Sub-pixel image processing
Image processingModelling


Basics of Fourier analysis and differential calculus.

Objectif du cours

Explore ways (and applications) of linking continuous and discrete image models: How to translate a continuous image processing model into a discrete numerical algorithm? Conversely, how to extract geometric informations from a discrete array of pixels?

Presentation : here

Organisation des séances

Half of course sessions, half of exercise/computer practice sessions

Mode de validation

Project or exam.


  • L. Moisan, Modeling and Image Processing (available on the course web page)
  • L. Moisan, « Periodic plus smooth image decomposition », Journal of Mathematical Imaging and Vision, vol 39:2, pp. 161-179, 2011 (available on the course web page)



Thèmes abordés

  • The image formation process: geometry, diffraction, sampling
  • FFT- and Spline-based interpolations,  lossless geometric transforms
  • Image reduction and the aliasing/ringing/blur trade-off
  • Implementation of differential operators, image iterative filtering
  • Sub-pixel image geometry
  • Phase spectrum and applications: sharpness metrics, texture synthesis
Les intervenants


(Université Paris Cité)

voir les autres cours du 1er semestre