Lie Algebra Image Processing Applied to Intrinsic Optical Imaging

Optical imaging and the underlying image analysis has seen tremendous progress in recent years. Although it is now possible to perform multi-modal acquisition, the analysis frameworks for multi-modal data remain elusive. For example, the different scales and resolutions at which the images are taken require the use of mathematical techniques to deform, analyze and co-register images in a coherent framework. In parallel, J. Patera and his research group have, over the last few years, developed new Lie Algebra-based techniques to process images and perform continuous operations on them. In particular, it is possible, with these mathematical tools, to perform image interpolation, zooming through a continuous extension of the image. In order to do this, two main challenges must be resolved and will be addressed in this internship. First, the application of these transforms to specific images originating from optical imaging (i.e. having specific features) will be done to characterize the ability of the technique to describe the underlying physiological data. Second, a coherent modelization of light propagation in MRI segmented tissues will be developed with the functional space originating from Lie Algebra.

Faculty Supervisor:

Dr. Frédéric Lesage


Nicolas Brieu


Centre de Recherche de l’Institut de Gériatrie de Montréal




Information and communications technologies


Polytechnique Montréal



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