Sylvain Bouix

Hamilton-Jacobi Skeletons

The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front and is typically based on level set methods. However, there are more classical approaches rooted in Hamiltonian physics which have yet to be widely used by the computer vision community. In this paper we review the Hamiltonian formulation, which offers specific advantages when it comes to the detection of singularities or shocks. We specialize to the case of Blums grassfire flow and measure the average outward flux of the vector field that underlies the Hamiltonian system. This measure has very different limiting behaviors depending upon whether the region over which it is computed shrinks to a singular point or a non-singular one. Hence, it is an effective way to distinguish between these two cases. We combine the flux measurement with a homotopy preserving thinning process applied in a discrete lattice. This leads to a robust and accurate algorithm for computing skeletons in 2D as well as 3D, which has low computational complexity. We illustrate the approach with several computational examples.

The Hamilton-Jacobi skeleton

The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front, and is typically based or, level set methods. However there are more classical approaches rooted in Hamiltonian physics, which have received little consideration in computer vision. In this paper we first introduce a new algorithm for simulating the eikonal equation, which offers a number of computational and conceptual advantages over the earlier methods when it comes to shock tracking. Next, we introduce a very efficient algorithm for shock detection, where the key idea is to measure the net outward flux of a vector field per unit volume, and to detect locations where a conservation of energy principle is violated. We illustrate the approach with several numerical examples including skeletons of complex 2D and 3D shapes.

Neocortical gray matter volume in first-episode schizophrenia and first-episode affective psychosis : A cross-sectional and longitudinal MRI study

BACKGROUND Overall neocortical gray matter (NCGM) volume has not been studied in first-episode schizophrenia (FESZ) at first hospitalization or longitudinally to evaluate progression, nor has it been compared with first-episode affective psychosis (FEAFF). METHODS Expectation-maximization/atlas-based magnetic resonance imaging (MRI) tissue segmentation into gray matter, white matter (WM), or cerebrospinal fluid (CSF) at first hospitalization of 29 FESZ and 34 FEAFF, plus 36 matched healthy control subjects (HC), and, longitudinally approximately 1.5 years later, of 17 FESZ, 21 FEAFF, and 26 HC was done. Manual editing separated NCGM and its lobar parcellation, cerebral WM (CWM), lateral ventricles (LV), and sulcal CSF (SCSF). RESULTS At first hospitalization, FESZ and FEAFF showed smaller NCGM volumes and larger SCSF and LV than HC. Longitudinally, FESZ showed NCGM volume reduction (-1.7%), localized to frontal (-2.4%) and temporal (-2.6%) regions, and enlargement of SCSF (7.2%) and LV (10.4%). Poorer outcome was associated with these LV and NCGM changes. FEAFF showed longitudinal NCGM volume increases (3.6%) associated with lithium or valproate administration but without clinical correlations and regional localization. CONCLUSIONS Longitudinal NCGM volume reduction and CSF component enlargement in FESZ are compatible with post-onset progression. Longitudinal NCGM volume increase in FEAFF may reflect neurotrophic effects of mood stabilizers.

Excessive Extracellular Volume Reveals a Neurodegenerative Pattern in Schizophrenia Onset

Diffusion MRI has been successful in identifying the existence of white matter abnormalities in schizophrenia in vivo. However, the role of these abnormalities in the etiology of schizophrenia is not well understood. Accumulating evidence from imaging, histological, genetic, and immunochemical studies support the involvement of axonal degeneration and neuroinflammation—ubiquitous components of neurodegenerative disorders—as the underlying pathologies of these abnormalities. Nevertheless, the current imaging modalities cannot distinguish neuroinflammation from axonal degeneration, and therefore provide little specificity with respect to the pathophysiology progression and whether it is related to a neurodegenerative process. Free-water imaging is a new methodology that is sensitive to water molecules diffusing in the extracellular space. Excessive extracellular volume is a surrogate biomarker for neuroinflammation and can be separated out to reveal abnormalities such as axonal degeneration that affect diffusion characteristics in the tissue. We applied free-water imaging on diffusion MRI data acquired from schizophrenia-diagnosed human subjects with a first psychotic episode. We found a significant increase in the extracellular volume in both white and gray matter. In contrast, significant signs of axonal degeneration were limited to focal areas in the frontal lobe white matter. Our findings demonstrate that neuroinflammation is more prominent than axonal degeneration in the early stage of schizophrenia, revealing a pattern shared by many neurodegenerative disorders, in which prolonged inflammation leads to axonal degeneration. These findings promote anti-inflammatory treatment for early diagnosed schizophrenia patients.

