Internship, 2019: Properties of the Hough Transform and applications to imaging issues in archaeology

TOMAT Internship Proposal, Applied Mathematics, for spring 2019.

Locations: INRIA Sophia Antipolis Mediterranee / CEPAM, MSHS, Nice.
Expected duration: 5-6 months.

Advisors: Laure Blanc-Feraud (CNRS, I3S), Vanna Lisa Coli (CEPAM), Juliette Leblond

Context of the intership
Pottery studies are known to be pivotal within the archaeological eld thanks to their
contributions to the understanding of cultural traditions, social interactions and peo-
pling dynamics. The reconstruction of pottery manufacturing was traditionally based
on macroscopic examination until the implementation of new 3D methods from CT
scan or synchrotron data. This enables to solve challenging questions on ancient
materials characterization at di erent scales, in terms of microstructure, i.e. fabric,
porosity and inclusions organization which inform on the manufacturing processes.
Our project provides a high level of expertise in Archaeology and Applied Mathematics
already experienced (CIMO ANR, TOMAT IDEX), supporting a new transdisciplinary
approach of ancient materials [1]. This project allows cutting edge developments both
in archaeological, physical, and mathematical sciences for modelling and detecting low
level signals.
The modelling of the material’s microstructure needs critical improvements thanks
to mathematical and physical developments, i.e. imaging issues, analysis of available
heterogeneous noisy data, segmentation, 2D and 3D{shape recognition, algorithms to
detect features induced by the technical gestures.

Goal of the intership
We plan to use the Hough transform, a discrete version of the Radon transform [2] in
order to detect line segments and arc of spirals in 2D images (as a rst step), which
characterize the manufacturing process.
The aim of this internship is the study and the extension of the properties of the Hough
transform. Indeed, the Hough transform is already eciently used/employed in aligne-
ment detection between points, although its behavior with respect to perturbations
(as non exact alignment, patches rather than points) requires deeper theoretical and
numerical investigation. Thus, robustness properties will be considered while develop-
ing new algorithms and software. Numerical testing and validation will be performed
on both synthetic and real images/data. The candidate will have access to computed
tomography datasets.

Candidate pro file
Second year of Master degree or Engineers School (PFE).
Strong background in applied mathematics.
Good knowledge of image processing, algorithms and numerical analysis.
Involvement in numerical simulation (MATLAB, C++, Python, …) and in applica-
A general interest and knowledge in Social Sciences is welcome.

Bibliographical references
[1] Louise Gomart, Allon Weiner, Marzia Gabriele, Gilles Durrenmath, Sabine Sorin,
Lucia Angeli, Marta Colombo, Cristina Fabbri, Roberto Maggi, Chiara Panelli, Didier
F. Pisani, Giovanna Radi, Carlo Tozzi, Didier Binder. Spiralled patchwork in pottery
manufacture and the introduction of farming to Southern Europe. Antiquity 91 360
(2017): 1501{1514, doi:10.15184/aqy.2017.187.
[2] M. van Ginkel, C.L. Luengo Hendriks and L.J. van Vliet. A short introduction to the
Radon and Hough transforms and how they relate to each other. Number QI-2004-01
in the Quantitative Imaging Group Technical Report Series.

About Juliette LEBLOND

Little biblio

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