Surface parameterization over regular domains

Surface parameterization has been widely studied and it has been playing a critical role in many geometric processing tasks in graphics, computer-aided design, visualization, vision, physical simulation and etc. Regular domains, such as polycubes, are favored due to their structural regularity and geometric simplicity. This thesis focuses on studying the surface parameterization over regular domains, i.e. polycubes, and develops effective computation algorithms. Firstly, the motivation for surface parameterization and polycube mapping is introduced. Secondly, we briefly review existing surface parameterization techniques, especially for extensively studied parameterization algorithms for topological disk surfaces and parameterizations over regular domains for closed surfaces. Then we propose a polycube parameterization algorithm for closed surfaces with general topology. We develop an efficient optimization framework to minimize the angle and area distortion of the mapping. Its applications on surface meshing, inter-shape morphing and volumetric polycube mapping are also discussed

Improved relationship between left and right ventricular electrical activation after cardiac resynchronization therapy in heart failure patients can be quantified by body surface potential mapping

OBJECTIVES: Few studies have evaluated cardiac electrical activation dynamics after cardiac resynchronization therapy. Although this procedure reduces morbidity and mortality in heart failure patients, many approaches attempting to identify the responders have shown that 30% of patients do not attain clinical or functional improvement. This study sought to quantify and characterize the effect of resynchronization therapy on the ventricular electrical activation of patients using body surface potential mapping, a noninvasive tool. METHODS: This retrospective study included 91 resynchronization patients with a mean age of 61 years, left ventricle ejection fraction of 28%, mean QRS duration of 182 ms, and functional class III/IV (78%/22%); the patients underwent 87-lead body surface mapping with the resynchronization device on and off. Thirty-six patients were excluded. Body surface isochronal maps produced 87 maximal/mean global ventricular activation times with three regions identified. The regional activation times for right and left ventricles and their inter-regional right-to-left ventricle gradients were calculated from these results and analyzed. The Mann-Whitney U-test and Kruskall-Wallis test were used for comparisons, with the level of significance set at p≤0.05. RESULTS: During intrinsic rhythms, regional ventricular activation times were significantly different (54.5 ms vs. 95.9 ms in the right and left ventricle regions, respectively). Regarding cardiac resynchronization, the maximal global value was significantly reduced (138 ms to 131 ms), and a downward variation of 19.4% in regional-left and an upward variation of 44.8% in regional-right ventricular activation times resulted in a significantly reduced inter-regional gradient (43.8 ms to 17 ms). CONCLUSIONS: Body surface potential mapping in resynchronization patients yielded electrical ventricular activation times for two cardiac regions with significantly decreased global and regional-left values but significantly increased regional-right values, thus showing an attenuated inter-regional gradient after the cardiac resynchronization therapy

Transport efficiency of metachronal waves in 3d cilia arrays immersed in a two-phase flow

The present work reports the formation and the characterization of antipleptic and symplectic metachronal waves in 3D cilia arrays immersed in a two-fluid environment, with a viscosity ratio of 20. A coupled lattice-Boltzmann-Immersed-Boundary solver is used. The periciliary layer is confined between the epithelial surface and the mucus. Its thickness is chosen such that the tips of the cilia can penetrate the mucus. A purely hydrodynamical feedback of the fluid is taken into account and a coupling parameter $\alpha$ is introduced allowing the tuning of both the direction of the wave propagation, and the strength of the fluid feedback. A comparative study of both antipleptic and symplectic waves, mapping a cilia inter-spacing ranging from 1.67 up to 5 cilia length, is performed by imposing the metachrony. Antipleptic waves are found to systematically outperform sympletic waves. They are shown to be more efficient for transporting and mixing the fluids, while spending less energy than symplectic, random, or synchronized motions

Surface-based versus volume-based fMRI group analysis: a case study

International audienceBeing able to detect reliably functional activity in a popula- tion of subjects is crucial in human brain mapping, both for the under- standing of cognitive functions in normal subjects and for the analysis of patient data. The usual approach proceeds by normalizing brain volumes to a common 3D template. However, a large part of the data acquired in fMRI aims at localizing cortical activity, and methods working on the cortical surface may provide better inter-subject registration than the standard procedures that process the data in 3D. Nevertheless, few as- sessments of the performance of surface-based (2D) versus volume-based (3D) procedures have been shown so far, mostly because inter-subject cortical surface maps are not easily obtained. In this paper we present a systematic comparison of 2D versus 3D group-level inference procedures, by using cluster-level and voxel-level statistics assessed by permutation, in random e ects (RFX) and mixed-e ects analyses (MFX). We nd that, using a voxel-level thresholding, and to some extent, cluster-level thresholding, the surface-based approach generally detects more, but smaller active regions than the corresponding volume-based approach for both RFX and MFX procedures, and that surface-based supra-threshold regions are more reproducible by bootstrap

Variance-Minimizing Transport Plans for Inter-surface Mapping

We introduce an efficient computational method for generating dense and low distortion maps between two arbitrary surfaces of same genus. Instead of relying on semantic correspondences or surface parameterization, we directly optimize a variance-minimizing transport plan between two input surfaces that defines an as-conformal-as-possible inter-surface map satisfying a user-prescribed bound on area distortion. The transport plan is computed via two alternating convex optimizations, and is shown to minimize a generalized Dirichlet energy of both the map and its inverse. Computational efficiency is achieved through a coarse-to-fine approach in diffusion geometry, with Sinkhorn iterations modified to enforce bounded area distortion. The resulting inter-surface mapping algorithm applies to arbitrary shapes robustly, with little to no user interaction

Retinotopic Maps, Spatial Tuning, and Locations of Human Visual Areas in Surface Coordinates Characterized with Multifocal and Blocked fMRI Designs

The localization of visual areas in the human cortex is typically based on mapping the retinotopic organization with functional magnetic resonance imaging (fMRI). The most common approach is to encode the response phase for a slowly moving visual stimulus and to present the result on an individual's reconstructed cortical surface. The main aims of this study were to develop complementary general linear model (GLM)-based retinotopic mapping methods and to characterize the inter-individual variability of the visual area positions on the cortical surface. We studied 15 subjects with two methods: a 24-region multifocal checkerboard stimulus and a blocked presentation of object stimuli at different visual field locations. The retinotopic maps were based on weighted averaging of the GLM parameter estimates for the stimulus regions. In addition to localizing visual areas, both methods could be used to localize multiple retinotopic regions-of-interest. The two methods yielded consistent retinotopic maps in the visual areas V1, V2, V3, hV4, and V3AB. In the higher-level areas IPS0, VO1, LO1, LO2, TO1, and TO2, retinotopy could only be mapped with the blocked stimulus presentation. The gradual widening of spatial tuning and an increase in the responses to stimuli in the ipsilateral visual field along the hierarchy of visual areas likely reflected the increase in the average receptive field size. Finally, after registration to Freesurfer's surface-based atlas of the human cerebral cortex, we calculated the mean and variability of the visual area positions in the spherical surface-based coordinate system and generated probability maps of the visual areas on the average cortical surface. The inter-individual variability in the area locations decreased when the midpoints were calculated along the spherical cortical surface compared with volumetric coordinates. These results can facilitate both analysis of individual functional anatomy and comparisons of visual cortex topology across studies