Volumetric Objects Research Articles

3D Space Shift from CityGML LoD3-Based Multiple Building Elements to a 3D Volumetric Object

In contrast with photorealistic visualizations, urban landscape applications, and building information system (BIM), 3D volumetric presentations highlight specific calculations and applications of 3D building elements for 3D city planning and 3D cadastres. Knowing the precise volumetric quantities and the 3D boundary locations of 3D building spaces is a vital index which must remain constant during data processing because the values are related to space occupation, tenure, taxes, and valuation. To meet these requirements, this paper presents a five-step algorithm for performing a 3D building space shift. This algorithm is used to convert multiple building elements into a single 3D volumetric building object while maintaining the precise volume of the 3D space and without changing the 3D locations or displacing the building boundaries. As examples, this study used input data and building elements based on City Geography Markup Language (CityGML) LoD3 models. This paper presents a method for 3D urban space and 3D property management with the goal of constructing a 3D volumetric object for an integral building using CityGML objects, by fusing the geometries of various building elements. The resulting objects possess true 3D geometry that can be represented by solid geometry and saved to a CityGML file for effective use in 3D urban planning and 3D cadastres.

Facing the Spectator.

We investigated the familiar phenomenon of the uncanny feeling that represented people in frontal pose invariably appear to “face you” from wherever you stand. We deploy two different methods. The stimuli include the conventional one—a flat portrait rocking back and forth about a vertical axis—augmented with two novel variations. In one alternative, the portrait frame rotates whereas the actual portrait stays motionless and fronto-parallel; in the other, we replace the (flat!) portrait with a volumetric object. These variations yield exactly the same optical stimulation in frontal view, but become grossly different in very oblique views. We also let participants sample their momentary awareness through “gauge object” settings in static displays. From our results, we conclude that the psychogenesis of visual awareness maintains a number—at least two, but most likely more—of distinct spatial frameworks simultaneously involving “cue–scission.” Cues may be effective in one of these spatial frameworks but ineffective or functionally different in other ones.

A two-muscle, continuum-mechanical forward simulation of the upper limb.

By following the common definition of forward-dynamics simulations, i.e. predicting movement based on (neural) muscle activity, this work describes, for the first time, a forward-dynamics simulation framework of a musculoskeletal system, in which all components are represented as continuous, three-dimensional, volumetric objects. Within this framework, the mechanical behaviour of the entire muscle-tendon complex is modelled as a nonlinear hyperelastic material undergoing finite deformations. The feasibility and the full potential of the proposed forward-dynamics simulation framework is demonstrated on a two-muscle, three-dimensional, continuum-mechanical model of the upper limb. The musculoskeletal model consists of three bones, i.e. humerus, ulna, and radius, an one-degree-of-freedom elbow joint, and an antagonistic muscle pair, i.e. the biceps and triceps brachii, and takes into consideration the contact between the skeletal muscles and the humerus. Numerical studies have shown that the proposed upper limb model is capable of predicting realistic moment arms and muscle forces for the entire range of activation and motion. Within the limitations of the model, the presented simulations provide, for the first time, insights into existing contact forces and their influence on the muscle fibre stretch. Based on the presented simulations, the overall change in fibre stretch is typically less than 3%, despite the fact that the contact forces reach up to 71% of the exerted muscle force. Movement-predicting simulations are achieved by minimising a nonlinear moment equilibrium equation. Based on the forward-dynamics simulation approach, an iterative solution procedures for position-driven (inverse dynamics) and force-driven scenarios have been proposed accordingly. Applying these methodologies to time-dependent scenarios demonstrates that the proposed methods can be linked to state-of-the-art control algorithms predicting time-dependent muscle activation levels based on principles of forward dynamics.

A robust method for high-precision quantification of the complex three-dimensional vasculatures acquired by X-ray microtomography.

