Volumetric Domain Research Articles

Derivatives of isogeometric functions on n-dimensional rational patches in [formula omitted

We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in Rd, an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represented by a NURBS parametrization of its graph. We take advantage of the projective representation of the NURBS patch as a B-spline patch in homogeneous coordinates.We derive a closed form representation of the graph of a partial derivative of an isogeometric function. The derivative can be interpreted as an isogeometric function of higher degree and lower smoothness on the same piecewise rational geometry mapping, hence the space of isogeometric functions is closed under differentiation. We distinguish the two cases n=d and n<d, with a focus on n=d−1 in the latter one.As a first application of the presented formula we derive conditions which guarantee C1 and C2 smoothness for isogeometric functions on several singularly parametrized planar and volumetric domains as well as on embedded surfaces. It is interesting to note that the presented conditions depend not only on the general structure of the patch, but on the exact representation of the interior of the given geometry mapping.

Multi-atlas segmentation with particle-based group-wise image registration.

We propose a novel multi-atlas segmentation method that employs a group-wise image registration method for the brain segmentation on rodent magnetic resonance (MR) images. The core element of the proposed segmentation is the use of a particle-guided image registration method that extends the concept of particle correspondence into the volumetric image domain. The registration method performs a group-wise image registration that simultaneously registers a set of images toward the space defined by the average of particles. The particle-guided image registration method is robust with low signal-to-noise ratio images as well as differing sizes and shapes observed in the developing rodent brain. Also, the use of an implicit common reference frame can prevent potential bias induced by the use of a single template in the segmentation process. We show that the use of a particle guided-image registration method can be naturally extended to a novel multi-atlas segmentation method and improves the registration method to explicitly use the provided template labels as an additional constraint. In the experiment, we show that our segmentation algorithm provides more accuracy with multi-atlas label fusion and stability against pair-wise image registration. The comparison with previous group-wise registration method is provided as well.

Lattice cleaving: a multimaterial tetrahedral meshing algorithm with guarantees.

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach.

GRACE: A Visual Comparison Framework for Integrated Spatial and Non-Spatial Geriatric Data

We present the design of a novel framework for the visual integration, comparison, and exploration of correlations in spatial and non-spatial geriatric research data. These data are in general high-dimensional and span both the spatial, volumetric domain--through magnetic resonance imaging volumes--and the non-spatial domain, through variables such as age, gender, or walking speed. The visual analysis framework blends medical imaging, mathematical analysis and interactive visualization techniques, and includes the adaptation of Sparse Partial Least Squares and iterated Tikhonov Regularization algorithms to quantify potential neurologymobility connections. A linked-view design geared specifically at interactive visual comparison integrates spatial and abstract visual representations to enable the users to effectively generate and refine hypotheses in a large, multidimensional, and fragmented space. In addition to the domain analysis and design description, we demonstrate the usefulness of this approach on two case studies. Last, we report the lessons learned through the iterative design and evaluation of our approach, in particular those relevant to the design of comparative visualization of spatial and non-spatial data.

Domain construction for volumetric cross-parameterization

We present an algorithm in this paper for constructing volumetric domains with consistent topology to parameterize three-manifold solid models having homeomorphic topology. The volumetric parameterizations generated by our approach share the same set of base domains and are constrained by the corresponding anchor points. Our approach allows users to control interior mappings by specifying interior anchor points, and the anchor points are interpolated exactly. With the help of a novel construction algorithm developed in this work, the volumetric cross-parameterization computed by our method demonstrates its functionality in several examples.

Continuous Representation of Projected Attribute Spaces of Multifields over Any Spatial Sampling

For the visual analysis of multidimensional data, dimension reduction methods are commonly used to project to a lower-dimensional visual space. In the context of multifields, i.e., volume data with a multidimensional attribute space, the spatial arrangement of the samples in the volumetric domain can be exploited to generate a Continuous Representation of the Projected Attribute Space (CoRPAS). Here, the sample locations in the volumetric domain may be arranged in a structured or unstructured way and may or may not be connected by a grid or a mesh. We propose an approach to generate CoRPAS for any sample arrangement using an isotropic density function. An interactive visual exploration system with three coordinated views of volume visualization, CoRPAS, and an interaction widget based on star coordinates is presented. The star-coordinates widget provides an intuitive means for the user to change the projection matrix. The coordinated views allow for feature selection in form of brushing and linking. The approach is applied to both synthetic data and data resulting from numerical simulations of physical phenomena. In particular, simulations based on Smoothed Particle Hydrodynamics are addressed, where the simulation kernel can be used to produce a CoRPAS that is consistent with the simulation. We also show how a logarithmic scaling of attribute values in CoRPAS is supported, which is of high practical relevance.

