and material sciences. We deal with direct and
inverse problems. Among direct problems, spatio-temporal pattern formation
deals with the analysis of how patterns are created and developed in
biology, medicine and materials science. Modeling, numerical simulation and
analyses of the corresponding systems are tasks of paramount importance for
direct problems. Among inverse problems, we study various statistical
techniques of shape analysis to measure in a quantitative way the random
variability of objects; recent methods of image analysis include optical
imaging of objects in turbid media, which can be used as a non-invasive
technique for the detection of tumors in the body.
1. Workshops or minisymposia with presentations of current problems by
”Industry” and/or of current methods by ”Academia”.
2. Awareness seminars for SME’s with
– ”industry” providing data/ proposing test cases,
– academics running test cases with innovative methods.
3. Scientific collaboration and research projects among the members.
4. Collaboration in international multidisciplinary training and formation
of early-stage researchers.
Collaborations with scientists in other fields, laboratories, industry and
hospitals are essential and actively encouraged and sought by the SIG.