The quantification of micro-vasculatures is important for the analysis of angiogenesis on which the detection of tumor growth or hepatic fibrosis depends. Synchrotron-based X-ray computed micro-tomography (SR-µCT) allows rapid acquisition of micro-vasculature images at micrometer-scale spatial resolution. Through skeletonization, the statistical features of the micro-vasculature can be extracted from the skeleton of the micro-vasculatures. Thinning is a widely used algorithm to produce the vascular skeleton in medical research. Existing three-dimensional thinning methods normally emphasize the preservation of topological structure rather than geometrical features in generating the skeleton of a volumetric object. This results in three problems and limits the accuracy of the quantitative results related to the geometrical structure of the vasculature. The problems include the excessively shortened length of elongated objects, eliminated branches of blood vessel tree structure, and numerous noisy spurious branches. The inaccuracy of the skeleton directly introduces errors in the quantitative analysis, especially on the parameters concerning the vascular length and the counts of vessel segments and branching points. In this paper, a robust method using a consolidated end-point constraint for thinning, which generates geometry-preserving skeletons in addition to maintaining the topology of the vasculature, is presented. The improved skeleton can be used to produce more accurate quantitative results. Experimental results from high-resolution SR-µCT images show that the end-point constraint produced by the proposed method can significantly improve the accuracy of the skeleton obtained using the existing ITK three-dimensional thinning filter. The produced skeleton has laid the groundwork for accurate quantification of the angiogenesis. This is critical for the early detection of tumors and assessing anti-angiogenesis treatments.

A B-spline based framework for volumetric object modeling

With the recent development of Iso-geometric Analysis (IGA) (Cottrell et al., 2009) and advanced manufacturing technologies employing heterogeneous materials, such as additive manufacturing (AM) of functionally graded material, there is a growing emerging need for a full volumetric representation of 3D objects, that prescribes the interior of the object in addition to its boundaries. In this paper, we propose a volumetric representation (V-rep) for geometric modeling that is based on trimmed B-spline trivariates and introduce its supporting volumetric modeling framework. The framework includes various volumetric model (V-model) construction methods from basic non-singular volumetric primitives to high level constructors, as well as Boolean operations’ support for V-models. A V-model is decomposed into and defined by a complex of volumetric cells (V-cells), each of which can also represent a variety of additional varying fields over it, and hence over the entire V-model. With these capabilities, the proposed framework is able of supporting volumetric IGA needs as well as represent and manage heterogeneous materials for AM. Further, this framework is also a seamless extension to existing boundary representations (B-reps) common in all contemporary geometric modeling systems, and allows a simple migration of existing B-rep data, tools and algorithms. Examples of volumetric models constructed using the proposed framework are presented.

Consistent Volumetric Warping Using Floating Boundaries for Stereoscopic Video Retargeting

The key to content-aware warping and cropping is adapting data to fit displays with various aspect ratios while preserving visually salient contents. Most previous studies achieve this objective by cropping insignificant contents near frame boundaries and consistently resizing frames through an optimization technique with various preservation constraints and fixed boundary conditions. These strategies significantly improve retargeting quality. However, warping under fixed boundary conditions may bound/limit the preservation of visually salient contents. Moreover, dynamic frame cropping and frame alignment may result in unnatural object/camera motions. In this paper, a floating boundary with volumetric warping and object-aware cropping is proposed to address these problems. In the proposed scheme, visually salient objects in the space-time domain are deformed as rigidly and as consistently as possible using information from matched objects and content-aware boundary constraints. The content-aware boundary constraints can retain visually salient contents in a fixed region with a desired resolution and aspect ratio, called critical region, during warping. Volumetric cropping with the fixed critical region is then performed to adjust stereoscopic videos to the desired aspect ratios. The strategies of warping and cropping using floating boundaries and spatiotemporal constraints enable our method to consistently preserve the temporal motions and spatial shapes of visually salient volumetric objects in the left and right videos as much as possible, thus leading to good content-aware retargeting. In addition, by considering shape, motion, and disparity preservation, the proposed scheme can be applied to various media, including images, stereoscopic images, videos, and stereoscopic videos. Qualitative and quantitative analyses of stereoscopic videos with diverse camera and considerable motions demonstrate a clear superiority of the proposed method over related methods in terms of retargeting quality.

Bayesian Abel Inversion in Quantitative X-Ray Radiography

A common image formation process in high-energy X-ray radiography is to have a pulsed power source that emits X-rays through a scene, a scintillator that absorbs X-rays and fluoresces in the visible spectrum in response to the absorbed photons, and a charge-coupled device camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the inverse Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type and scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown density profile, the prior precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posterior distribution for the unknown density profile, the prior parameters, and the spatial structure of the precision matrix. Results of the density reconstructions and pointwise uncertainty estimates are presented for both synthetic signals and real data from a U.S. Department of Energy X-ray imaging facility.

