Topo-Geometric Filtration Scheme for Geometric Active Contours and Level Sets: Application to Cerebrovascular Segmentation

One of the main problems of the existing methods for the segmentation of cerebral vasculature is the appearance in the segmentation result of wrong topological artefacts such as the kissing vessels. In this paper, a new approach for the detection and correction of such errors is presented. The proposed technique combines robust topological information given by Persistent Homology with complementary geometrical information of the vascular tree. The method was evaluated on 20 images depicting cerebral arteries. Detection and correction success rates were 81.80% and 68.77%, respectively

Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Our software---CHUNKYEuler---is available as open source on Bitbucket. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams

Cortical thickness, surface area and volume measures in Parkinson's disease, multiple system atrophy and progressive supranuclear palsy

OBJECTIVE Parkinson's disease (PD), Multiple System Atrophy (MSA) and Progressive Supranuclear Palsy (PSP) are neurodegenerative diseases that can be difficult to distinguish clinically. The objective of the current study was to use surface-based analysis techniques to assess cortical thickness, surface area and grey matter volume to identify unique morphological patterns of cortical atrophy in PD, MSA and PSP and to relate these patterns of change to disease duration and clinical features. METHODS High resolution 3D T1-weighted MRI volumes were acquired from 14 PD patients, 18 MSA, 14 PSP and 19 healthy control participants. Cortical thickness, surface area and volume analyses were carried out using the automated surface-based analysis package FreeSurfer (version 5.1.0). Measures of disease severity and duration were assessed for correlation with cortical morphometric changes in each clinical group. RESULTS Results show that in PSP, widespread cortical thinning and volume loss occurs within the frontal lobe, particularly the superior frontal gyrus. In addition, PSP patients also displayed increased surface area in the pericalcarine. In comparison, PD and MSA did not display significant changes in cortical morphology. CONCLUSION These results demonstrate that patients with clinically established PSP exhibit distinct patterns of cortical atrophy, particularly affecting the frontal lobe. These results could be used in the future to develop a useful clinical application of MRI to distinguish PSP patients from PD and MSA patients

Digitally Continuous Multivalued Functions, Morphological Operations and Thinning Algorithms

In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81–92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In this work we develop properties of this family of continuous functions, now concentrating on morphological operations and thinning algorithms. We show that our notion of continuity provides a suitable framework for the basic operations in mathematical morphology: erosion, dilation, closing, and opening. On the other hand, concerning thinning algorithms, we give conditions under which the existence of a retraction F:X⟶X∖D guarantees that D is deletable. The converse is not true, in general, although it is in certain particular important cases which are at the basis of many thinning algorithms

Incidence Simplicial Matrices Formalized in Coq/SSReflect

International audienceSimplicial complexes are at the heart of Computational Algebraic Topology, since they give a concrete, combinatorial description of otherwise rather abstract objects which makes many important topological computations possible. The whole theory has many applications such as coding theory, robotics or digital image analysis. In this paper we present a formalization in the COQ theorem prover of simplicial complexes and their incidence matrices as well as the main theorem that gives meaning to the definition of homology groups and is a first step towards their computation

Does congenital deafness affect the structural and functional architecture of primary visual cortex?

Deafness results in greater reliance on the remaining senses. It is unknown whether the cortical architecture of the intact senses is optimized to compensate for lost input. Here we performed widefield population receptive field (pRF) mapping of primary visual cortex (V1) with functional magnetic resonance imaging (fMRI) in hearing and congenitally deaf participants, all of whom had learnt sign language after the age of 10 years. We found larger pRFs encoding the peripheral visual field of deaf compared to hearing participants. This was likely driven by larger facilitatory center zones of the pRF profile concentrated in the near and far periphery in the deaf group. pRF density was comparable between groups, indicating pRFs overlapped more in the deaf group. This could suggest that a coarse coding strategy underlies enhanced peripheral visual skills in deaf people. Cortical thickness was also decreased in V1 in the deaf group. These findings suggest deafness causes structural and functional plasticity at the earliest stages of visual cortex

Brain structural concomitants of resting state heart rate variability in the young and old: evidence from two independent samples

