The constitution of visual perceptual units in the functional architecture of V1

Scope of this paper is to consider a mean field neural model which takes into account the functional neurogeometry of the visual cortex modelled as a group of rotations and translations. The model generalizes well known results of Bressloff and Cowan which, in absence of input, accounts for hallucination patterns. The main result of our study consists in showing that in presence of a visual input, the eigenmodes of the linearized operator which become stable represent perceptual units present in the image. The result is strictly related to dimensionality reduction and clustering problems

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

Whither All the Scope and Generality of Bell's Theorem?

In a recent paper James Owen Weatherall has attempted a simple local-deterministic model for the EPR-Bohm correlation and speculated about why his model fails when my counterexample to Bell's theorem succeeds. Here I bring out the physical, mathematical, and conceptual reasons why his model fails. In particular, I demonstrate why no model based on a tensor representation of the rotation group SU(2) can reproduce the EPR-Bohm correlation. I demonstrate this by calculating the correlation explicitly between measurement results A = +1 or -1 and B = +1 or -1 in a local and deterministic model respecting the spinor representation of SU(2). I conclude by showing how Weatherall's reading of my model is misguided, and bring out a number of misconceptions and unwarranted assumptions in his imitation of my model as it relates to the Bell-CHSH inequalities

Modulation of cortical resting state functional connectivity during a visuospatial attention task in Parkinson's disease

Visual dysfunction is a recognized early symptom of Parkinson's disease (PD) that partly scales motor symptoms, yet its background is heterogeneous. With additional deficits in visuospatial attention, the two systems are hard to disentangle and it is not known whether impaired functional connectivity in the visual cortex is translative in nature or disrupted attentional modulation also contributes. In this study, we investigate functional connectivity modulation during a visuospatial attention task in patients with PD. In total, 15 PD and 16 age-matched healthy controls performed a visuospatial attention task while undergoing fMRI, in addition to a resting-state fMRI scan. Tensorial independent component analysis was used to investigate task-related network activity patterns. Independently, an atlas-based connectivity modulation analysis was performed using the task potency method. Spearman's rank correlation was calculated between task-related network expression, connectivity modulation, and clinical characteristics. Task-related networks including mostly visual, parietal, and prefrontal cortices were expressed to a significantly lesser degree in patients with PD (p < 0.027). Resting-state functional connectivity did not differ between the healthy and diseased cohorts. Connectivity between the precuneus and ventromedial prefrontal cortex was modulated to a higher degree in patients with PD (p < 0.004), while connections between the posterior parietal cortex and primary visual cortex, and also the superior frontal gyrus and opercular cortex were modulated to a lesser degree (p < 0.001 and p < 0.011). Task-related network expression and superior frontal gyrus-opercular cortex connectivity modulation were significantly associated with UPDRSIII motor scores and the Hoehn-Yahr stages (R = -0.72, p < 0.006 and R = -0.90, p < 0.001; R = -0.68, p < 0.01 and R = -0.71, p < 0.007). Task-related networks function differently in patients with PD in association with motor symptoms, whereas impaired modulation of visual and default-mode network connectivity was not correlated with motor function

Interactive volumetric segmentation for textile micro-tomography data using wavelets and nonlocal means

This work addresses segmentation of volumetric images of woven carbon fiber textiles from micro-tomography data. We propose a semi-supervised algorithm to classify carbon fibers that requires sparse input as opposed to completely labeled images. The main contributions are: (a) design of effective discriminative classifiers, for three-dimensional textile samples, trained on wavelet features for segmentation; (b) coupling of previous step with nonlocal means as simple, efficient alternative to the Potts model; and (c) demonstration of reuse of classifier to diverse samples containing similar content. We evaluate our work by curating test sets of voxels in the absence of a complete ground truth mask. The algorithm obtains an average 0.95 F1 score on test sets and average F1 score of 0.93 on new samples. We conclude with discussion of failure cases and propose future directions toward analysis of spatiotemporal high-resolution micro-tomography images

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

Purpose: The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts. Methods: QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages. Results: The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups. Conclusion: The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

Investigating microstructural variation in the human hippocampus using non-negative matrix factorization

In this work we use non-negative matrix factorization to identify patterns of microstructural variance in the human hippocampus. We utilize high-resolution structural and diffusion magnetic resonance imaging data from the Human Connectome Project to query hippocampus microstructure on a multivariate, voxelwise basis. Application of non-negative matrix factorization identifies spatial components (clusters of voxels sharing similar covariance patterns), as well as subject weightings (individual variance across hippocampus microstructure). By assessing the stability of spatial components as well as the accuracy of factorization, we identified 4 distinct microstructural components. Furthermore, we quantified the benefit of using multiple microstructural metrics by demonstrating that using three microstructural metrics (T1-weighted/T2-weighted signal, mean diffusivity and fractional anisotropy) produced more stable spatial components than when assessing metrics individually. Finally, we related individual subject weightings to demographic and behavioural measures using a partial least squares analysis. Through this approach we identified interpretable relationships between hippocampus microstructure and demographic and behavioural measures. Taken together, our work suggests non-negative matrix factorization as a spatially specific analytical approach for neuroimaging studies and advocates for the use of multiple metrics for data-driven component analyses