Diffusion tensor tractography findings in schizophrenia across the adult lifespan

In healthy adult individuals, late life is a dynamic time of change with respect to the microstructural integrity of white matter tracts. Yet, elderly individuals are generally excluded from diffusion tensor imaging studies in schizophrenia. Therefore, we examined microstructural integrity of frontotemporal and interhemispheric white matter tracts in schizophrenia across the adult lifespan. Diffusion tensor imaging data from 25 younger schizophrenic patients (< or = 55 years), 25 younger controls, 25 older schizophrenic patients (> or = 56 years) and 25 older controls were analysed. Patients with schizophrenia in each group were individually matched to controls. Whole-brain tractography and clustering segmentation were employed to isolate white matter tracts. Groups were compared using repeated measures analysis of variance with 12 within-group measures of fractional anisotropy: (left and right) uncinate fasciculus, arcuate fasciculus, inferior longitudinal fasciculus, inferior occipito-frontal fasciculus, cingulum bundle, and genu and splenium of the corpus callosum. For each white matter tract, fractional anisotropy was then regressed against age in patients and controls, and correlation coefficients compared. The main effect of group (F(3,92) = 12.2, P < 0.001), and group by tract interactions (F(26,832) = 1.68, P = 0.018) were evident for fractional anisotropy values. Younger patients had significantly lower fractional anisotropy than younger controls (Bonferroni-corrected alpha = 0.0042) in the left uncinate fasciculus (t(48) = 3.7, P = 0.001) and right cingulum bundle (t(48) = 3.6, P = 0.001), with considerable effect size, but the older groups did not differ. Schizophrenic patients did not demonstrate accelerated age-related decline compared with healthy controls in any white matter tract. To our knowledge, this is the first study to examine the microstructural integrity of frontotemporal white matter tracts across the adult lifespan in schizophrenia. The left uncinate fasciculus and right cingulum bundle are disrupted in younger chronic patients with schizophrenia compared with matched controls, suggesting that these white matter tracts are related to frontotemporal disconnectivity. The absence of accelerated age-related decline, or differences between older community-dwelling patients and controls, suggests that these patients may possess resilience to white matter disruption.

Hippocampal shape analysis using medial surfaces

In magnetic resonance imaging (MRI) research, significant attention has been paid to the analysis of the hippocampus (HC) within the medial temporal lobe because of its importance in memory and learning, and its role in neurodegenerative diseases. Manual segmentation protocols have established a volume decline in the HC in conjunction with Alzheimers disease, epilepsy, post-traumatic stress disorder, and depression. Furthermore, recent studies have investigated age-related changes of HC volume which show an interaction with gender; in early adulthood, volume reduction of the HC is found in men but not in women. In this paper, we investigated gender differences in normal subjects in young adulthood by employing a shape analysis of the HC using medial surfaces. For each subject, the most prominent medial manifold of the HC was extracted and flattened. The flattened sheets were then registered using both a rigid and a non-rigid alignment technique, and the medial surface radius was expressed as a height function over them. This allowed for an investigation of the association between subject variables and the local width of the HC. With regard to the effects of age and gender, it could be shown that the previously observed gender differences were mostly due to volume loss in males in the lateral areas of the HC head and tail. We suggest that the analysis of HC shape using medial surfaces might thus serve as a complimentary technique to investigate group differences to the established segmentation protocols for volume quantification in MRI.

Longitudinal Loss of Gray Matter Volume in Patients with First- Episode Schizophrenia: DARTEL Automated Analysis and ROI Validation