A Three-Dimensional Adaptive Mesh Generation Approach Using Geometric Modeling With Multi-Regions and Parametric Surfaces

This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.

Volumetric Optical Frequency Domain Imaging of Pulmonary Pathology With Precise Correlation to Histopathology

Lung cancer is the leading cause of cancer-related mortality. Radiology and bronchoscopy techniques do not have the necessary resolution to evaluate lung lesions on the microscopic scale, which is critical for diagnosis. Bronchial biopsy specimens can be limited by sampling error and small size. Optical frequency domain imaging (OFDI) provides volumetric views of tissue microstructure at near-histologic resolution and may be useful for evaluating pulmonary lesions to increase diagnostic accuracy. Bronchoscopic OFDI has been evaluated in vivo, but a lack of correlated histopathology has limited the ability to develop accurate image interpretation criteria. We performed OFDI through two approaches (airway-centered and parenchymal imaging) in 22 ex vivo lung specimens, using tissue dye to precisely correlate imaging and histology. OFDI of normal airway allowed visualization of epithelium, lamina propria, cartilage, and alveolar attachments. Carcinomas exhibited architectural disarray, loss of normal airway and alveolar structure, and rapid light attenuation. Squamous cell carcinomas showed nested architecture. Atypical glandular formation was appreciated in adenocarcinomas, and uniform trabecular gland formation was seen in salivary gland carcinomas. Mucinous adenocarcinomas showed alveolar wall thickening with intraalveolar mucin. Interstitial fibrosis was visualized as signal-dense tissue, with an interstitial distribution in mild interstitial fibrotic disease and a diffuse subpleural pattern with cystic space formation in usual interstitial pneumonitis. To our knowledge, this study is the first demonstration of volumetric OFDI with precise correlation to histopathology in lung pathology. We anticipate that OFDI may play a role in assessing airway and parenchymal pathology, providing fresh insights into the volumetric features of pulmonary disease.

Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality.

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

A Pilot Study of Morphometric Analysis of Choroidal Vasculature In Vivo, Using En Face Optical Coherence Tomography

PurposeTo study the ability of volumetric spectral domain optical coherence tomography (SD-OCT) to perform quantitative measurement of the choroidal vasculature in vivo.MethodsChoroidal vascular density and vessel size were quantified using en face choroidal scans from various depths below the retinal pigment epithelium (RPE) in 58 eyes of 58 patients with either epiretinal membranes (ERM), early age-related macular degeneration (AMD), or reticular pseudo-drusen (RPD). For each patient, we used the macular volume scan (6×6 mm cube) for vessel quantification, while high-definition (HD) cross-section raster scans were used to qualitatively assess vascularity of the choroidal sub-layers, and measure choroidal thickness.ResultsOf the 58 patients, more were female (66% versus 34% male), of whom 14 (24%) had ERM, 11 (19%) early AMD, and 33 (57%) RPD. Compared to intact choriocapillaris in all ERM (100%), none of the RPD and only 5/11 (45%) early AMD eyes had visible choriocapillaris on either cross section or C-scans (p-value<0.001). When comparing select regions from the most superficial C-scans, early AMD group had lowest vascular density and RPD had highest (p-value 0.04). Qualitative evaluation of C-scans from all three groups revealed a more granular appearance of the choriocapillaris in ERM versus increased stroma and larger vessels in the RPD eyes.ConclusionsSD-OCT can be used to qualitatively and quantitatively assess choroidal vascularity in vivo. Our findings correlate to previously reported histopathologic studies. Lack of choriocapillaris on HD cross-sections or C-scans in all RPD and about half of early AMD eyes suggests earlier choroidal involvement in AMD and specifically, RPD.

Multi-scale local features based on anisotropic heat diffusion and global eigen-structure

Multi-scale local feature detection enables downstream registration and recognition tasks in medical image analysis. This paper articulates a novel robust method for multi-scale local feature extraction on volumetric data. The central idea is the elegant unification of local/global eigen-structures within the powerful framework of anisotropic heat diffusion. First, the local vector field is constructed by way of Hessian matrix and its eigenvectors/eigenvalues. Second, anisotropic heat kernels are computed using the vector field’s global graph Laplacian. Robust local features are manifested as extrema across multiple time scales, serving as volumetric heat kernel signature. To tackle the computational challenge for massive volumetric data, we propose a multiresolution strategy for hierarchical feature extraction based on our feature-preserving down-sampling approach. As a result, heat kernels and local feature identification can be approximated at a coarser level first, and then are pinpointed in a localized region at a finer resolution. Another novelty of this work lies at the initial heat design directly using local eigenvalue for anisotropic heat diffusion across the volumetric domain. We conduct experiments on various medical datasets, and draw comparisons with 3D SIFT method. The diffusion property of our local features, which can be interpreted as random walks in statistics, makes our method robust to noise, and gives rise to intrinsic multi-scale characteristics.

