Tractogram Atlasing

I studied several questions revolving around tractogram atlasing during the internship I made at the IMAGES team. I worked there under the supervision of Pietro Gori, Pierre Rousillon and Jean Feydy.

We proposed to use ideas from Optimal Transport theory to enhance the robustness of tractogram segmentation through atlasing transfer.

Limits of Standard Methods

Numerous classes of methods exist to perform spatial registration of medical data. They range from very simple linear transformations suited to small deformations to more complex non linear settings such as the Large Deformation Diffeomorphic Metric Mapping able to model more involved registrations.

Example of small-deformation based registration of a hand
The upper-left hand is registrated onto the bottom-left hand using a small-deformation based method. The different colmuns showcase the effect of an hyperparameter of the method (from low values to high): here the size of the kernel upon which the vector-field of landmarks momentum is convoluted.

Those methods are robust and widely used for instance for MRI image (T1, T2, ...) registration. They often enforce a high regularity of the resulting deformation field. This reflects anatomical priors underlying the observed image. Indeed, such deformations should not introduce wholes or anatomically incorrect effects in the images. While this increases the robustness of the registration, those assumptions might not be suited when non homeomorphic changes appear in images (such as tumors) and quickly reaches their limits when applied on geometric data such as anatomical fibers.

Example of a LDDMM registration of curves without topology break
Two example of curve registration where no topology rupture are needed to correctly match the curves. Here I used the LDDMM framework with a varifold metric.
Example of a LDDMM registration of curves with a topology break
Conservation of topology during registration. The left problem is easy, since no topology rupture is needed to match the curves. The right problem is harder because the ideal registration would involve to un-cross the curves, which is not allowed in the LDDMM framework used here, hence the weird result.


Appendix: overview of all anatomical bundles considered

You can click on a bundle to observe the fibers composing it (segmented on a Human Connectome Project tractogram).

Corpus Callosum

Forceps Major

Forceps Minor


Right IFOF

Left Cingulum1

Right Cingulum1

Left Cingulum2

Right Cingulum2

Left Cingulum3

Right Cingulum3


Right SFOF

Left Uncinate

Right Uncinate

Left Arcuate

Right Arcuate

Left cortico-spinal

Right cortico-spinal

Left anterior thalamic

Right anterior thalamic

Left inferior thalamic

Right inferior thalamic

Left superior thalamic

Right superior thalamic

Left posterior thalamic

Right posterior thalamic

Left VOF

Right VOF

Left AntVOF

Right AntVOF

Left VisionU

Right VisionU

Right OccipitalU

Left Thalamico-spinal

Right Thalamico-spinal

Left pArc

Right pArc

Left TPC

Right TPC


Right MdLF-SPL

Left MdLF-Ang

Right MdLF-Ang

Left SLF1

Right SLF1

Left SLF2

Right SLF2

Left SLF3

Right SLF3

Left ILF

Right ILF

Left Aslant

Right Aslant

Right Lenti2ceb

Left Lenti2ceb

Right Red2Ceb1

Left Red2Ceb1

Right Red2Ceb2

Left Red2Ceb2

Right Thal2ceb

Left Thal2ceb

Right ContraCorticoPontine

Left ContraCorticoPontine

Right ContraFrontoPontine

Left ContraFrontoPontine

Right IpsiCorticoPontine

Left IpsiCorticoPontine

Right IpsiFrontoPontine

Left IpsiFrontoPontine

Left Meyers Loop

Right Meyers Loop

Left Baums Loop

Right Baums Loop

Left Optic Unclassified

Right Optic Unclassified

Left Optic Accesory

Right Optic Accesory