Region of Interest (ROI) longitudinal studies have detected progressive gray matter (GM) volume reductions in patients with first-episode schizophrenia (FESZ). However, there are only a few longitudinal voxel-based morphometry (VBM) studies, and these have been limited in ability to detect relationships between volume loss and symptoms, perhaps because of methodologic issues. Nor have previous studies compared and validated VBM results with manual Region of Interest (ROI) analysis. In the present VBM study, high-dimensional warping and individualized baseline-rescan templates were used to evaluate longitudinal volume changes within subjects and compared with longitudinal manual ROI analysis on the same subjects. VBM evaluated thirty-three FESZ and thirty-six matched healthy control subjects (HC) at baseline (cross-sectionally) and longitudinally evaluated 21 FESZ and 23 HC after an average of 1.5 years from baseline scans. Correlation analyses detected the relationship between changes in regional GM volumes in FESZ and clinical symptoms derived from the Brief Psychiatric Rating Scale, as well as cognitive function as assessed by the Mini-Mental State Examination. At baseline, patients with FESZ had significantly smaller GM volume compared to HC in some regions including the left superior temporal gyrus (STG). On rescan after 1.5 years, patients showed significant GM volume reductions compared with HC in the left STG including Heschls gyrus, and in widespread brain neocortical regions of frontal, parietal, and limbic regions including the cingulate gyrus. FESZ showed an association of positive symptoms and volume loss in temporal (especially STG) and frontal regions, and negative symptoms and volume loss in STG and frontal regions. Worse cognitive function was linked to widespread volume reduction, in frontal, temporal and parietal regions. The validation VBM analyses showed results similar to our previous ROI findings for STG and cingulate gyrus. We conclude FESZ show widespread, progressive GM volume reductions in many brain regions. Importantly, these reductions are directly associated with a worse clinical course. Congruence with ROI analyses suggests the promise of this longitudinal VBM methodology.

A Hierarchical Algorithm for MR Brain Image Parcellation

We introduce an algorithm for segmenting brain magnetic resonance (MR) images into anatomical compartments such as the major tissue classes and neuro-anatomical structures of the gray matter. The algorithm is guided by prior information represented within a tree structure. The tree mirrors the hierarchy of anatomical structures and the subtrees correspond to limited segmentation problems. The solution to each problem is estimated via a conventional classifier. Our algorithm can be adapted to a wide range of segmentation problems by modifying the tree structure or replacing the classifier. We evaluate the performance of our new segmentation approach by revisiting a previously published statistical group comparison between first-episode schizophrenia patients, first-episode affective psychosis patients, and comparison subjects. The original study is based on 50 MR volumes in which an expert identified the brain tissue classes as well as the superior temporal gyrus, amygdala, and hippocampus. We generate analogous segmentations using our new method and repeat the statistical group comparison. The results of our analysis are similar to the original findings, except for one structure (the left superior temporal gyrus) in which a trend-level statistical significance (p = 0.07) was observed instead of statistical significance.

Divergence-Based Medial Surfaces

The medial surface of a volumetric object is of significant interest for shape analysis. However, its numerical computation can be subtle. Methods based on Voronoi techniques preserve the objects topology, but heuristic pruning measures are introduced to remove unwanted faces. Approaches based on Euclidean distance functions can localize medial surface points accurately, but often at the cost of altering the objects topology. In this paper we introduce a new algorithm for computing medial surfaces which addresses these concerns. The method is robust and accurate, has low computational complexity, and preserves topology. The key idea is to measure the net outward flux of a vector field per unit volume, and to detect locations where a conservation of energy principle is violated. This is done in conjunction with a thinning process applied in a cubic lattice. We illustrate the approach with examples of medial surfaces of synthetic objects and complex anatomical structures obtained from medical images.

Reduced Interhemispheric Connectivity in Schizophrenia- Tractography Based Segmentation of the Corpus Callosum

BACKGROUND A reduction in interhemispheric connectivity is thought to contribute to the etiology of schizophrenia. Diffusion Tensor Imaging (DTI) measures the diffusion of water and can be used to describe the integrity of the corpus callosum white matter tracts, thereby providing information concerning possible interhemispheric connectivity abnormalities. Previous DTI studies in schizophrenia are inconsistent in reporting decreased Fractional Anisotropy (FA), a measure of anisotropic diffusion, within different portions of the corpus callosum. Moreover, none of these studies has investigated corpus callosum systematically, using anatomical subdivisions. METHODS DTI and structural MRI scans were obtained from 32 chronic schizophrenic subjects and 42 controls. Corpus callosum cross sectional area and its probabilistic subdivisions were determined automatically from structural MRI scans using a model based deformable contour segmentation. These subdivisions employ a previously generated probabilistic subdivision atlas, based on fiber tractography and anatomical lobe subdivision. The structural scan was then co-registered with the DTI scan and the anatomical corpus callosum subdivisions were propagated to the associated FA map. RESULTS Results revealed decreased FA within parts of the corpus interconnecting frontal regions in schizophrenia compared with controls, but no significant changes for callosal fibers interconnecting parietal and temporo-occipital brain regions. In addition, integrity of the anterior corpus was statistically significantly correlated with negative as well as positive symptoms, while posterior measures correlated with positive symptoms only. CONCLUSIONS This study provides quantitative evidence for a reduction of interhemispheric brain connectivity in schizophrenia, involving corpus callosum, and further points to frontal connections as possibly disrupted in schizophrenia.