A meshless strategy for shape diameter analysis

An approach to computing an intuitive local thickness from surface meshes was introduced with the shape diameter function (SDF) in Shapira et al. (Vis Comput 24(4):249---259, 2008). In this paper, we present a new dynamic approach to the computation of the SDF for a cloud of points on the boundary of a volumetric object. We employ a particle flow driven by a simple collision test. The resulting SDF scalar field can be naturally exploited as a shape property for the volume-oriented object decomposition. Experimental results show the effectiveness and efficiency of our proposals.

Modeling Channel Forms and Related Sedimentary Objects Using a Boundary Representation Based on Non-uniform Rational B-Splines

In this paper, we aim at providing a flexible and compact volumetric object model capable of representing many sedimentary structures at different scales. Geo-bodies are defined by a boundary representation; each bounding surface is constructed as a parametric deformable surface. We propose a three-dimensional sedimentary object with a compact parametrization which allows for representing various geometries and provides a curvilinear framework for modeling internal heterogeneities. This representation is based on Non Uniform Rational B-Splines (NURBS) smoothly interpolate between a set of points. The three-dimensional models of geobodies are generated using a small number of parameters, and hence can be easily modified. This can be done by a point and click user interactions for manual editing or by a Monte-Carlo sampling for stochastic simulation. Each elementary shape is controlled by deformation rules and has connection constraints with associated objects, in order to maintain the geometry and the consistency through editing. The boundary representations of the different sedimentary structures are used to construct hexahedral conformal grids in order to perform petrophysical property simulations following the particular three-dimensional parametric space of each object. Finally these properties can be upscaled, according to erosion rules, to a global grid that represents the global depositional environment.

A two-level clustering approach for multidimensional transfer function specification in volume visualization

Multidimensional transfer functions can perform more sophisticated classification of volumetric objects compared to 1-D transfer functions. However, visualizing and manipulating the transfer function space is non-intuitive when its dimension goes beyond 3-D, thus making user interaction difficult. In this paper, we propose to address the multidimensional transfer function design problem by taking a two-level clustering approach, where the first-level clustering by the self-organizing map (SOM) projects high-dimensional feature data to a 2-D topology preserving map, and the second-level clustering on the SOM neurons reduces the design freedom from a large number of SOM neurons to a manageable number of clusters. Based on the two-level clustering results, we propose a novel volume exploration scheme that provides top-down navigation to users exploring the volume. Guided by an informative volume overview, interesting structures in the volume are discovered interactively by the user selecting clusters to visualize and modifying the clustering results when necessary. Our interface keeps track of each interesting structure discovered, which not only enables users to inspect individual structures closely, but also allows them to compose the final visualization by fusing the structures deemed important.

Local Solid Shape.

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution.

EVALUATING THE POTENTIAL OF MULTISPECTRAL AIRBORNE LIDAR FOR TOPOGRAPHIC MAPPING AND LAND COVER CLASSIFICATION

Abstract. Recently multispectral LiDAR became a promising research field for enhanced LiDAR classification workflows and e.g. the assessment of vegetation health. Current analyses on multispectral LiDAR are mainly based on experimental setups, which are often limited transferable to operational tasks. In late 2014 Optech Inc. announced the first commercially available multispectral LiDAR system for airborne topographic mapping. The combined system makes synchronic multispectral LiDAR measurements possible, solving time shift problems of experimental acquisitions. This paper presents an explorative analysis of the first airborne collected data with focus on class specific spectral signatures. Spectral patterns are used for a classification approach, which is evaluated in comparison to a manual reference classification. Typical spectral patterns comparable to optical imagery could be observed for homogeneous and planar surfaces. For rough and volumetric objects such as trees, the spectral signature becomes biased by signal modification due to multi return effects. However, we show that this first flight data set is suitable for conventional geometrical classification and mapping procedures. Additional classes such as sealed and unsealed ground can be separated with high classification accuracies. For vegetation classification the distinction of species and health classes is possible.

A New Approach for Simulation of Hot Mix Asphalt; Numerical and Experimental

ABSTRACTIn this study a novel approach for 3D modeling of cylindrical sample of hot mix asphalt (HMA) is presented. To this end, the cylindrical sample was divided into several slices and using a developed algorithm the processed images were extended to 3D volumetric objects to reconstruct the 3D microstructure of HMA. To evaluate the efficiency of the presented 3D model for prediction of mechanical behavior, HMA was regarded as a two-phase mixture; mastic phase and aggregate phase. The asphalt binder, filler, air voids and fine aggregates were considered as mastic with viscoelastic behavior and the aggregate was considered as an elastic material. Two models (Burger and generalized Kelvin) were studied for determining viscoelastic behavior of mastic. Finally, to verify the model using Finite Element Method (FEM) the behavior of the 3D model was simulated under different uniaxial compressive loads. A good agreement was observed between the simulated results and corresponding experimental data which indicates the efficiency of the proposed model to simulate three-dimensional asphalt.

