Programs M2 mathematics for data sciences MACS program of Sup'Galiée
Semester2
BlocProblems and techniques adapted to some data types
Teaching staffLecture and TA sessions : John Chaussard, Jacques Liandrat et Jiaping Wang
Credits 3 ECTS
Teaching hours 15h of lecture + 15h of TA
Validation schemeContinuous examination+final exam

Presentation

Images are rich and large data sets, scientifi methods for their analysis and for extraction of informations are very different to the one used for time signals. Image processing has developped a lot and occupies now a special role in data analysis. Among the numerous domains of which image processing forms a staple, one can mention medical imaging (MRI image analysis, CT-scans, etc.), computer vision and its numerous applications to artificial intelligence, microscopic imaging in biotechnologies, anaysis of shapes and textures in industrial control, etc. The aim of this series of lectures is to introduce to image processing, the main aim being to familiarize students with fundamental methods and techniques for image processing filtering, detection, restauration, modelisation, segmentation, etc.

Techincal points that will addressed are the following ones:

  • Image handling and processing, via spatial and frequencial filtering:
  • multidimensional discrete Fourier transform, low-pass and high-pass filtering, 
  • mathematical morphology applied to data,
  • techniques for image improvement, edge detection.
  • Image modelling : 
  • Random Gaussian fields methods : Gaussian modelling, simulation of Gaussian fields, image restauration, image unnoising, Wiener filtering.
  • Markovian fields, Gibbs laws and their applications, stochastic relaxations.
  • Bayesian approaches, methods of the a posteriori maximum.
  • Continuous (wavelettes) and discrete (subdivision schemes) multi-scale approximation.