Left-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)

In this work we study the formulation of convection/diffusion equations on the 3D motion group SE(3) in terms of the irreducible representations of SO(3). Therefore, the left-invariant vector-fields on SE(3) are expressed as linear operators, that are differential forms in the translation coordinate and algebraic in the rotation. In the context of 3D image processing this approach avoids the explicit discretization of SO(3) or $S_2$, respectively. This is particular important for SO(3), where a direct discretization is infeasible due to the enormous memory consumption. We show two applications of the framework: one in the context of diffusion-weighted magnetic resonance imaging and one in the context of object detection

Connectivity of the Superficial Muscles of the Human Perineum: A Diffusion Tensor Imaging-Based Global Tractography Study.

Despite the importance of pelvic floor muscles, significant controversy still exists about the true structural details of these muscles. We provide an objective analysis of the architecture and orientation of the superficial muscles of the perineum using a novel approach. Magnetic Resonance Diffusion Tensor Images (MR-DTI) were acquired in 10 healthy asymptomatic nulliparous women, and 4 healthy males. Global tractography was then used to generate the architecture of the muscles. Micro-CT imaging of a male cadaver was performed for validation of the fiber tracking results. Results show that muscles fibers of the external anal sphincter, from the right and left side, cross midline in the region of the perineal body to continue as transverse perinea and bulbospongiosus muscles of the opposite side. The morphology of the external anal sphincter resembles that of the number '8' or a "purse string". The crossing of muscle fascicles in the perineal body was supported by micro-CT imaging in the male subject. The superficial muscles of the perineum, and external anal sphincter are frequently damaged during child birth related injuries to the pelvic floor; we propose the use of MR-DTI based global tractography as a non-invasive imaging technique to assess damage to these muscles

PatchMorph: A Stochastic Deep Learning Approach for Unsupervised 3D Brain Image Registration with Small Patches

We introduce "PatchMorph," an new stochastic deep learning algorithm tailored for unsupervised 3D brain image registration. Unlike other methods, our method uses compact patches of a constant small size to derive solutions that can combine global transformations with local deformations. This approach minimizes the memory footprint of the GPU during training, but also enables us to operate on numerous amounts of randomly overlapping small patches during inference to mitigate image and patch boundary problems. PatchMorph adeptly handles world coordinate transformations between two input images, accommodating variances in attributes such as spacing, array sizes, and orientations. The spatial resolution of patches transitions from coarse to fine, addressing both global and local attributes essential for aligning the images. Each patch offers a unique perspective, together converging towards a comprehensive solution. Experiments on human T1 MRI brain images and marmoset brain images from serial 2-photon tomography affirm PatchMorph's superior performance.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Histological and MRI brain atlas of the common shrew, Sorex araneus, with brain region-specific gene expression profiles

The common shrew, Sorex araneus, is a small mammal of growing interest in neuroscience research, as it exhibits dramatic and reversible seasonal changes in individual brain size and organization (a process known as Dehnel’s phenomenon). Despite decades of studies on this system, the mechanisms behind the structural changes during Dehnel’s phenomenon are not yet understood. To resolve these questions and foster research on this unique species, we present the first combined histological, magnetic resonance imaging (MRI), and transcriptomic atlas of the common shrew brain. Our integrated morphometric brain atlas provides easily obtainable and comparable anatomic structures, while transcriptomic mapping identified distinct expression profiles across most brain regions. These results suggest that high-resolution morphological and genetic research is pivotal for elucidating the mechanisms underlying Dehnel’s phenomenon while providing a communal resource for continued research on a model of natural mammalian regeneration. Morphometric and NCBI Sequencing Read Archive are available at https://doi.org/10.17617/3.HVW8ZNpublishe

Quantitative evaluation of 10 tractography algorithms on a realistic diffusion MR phantom.

International audienceAs it provides the only method for mapping white matter fibers in vivo, diffusion MRI tractography is gaining importance in clinical and neuroscience research. However, despite the increasing availability of different diffusion models and tractography algorithms, it remains unclear how to select the optimal fiber reconstruction method, given certain imaging parameters. Consequently, it is of utmost importance to have a quantitative comparison of these models and algorithms and a deeper understanding of the corresponding strengths and weaknesses. In this work, we use a common dataset with known ground truth and a reproducible methodology to quantitatively evaluate the performance of various diffusion models and tractography algorithms. To examine a wide range of methods, the dataset, but not the ground truth, was released to the public for evaluation in a contest, the "Fiber Cup". 10 fiber reconstruction methods were evaluated. The results provide evidence that: 1. For high SNR datasets, diffusion models such as (fiber) orientation distribution functions correctly model the underlying fiber distribution and can be used in conjunction with streamline tractography, and 2. For medium or low SNR datasets, a prior on the spatial smoothness of either the diffusion model or the fibers is recommended for correct modelling of the fiber distribution and proper tractography results. The phantom dataset, the ground truth fibers, the evaluation methodology and the results obtained so far will remain publicly available on: http://www.lnao.fr/spip.php?rubrique79 to serve as a comparison basis for existing or new tractography methods. New results can be submitted to [email protected] and updates will be published on the webpage