Rule‐Enhanced Transfer Function Generation for Medical Volume Visualization

AbstractIn volume visualization, transfer functions are used to classify the volumetric data and assign optical properties to the voxels. In general, transfer functions are generated in a transfer function space, which is the feature space constructed by data values and properties derived from the data. If volumetric objects have the same or overlapping data values, it would be difficult to separate them in the transfer function space. In this paper, we present a rule‐enhanced transfer function design method that allows important structures of the volume to be more effectively separated and highlighted. We define a set of rules based on the local frequency distribution of volume attributes. A rule‐selection method based on a genetic algorithm is proposed to learn the set of rules that can distinguish the user‐specified target tissue from other tissues. In the rendering stage, voxels satisfying these rules are rendered with higher opacities in order to highlight the target tissue. The proposed method was tested on various volumetric datasets to enhance the visualization of important structures that are difficult to be visualized by traditional transfer function design methods. The results demonstrate the effectiveness of the proposed method.

Construction of 3D Volumetric Objects for a 3D Cadastral System

AbstractThis article presents a new method to illustrate the feasibility of 3D topology creation. We base the 3D construction process on testing real cases of implementation of 3D parcels construction in a 3D cadastral system. With the utilization and development of dense urban space, true 3D geometric volume primitives are needed to represent 3D parcels with the adjacency and incidence relationship. We present an effective straightforward approach to identifying and constructing the valid volumetric cadastral object from the given faces, and build the topological relationships among 3D cadastral objects on‐the‐fly, based on input consisting of loose boundary 3D faces made by surveyors. This is drastically different from most existing methods, which focus on the validation of single volumetric objects after the assumption of the object's creation. Existing methods do not support the needed types of geometry/topology (e.g. non 2‐manifold, singularities) and how to create and maintain valid 3D parcels is still a challenge in practice. We will show that the method does not change the faces themselves and faces in a given input are independently specified. Various volumetric objects, including non‐manifold 3D cadastral objects (legal spaces), can be constructed correctly by this method, as will be shown from the results.

3-D object modeling from 2-D occluding contour correspondences by opti-acoustic stereo imaging

Utilizing in situ measurements to build 3-D volumetric object models under variety of turbidity conditions is highly desirable for marine sciences. To address the ineffectiveness of feature-based structure from motion and stereo methods under poor visibility, we explore a multi-modal stereo imaging technique that utilizes coincident optical and forward-scan sonar cameras, a so-called opti-acoustic stereo imaging system. The challenges of establishing dense feature correspondences in either opti-acoustic or low-contrast optical stereo images are avoided, by employing 2-D occluding contour correspondences, namely, the images of 3-D object occluding rims. Collecting opti-acoustic stereo pairs while circling an object, matching 2-D apparent contours in optical and sonar views to construct the 3-D occluding rim, and computing the stereo rig trajectory by opti-acoustic bundle adjustment, we generate registered samples of 3-D surface in a reference coordinate system. A surface interpolation gives the 3-D object model.In addition to the key advantage of utilizing range measurements from sonar, the proposed paradigm requires no assumption about local surface curvature as traditionally made in 3-D shape reconstruction from occluding contours. The reconstruction accuracy is improved by computing both the 3-D positions and local surface normals of sampled contours. We also present (1) a simple calibration method to estimate and correct for small discrepancy from the desired relative stereo pose; (2) an analytical analysis of the degenerate configuration that enables special treatment in mapping (tall) elongated objects with dominantly vertical edges. We demonstrate the performance of our method based on the 3-D surface rendering of certain objects, imaged by an underwater opti-acoustic stereo system.

