Annonce en lien avec l’Action/le Réseau : aucun
Laboratoire/Entreprise : Institut Camille Jordan
Durée : 3 ans
Contact : tugaut@math.cnrs.fr
Date limite de publication : 2017-04-15
Contexte :
The thesis will take place in the Saint-Etienne part of Camille Jordan Institute. The research will be undertaken in the context of an interdisciplinary project involving also Hubert Curien Laboratory from the University Jean Monnet of St Etienne.
The consortium has scientific expertise on probability and
statistics, information and image processing, and machine learning, providing a stimulating scientific environment for this
thesis.
Sujet :
Gaussian processes are non-linear models of continuous random processes which are widely used to describe numerical data as sounds, images, videos, etc. (see for e.g. [W08,Z16]).
A Gaussian process is defined mainly by its expectation function and its covariance function (the kernel).
The description of the kernel using parametric functions and the estimation of these parameters form the focus of many recent works [L05,D16].
In the context of image sequences (knowing that our study is intended to address other types of data), the main objective is no longer to describe a Gaussian process but a set of Gaussian processes that can possess instances (Different temporal or spatial supports), with the aim to analyse videos with dynamic textures (lights, waves, clouds, fields of wheat …) taken from different angles for example.
The main objective of the thesis is to provide a precise mathematical framework for these instanciated Gaussian processes in order to be able to estimate the different parameters (instances, mathematical expectations and kernels’ parameters).
First, the PhD student will be intended to make a state-of-the-art about the different kernels and their properties, mainly their stationarity in time and space in order to propose new kernels. The next step is to develop robust parameter estimation methods and to work on the automatic selection of the kernels. Then, the formalism of non-stationary and instanciated Gaussian processes will be developed, together with their numerical simulations. The last step concerns the mixture of instanciated Gaussian processes and their application to real data like videos.
Profil du candidat :
Application process : Your application should include the following documents:
– Letter of intent
– Grades and ranking during Master 1 and Master 2
– Scientific CV
– List of publications (if it exists of course)
– Names of Referees (at least 2)
Formation et compétences requises :
We are looking for a motivated student holding a Master degree (on the 1st of September 2015) in the field of applied mathematics (probability, data analysis, estimation and optimization, …) or “computer science” (or “computer vision”) with strong skills in applied mathematics. A good background in software development (algorithmic, Matlab/Octave/Scilab or Python, …) is expected. Knowledges in image processing and machine learning would also be appreciated.
Adresse d’emploi :
Faculté des Sciences et Techniques
23, rue du Docteur Paul Michelon
42023 Saint-Étienne
France