Corneal biometry from volumetric SDOCT and comparison with existing clinical modalities

We present a comparison of corneal biometric values from dense volumetric spectral domain optical coherence tomography (SDOCT) scans to reference values in both phantoms and clinical subjects. We also present a new optically based “keratometric equivalent power” formula for SDOCT that eliminates previously described discrepancies between corneal power form SDOCT and existing clinical modalities. Phantom objects of varying radii of curvature and corneas of normal subjects were imaged with a clinical SDOCT system. The optically corrected three-dimensional surfaces were used to recover radii of curvature and power as appropriate. These were then compared to the manufacturer’s reference values in phantoms and to measurements from topography and Scheimpflug photography in subjects. In phantom objects, paired differences between SDOCT and reference values for radii of curvature were not statistically significant. In subjects, there were no significant paired differences between SDOCT and reference values from the other modalities for anterior radius and corneal keratometric power. In contrast to other studies, we found that dense volumetric scans with available SDOCT can be used to recover corneal biometric values—including power—that correspond well with existing clinical measurements.

Local approximation of scalar functions on 3D shapes and volumetric data

In this paper, we tackle the problem of computing a map that locally interpolates or approximates the values of a scalar function, which have been sampled on a surface or a volumetric domain. We propose a local approximation with radial basis functions, which conjugates different features such as locality, independence of any tessellation of the sample points, and approximation accuracy. The proposed approach handles maps defined on both 3D shapes and volumetric data and has extrapolation capabilities higher than linear precision methods and moving least-squares techniques with polynomial functions. It is also robust with respect to data discretization and computationally efficient through the solution of a small and well-conditioned linear system. With respect to previous work, it allows an easy control on the preservation of local details and smoothness through both interpolating and least-squares constraints. The main application we consider is the approximation of maps defined on grids, 3D shapes, and volumetric data.

Interactive isosurfaces with quadratic C 1 splines on truncated octahedral partitions

The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C1 splines on uniform tetrahedrat partitions to achieve a globally smooth function. The spline is based on a truncated octahedral partition of the volumetric domain, where each truncated octahedron is further split into a fixed number of disjunct tetrahedra. The Bernstein-Brzier coefficients of the piecewise polynomials are directly determined by appropriate combinations of the data values in a local neighbourhood. As previously shown, the splines provide an approximation order two for smooth functions as well as their derivatives. We present the first visualizations using these sptines and show that they are welt suited for graphics processing unit {GPU}- based, interactive, high-quality visualization of isosurfaces from discrete data.

Coupled Gas Flow, Diffusion and Reaction in a ppb-level SnO2-NiO Formaldehyde Sensor System

The present project is part of an effort towards the development of a ppb-level formaldehyde sensor system for indoor air quality. An electroceramic response model for a SnO 2 -NiO composite solid oxide sensing material of n -type conductivity inside the porous material is coupled with a transient flow field simulation of the delivery of a formaldehyde pulse to the sensor surface. Coupled volumetric CFD domains are used to examine the effects of the transport of formaldehyde from a preconcentrator unit to the sensor, and its implications for interpreting the sensor signals from laboratory experiments.

SU‐E‐T‐772: Volume Matching for Brachytherapy Planning

Purpose: To perform brachytherapy treatment plan by comparing it with existing data base from earlier treatments of similar type. Method: When brachytherapy target to be treated is closely related in shape and volume to the target treated in the past for which we had well developed plan based on sources energy, activity and spatial distribution we can assume that plan of essentially the same quality will be achieved when the same distribution of sources that was used in the past will be imposed over the new, identical to one in the past treatment volume. The planning strategy under these circumstances relies on matching the volume under consideration with the volume of the target from earlier treatment. Characteristic scalar parameters of volumes will be compared first to filter the database (these will include volume, orientation of principal axes and moments of the characteristic set of the compared volumetric domains). When these parameters match closely between considered volume and one of stored in library volumes they are suspect of close similarity. The next stage of comparisons matches volumes by translating them in 3D space so that the maximal intersection between them is achieved. When closeness criterion is satisfied for this matching the distribution of sources is moved from the old plan to the new target completing the planning process. Results: The program for the algorithm has been written and sequence of plans have been computed for dose distributions obtained by sources placement based on domain comparison planning described above. Conclusion: The excellent agreement between set of plans based on geometrical planning approach and traditional planning optimization approach has been discovered. The domain comparison planning leads to enviable dose distribution in brachytherapy treatment and it is fast enough to be applicable to real time treatments.