An immersogeometric variational framework for fluid–structure interaction: Application to bioprosthetic heart valves

In this paper, we develop a geometrically flexible technique for computational fluid–structure interaction (FSI). The motivating application is the simulation of tri-leaflet bioprosthetic heart valve function over the complete cardiac cycle. Due to the complex motion of the heart valve leaflets, the fluid domain undergoes large deformations, including changes of topology. The proposed method directly analyzes a spline-based surface representation of the structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain. This places our method within an emerging class of computational techniques that aim to capture geometry on non-boundary-fitted analysis meshes. We introduce the term “immersogeometric analysis” to identify this paradigm.The framework starts with an augmented Lagrangian formulation for FSI that enforces kinematic constraints with a combination of Lagrange multipliers and penalty forces. For immersed volumetric objects, we formally eliminate the multiplier field by substituting a fluid–structure interface traction, arriving at Nitsche’s method for enforcing Dirichlet boundary conditions on object surfaces. For immersed thin shell structures modeled geometrically as surfaces, the tractions from opposite sides cancel due to the continuity of the background fluid solution space, leaving a penalty method. Application to a bioprosthetic heart valve, where there is a large pressure jump across the leaflets, reveals shortcomings of the penalty approach. To counteract steep pressure gradients through the structure without the conditioning problems that accompany strong penalty forces, we resurrect the Lagrange multiplier field. Further, since the fluid discretization is not tailored to the structure geometry, there is a significant error in the approximation of pressure discontinuities across the shell. This error becomes especially troublesome in residual-based stabilized methods for incompressible flow, leading to problematic compressibility at practical levels of refinement. We modify existing stabilized methods to improve performance.To evaluate the accuracy of the proposed methods, we test them on benchmark problems and compare the results with those of established boundary-fitted techniques. Finally, we simulate the coupling of the bioprosthetic heart valve and the surrounding blood flow under physiological conditions, demonstrating the effectiveness of the proposed techniques in practical computations.

Design of a 4-DOF MR haptic master for application to robot surgery: virtual environment work

This paper presents the design and control performance of a novel type of 4-degrees-of-freedom (4-DOF) haptic master in cyberspace for a robot-assisted minimally invasive surgery (RMIS) application. By using a controllable magnetorheological (MR) fluid, the proposed haptic master can have a feedback function for a surgical robot. Due to the difficulty in utilizing real human organs in the experiment, the cyberspace that features the virtual object is constructed to evaluate the performance of the haptic master. In order to realize the cyberspace, a volumetric deformable object is represented by a shape-retaining chain-linked (S-chain) model, which is a fast volumetric model and is suitable for real-time applications. In the haptic architecture for an RMIS application, the desired torque and position induced from the virtual object of the cyberspace and the haptic master of real space are transferred to each other. In order to validate the superiority of the proposed master and volumetric model, a tracking control experiment is implemented with a nonhomogenous volumetric cubic object to demonstrate that the proposed model can be utilized in real-time haptic rendering architecture. A proportional-integral-derivative (PID) controller is then designed and empirically implemented to accomplish the desired torque trajectories. It has been verified from the experiment that tracking the control performance for torque trajectories from a virtual slave can be successfully achieved.

Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone

Isogeometric analysis (IGA) of geometrically complex three-dimensional objects is possible when used in combination with the Finite Cell method (FCM). In this contribution we propose a computational methodology to automatically analyze the effective elastic properties of scan-based volumetric objects of arbitrary geometric and topological complexity. The first step is the reconstruction of a smooth geometry from scan-based voxel data using a B-spline level set function. The second step is a goal-oriented adaptive isogeometric linear elastic analysis. Elements are selected for refinement using dual-weighted residual shape function indicators, and hierarchical splines are employed to construct locally refined spline spaces. The proposed methodology is studied in detail for various numerical test cases, including the computation of the effective Young’s modulus of a trabecular bone micro-structure reproduced from μCT-scan data.

Variational time discretization of geodesic calculus

We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete parallel transport, and we prove convergence to their continuous counterparts. The presented analysis is based on the direct methods in the calculus of variation, on $\Gamma$-convergence, and on weighted finite element error estimation. The convergence results of the discrete geodesic calculus are experimentally confirmed for a basic model on a two-dimensional Riemannian manifold. This provides a theoretical basis for applications in computer vision: In particular, discrete geodesics offer an effective tool for shape morphing and the computation of a distance between shapes, the discrete logarithm allows a linear representation of strongly nonlinear shape variability, the discrete exponential map provides a robust tool for shape extrapolation, and the discrete parallel transport can be used to transfer geometric details from one shape to another. The basic operations are exemplarily illustrated for two different shape spaces, the space of viscous volumetric objects and the space of discrete viscous shells.