Hodge decomposition of wall shear stress vector fields characterizing biological flows.

A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free) and three harmonic fields induced from the boundary, which are called the centre, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the nature of the five components. It was shown that the decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 control patients was done. The study shows a significant difference between the CoA patients before and after the treatment, and the healthy controls. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.

Robust and High Fidelity Mesh Denoising.

This paper presents a simple and effective two-stage mesh denoising algorithm, where in the first stage, face normal filtering is done by using bilateral normal filtering in a robust statistics framework. Tukey's bi-weight function is used as similarity function in the bilateral weighting, which is a robust estimator and stops the diffusion at sharp edges to retain features and removes noise from flat regions effectively. In the second stage, an edge-weighted Laplace operator is introduced to compute a differential coordinate. This differential coordinate helps the algorithm to produce a high-quality mesh without any face normal flips and makes the method robust against high-intensity noise.

Optic nerve head three-dimensional shape analysis.

We present a method for optic nerve head (ONH) 3-D shape analysis from retinal optical coherence tomography (OCT). The possibility to noninvasively acquire in vivo high-resolution 3-D volumes of the ONH using spectral domain OCT drives the need to develop tools that quantify the shape of this structure and extract information for clinical applications. The presented method automatically generates a 3-D ONH model and then allows the computation of several 3-D parameters describing the ONH. The method starts with a high-resolution OCT volume scan as input. From this scan, the model-defining inner limiting membrane (ILM) as inner surface and the retinal pigment epithelium as outer surface are segmented, and the Bruch's membrane opening (BMO) as the model origin is detected. Based on the generated ONH model by triangulated 3-D surface reconstruction, different parameters (areas, volumes, annular surface ring, minimum distances) of different ONH regions can then be computed. Additionally, the bending energy (roughness) in the BMO region on the ILM surface and 3-D BMO-MRW surface area are computed. We show that our method is reliable and robust across a large variety of ONH topologies (specific to this structure) and present a first clinical application.

Mesh Denoising Based on Normal Voting Tensor and Binary Optimization.

This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.

CuBe: parametric modeling of 3D foveal shape using cubic Bézier.

Optical coherence tomography (OCT) allows three-dimensional (3D) imaging of the retina, and is commonly used for assessing pathological changes of fovea and macula in many diseases. Many neuroinflammatory conditions are known to cause modifications to the fovea shape. In this paper, we propose a method for parametric modeling of the foveal shape. Our method exploits invariant features of the macula from OCT data and applies a cubic Bézier polynomial along with a least square optimization to produce a best fit parametric model of the fovea. Additionally, we provide several parameters of the foveal shape based on the proposed 3D parametric modeling. Our quantitative and visual results show that the proposed model is not only able to reconstruct important features from the foveal shape, but also produces less error compared to the state-of-the-art methods. Finally, we apply the model in a comparison of healthy control eyes and eyes from patients with neuroinflammatory central nervous system disorders and optic neuritis, and show that several derived model parameters show significant differences between the two groups.

Optic nerve head quantification in idiopathic intracranial hypertension by spectral domain OCT.

OBJECTIVE: To evaluate 3D spectral domain optical coherence tomography (SDOCT) volume scans as a tool for quantification of optic nerve head (ONH) volume as a potential marker for treatment effectiveness and disease progression in idiopathic intracranial hypertension (IIH). DESIGN AND PATIENTS: Cross-sectional pilot trial comparing 19 IIH patients and controls matched for gender, age and body mass index. Each participant underwent SDOCT. A custom segmentation algorithm was developed to quantify ONH volume (ONHV) and height (ONHH) in 3D volume scans. RESULTS: Whereas peripapillary retinal nerve fiber layer thickness did not show differences between controls and IIH patients, the newly developed 3D parameters ONHV and ONHH were able to discriminate between controls, treated and untreated patients. Both ONHV and ONHH measures were related to levels of intracranial pressure (ICP). CONCLUSION: Our findings suggest 3D ONH measures as assessed by SDOCT as potential diagnostic and progression markers in IIH and other disorders with increased ICP. SDOCT may promise a fast and easy diagnostic alternative to repeated lumbar punctures and could therefore ease monitoring of treatment or disease progression.

Hexagonal global parameterization of arbitrary surfaces.

We introduce hexagonal global parameterization, a new type of surface parameterization in which parameter lines respect sixfold rotational symmetries (6-RoSy). Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for triangular remeshing. Our framework to construct a hexagonal parameterization, referred to as HEXCOVER, extends the QUADCOVER algorithm and formulates necessary conditions for hexagonal parameterization. We also provide an algorithm to automatically generate a 6-RoSy field that respects directional and singularity features in the surface. We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal remeshing.

Domain coloring of complex functions: an implementation-oriented introduction.

This article gives a short overview of domain coloring for complex functions that have four-dimensional function graphs and therefore can't be visualized traditionally. The authors discuss several color schemes, focus on various aspects of complex functions, and provide Java-like pseudocode examples explaining the crucial ideas of the coloring algorithms to allow for easy reproduction.