Previous research has shown associations between brain structure and resting state high-frequency heart rate variability (HF-HRV). Age affects both brain structure and HF-HRV. Therefore we sought to examine the relationship between brain structure and HF-HRV as a function of age. Data from two independent studies were used for the present analysis. Study 1 included 19 older adults (10 male, age range 62-78 years) and 19 younger adults (12 male, age range 19-37). Study 2 included 23 older adults (13 males; age range 55-75) and 27 younger adults (19 males; age range 18-34). The rootmean- square of successive R-R-interval differences (RMSSD) from ECG recordings was used as timedomain measure of HF-HRV. MRI scans were performed on a 3.0-T Siemens Magnetom Trio scanner. Cortical reconstruction and volumetric segmentation were performed with the Freesurfer image analysis suite, including 12 regions as regions-of-interests (ROI). Zero-order and partial correlations were used to assess the correlation of RMSSD with cortical thickness in selected ROIs. Lateral orbitofrontal cortex (OFC) cortical thickness was significantly associated with RMSSD. Further, both studies, in line with previous research, showed correlations between RMSSD and anterior cingulate cortex (ACC) cortical thickness. Meta-analysis on adjusted correlation coefficients from individual studies confirmed an association of RMSSD with the left rostral ACC and the left lateral OFC. Future longitudinal studies are necessary to trace individual trajectories in the association of HRV and brain structure across aging

Surface-Based Analyses of Anatomical Properties of the Visual Cortex in Macular Degeneration

INTRODUCTION: Macular degeneration (MD) can cause a central visual field defect. In a previous study, we found volumetric reductions along the entire visual pathways of MD patients, possibly indicating degeneration of inactive neuronal tissue. This may have important implications. In particular, new therapeutic strategies to restore retinal function rely on intact visual pathways and cortex to reestablish visual function. Here we reanalyze the data of our previous study using surface-based morphometry (SBM) rather than voxel-based morphometry (VBM). This can help determine the robustness of the findings and will lead to a better understanding of the nature of neuroanatomical changes associated with MD. METHODS: The metrics of interest were acquired by performing SBM analysis on T1-weighted MRI data acquired from 113 subjects: patients with juvenile MD (JMD; n = 34), patients with age-related MD (AMD; n = 24) and healthy age-matched controls (HC; n = 55). RESULTS: Relative to age-matched controls, JMD patients showed a thinner cortex, a smaller cortical surface area and a lower grey matter volume in V1 and V2, while AMD patients showed thinning of the cortex in V2. Neither patient group showed a significant difference in mean curvature of the visual cortex. DISCUSSION: The thinner cortex, smaller surface area and lower grey matter volume in the visual cortex of JMD patients are consistent with our previous results showing a volumetric reduction in their visual cortex. Finding comparable results using two rather different analysis techniques suggests the presence of marked cortical degeneration in the JMD patients. In the AMD patients, we found a thinner cortex in V2 but not in V1. In contrast to our previous VBM analysis, SBM revealed no volumetric reductions of the visual cortex. This suggests that the cortical changes in AMD patients are relatively subtle, as they apparently can be missed by one of the methods

The Human Connectome Project's neuroimaging approach

Noninvasive human neuroimaging has yielded many discoveries about the brain. Numerous methodological advances have also occurred, though inertia has slowed their adoption. This paper presents an integrated approach to data acquisition, analysis and sharing that builds upon recent advances, particularly from the Human Connectome Project (HCP). The 'HCP-style' paradigm has seven core tenets: (i) collect multimodal imaging data from many subjects; (ii) acquire data at high spatial and temporal resolution; (iii) preprocess data to minimize distortions, blurring and temporal artifacts; (iv) represent data using the natural geometry of cortical and subcortical structures; (v) accurately align corresponding brain areas across subjects and studies; (vi) analyze data using neurobiologically accurate brain parcellations; and (vii) share published data via user-friendly databases. We illustrate the HCP-style paradigm using existing HCP data sets and provide guidance for future research. Widespread adoption of this paradigm should accelerate progress in understanding the brain in health and disease