Physical modeling with orthotropic material based on harmonic fields

Although it is well known that human bone tissues have obvious orthotropic material properties, most works in the physical modeling field adopted oversimplified isotropic or approximated transversely isotropic elasticity due to the simplicity. This paper presents a convenient methodology based on harmonic fields, to construct volumetric finite element mesh integrated with complete orthotropic material. The basic idea is taking advantage of the fact that the longitudinal axis direction indicated by the shape configuration of most bone tissues is compatible with the trajectory of the maximum material stiffness. First, surface harmonic fields of the longitudinal axis direction for individual bone models were generated, whose scalar distribution pattern tends to conform very well to the object shape. The scalar iso-contours were extracted and sampled adaptively to construct volumetric meshes of high quality. Following, the surface harmonic fields were expanded over the whole volumetric domain to create longitudinal and radial volumetric harmonic fields, from which the gradient vector fields were calculated and employed as the orthotropic principal axes vector fields. Contrastive finite element analyses demonstrated that elastic orthotropy has significant effect on simulating stresses and strains, including the value as well as distribution pattern, which underlines the relevance of our orthotropic modeling scheme.

Inhomogeneous volumetric Laplacian deformation for rhinoplasty planning and simulation system

AbstractThis paper presents an intuitive rhinoplasty planning and simulation system, to provide high quality prediction of postoperative appearance, and design patient specific nose prosthesis automatically. The key component is a novel volumetric Laplacian deformation tool inspired by the state‐of‐the‐art differential surface deformation techniques. Working on the volumetric domain and incorporating inhomogeneous material from CT data make the new approach suitable for soft tissue simulation. In particular, the system employs a special sketch contour driving deformation interface, which can provide realistic 3D rhinoplasty simulation with intuitive and straightforward 2D manipulation. When satisfied with the appearance, the change of soft tissue before and after simulation is utilized to generate the individual prosthesis model automatically. Clinical validation using post‐operative CT data demonstrated that the system can provide prediction results of high quality. And the surgeons who used the system confirmed that this planning system is attractive and has potential for daily clinical practice. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Electric-field-induced phase transformation at a lead-free morphotropic phase boundary: Case study in a 93%(Bi0.5Na0.5)TiO3–7% BaTiO3 piezoelectric ceramic

The electric-field-induced strain in 93%(Bi0.5Na0.5)TiO3–7%BaTiO3 polycrystalline ceramic is shown to be the result of an electric-field-induced phase transformation from a pseudocubic to tetragonal symmetry. High-energy x-ray diffraction is used to illustrate the microstructural nature of the transformation. A combination of induced unit cell volumetric changes, domain texture, and anisotropic lattice strains are responsible for the observed macroscopic strain. This strain mechanism is not analogous to the high electric-field-induced strains observed in lead-based morphotropic phase boundary systems. Thus, systems which appear cubic under zero field should not be excluded from the search for lead-free piezoelectric compositions.

Digital holographic microscopy applied to measurement of a flow in a T-shaped micromixer

In this paper, we describe measurements of a three-dimensional (3D) flow in a T-shaped micromixer by means of digital holographic microscopy. Imaging tracer particles in a microscopic flow with conventional microscopy is accompanied by a small depth-of-field, which hinders true volumetric flow measurements. In holographic microscopy, the depth of the measurement domain does not have this limitation because any desired image plane can be reconstructed after recording. Our digital holographic microscope (DHM) consists of a conventional in-line recording system with an added magnifying optical element. The measured flow velocity and the calculated vorticity illustrate four streamwise vortices in the micromixer outflow channel. Because the investigated flow is stationary and strongly 3D, the DHM performance (i.e. accuracy and resolution) can be precisely investigated. The obtained Dynamic spatial range and Dynamic velocity range are larger than 20 and 30, respectively. High-speed multiple-frame measurements illustrate the capability to simultaneously track about 80 particles in a volumetric measurement domain.