About this Topic - Mathematical Tools for Shape Analysis and Description - page 5

• A bridge to mathematical textbooks where additional information about theoretical details
can be found;

• A pointer to resources for 3D shape analysis, including websites, software, data repositories.

is topic was conceived as a synthetic guide to mathematics for shape analysis: it is neither
meant to be a comprehensive topic on every kind of mathematics useful for shape analysis, nor
an exhaustive review of the literature in the field. e methods selected from the literature serve
as examples, to show the usage context of the mathematics described and its usefulness in shape
analysis.
We do not cover important aspects of mathematics: for instance, approximation theory, al-
gebraic geometry, mathematical morphology are not covered by the topic. e selection of math-
ematical topics has been imposed by space limits, with no implication that what has not been
covered is unimportant: the choice has been guided by our feeling as practitioners, and we believe
the material collected in this topic is enough to enable readers to search and find elsewhere specific
topics which have been possibly left out. Also, this text does not cover, if not for some examples,
the very important problem of the discretization of the mathematical concepts to the domain
of 3D digital shapes. ere are very good and exhaustive topics, tutorials and teaching material
that fully cover this part of the discussion about mathematics and shape analysis. e Discrete
Exterior Calculus, DEC for short, is the right keyword to find reference material in this area (see
also [ 1 , 103 ]). Finally, we mention algorithms that implement the techniques described without
digging into the technical details. We believe that knowledge of the underlying mathematics is
extremely important to devise a correct implementation of shape analysis techniques. We hope
that, after going through the topic, the reader will have a better perspective on the mathematical
framework that lies behind an algorithm.

1.4 EXPECTED READERS

is topic is intended for an audience having an undergraduate mathematics background, for
instance:

• University students (graduate or postgraduate) in computer science, engineering, architec-
ture, medicine, bioinformatics, information technology and communication, mathematics,
physics;

• Researchers, professionals with a background in mathematics, in particular basic notions of
calculus, geometry, algebra and topology;

• Teachers and students of professional training courses;

• Researchers and academics interested in learning the mathematical fundamentals of 3D
shape analysis;