Spherical Domain Research Articles

CubeGAN: Omnidirectional Image Synthesis Using Generative Adversarial Networks

AbstractWe propose a framework to create projectively‐correct and seam‐free cube‐map images using generative adversarial learning. Deep generation of cube‐maps that contain the correct projection of the environment onto its faces is not straightforward as has been recognized in prior work. Our approach extends an existing framework, StyleGAN3, to produce cube‐maps instead of planar images. In addition to reshaping the output, we include a cube‐specific volumetric initialization component, a projective resampling component, and a modification of augmentation operations to the spherical domain. Our results demonstrate the network's generation capabilities trained on imagery from various 3D environments. Additionally, we show the power and quality of our GAN design in an inversion task, combined with navigation capabilities, to perform novel view synthesis.

Role of Kidney Stones in Renal Pelvis Flow.

Ureteroscopy is a commonly performed medical procedure to treat stones in the kidney and ureter using a ureteroscope. Throughout the procedure, saline is irrigated through the scope to aid visibility and wash-out debris from stone fragmentation. The key challenge that this research addresses is to build a fundamental understanding of the interaction between the kidney stones/stone fragments and the flow dynamics in the renal pelvis flow. We examine the time-dependent flow dynamics inside an idealized renal pelvis in the context of a surgical procedure for kidney stone removal. Here, we examine the time-dependent evolution of these vortical flow structures in three dimensions, and incorporate the presence of rigid kidney stones. We perform direct numerical simulations, solving the transient Navier-Stokes equations in a spherical domain. Our numerical predictions for the flow dynamics in the absence of stones are validated with available experimental and numerical data, and the governing parameters and flow regimes are chosen carefully in order to satisfy several clinical constraints. The results shed light on the crucial role of flow circulation in the renal cavity and its effect on the trajectories of rigid stones. We demonstrate that stones can either be washed out of the cavity along with the fluid, or be trapped in the cavity via their interaction with vortical flow structures. Additionally, we study the effect of multiple stones in the flow field within the cavity in terms of the kinetic energy, entrapped fluid volume, and the clearance rate of a passive tracer modeled via an advection-diffusion equation. We demonstrate that the flow in the presence of stones features a higher vorticity production within the cavity compared with the stone-free cases.

DOA Estimation of Indoor Sound Sources Based on Spherical Harmonic Domain Beam-Space MUSIC

The Multiple Signal Classification (MUSIC) algorithm has become one of the most popular algorithms for estimating the direction-of-arrival (DOA) of multiple sources due to its simplicity and ease of implementation. Spherical microphone arrays can capture more sound field information than planar arrays. The collected multichannel speech signals can be transformed from the space domain to the spherical harmonic domain (SHD) for processing through spherical modal decomposition. The spherical harmonic domain MUSIC (SHD-MUSIC) algorithm reduces the dimensionality of the covariance matrix and achieves better DOA estimation performance than the conventional MUSIC algorithm. However, the SHD-MUSIC algorithm is prone to failure in low signal-to-noise ratio (SNR), high reverberation time (RT), and other multi-source environments. To address these challenges, we propose a novel joint spherical harmonic domain beam-space MUSIC (SHD-BMUSIC) algorithm in this paper. The advantage of decoupling the signal frequency and angle information in the SHD is exploited to improve the anti-reverberation property of the DOA estimation. In the SHD, the broadband beamforming matrix converts the SHD sound pressure to the beam domain output. Beamforming enhances the incoming signal in the desired direction and reduces the SNR threshold as well as the dimension of the signal covariance matrix. In addition, the 3D beam of the spherical array has rotational symmetry and its beam steering is decoupled from the beam shape. Therefore, the broadband beamforming constructed in this paper allows for the arbitrary adjustment of beam steering without the need to redesign the beam shape. Both simulation experiments and practical tests are conducted to verify that the proposed SHD-BMUSIC algorithm has a more robust adjacent source discrimination capability than the SHD-MUSIC algorithm.

Learning based method for near field acoustic range estimation in spherical harmonics domain using intensity vectors

Near-field acoustic range estimation is considered one of the least explored research problems in digital signal processing under noise and reverberant conditions. This letter develops a new learning-based range estimation technique utilizing the spherical harmonics intensity (SH-INT) coefficients. The conventional range estimation in the spherical harmonics (SH) domain relies on the pressure coefficients. However, at high frequencies, these coefficients of different order and range overlap and hinder the accuracy of range estimation. On the contrary, the SH-INT coefficients are well distinguished at high frequencies for various orders and ranges, making these features favorable for accurate range estimation using learning algorithms. Since the SH-INT coefficients in the radial direction are independent of the source signal and vary with range, a convolutional neural network (CNN) model has been adopted to map the SH-INT coefficients with the range classes. The performance of the proposed spherical harmonic intensity (SH-INT) features in the context of near-field range estimation is validated by conducting exhaustive experiments on simulated and real data. Further, the error in near-field source range estimates is characterized using root mean square error (RMSE) criteria. The results are impactful and encourage the use of this method for practical near-field source range estimation applications.

Speech improvement in noisy reverberant environments using virtual microphones along with proposed array geometry

This paper proposes a novel approach for improving the speech of a single speaker in noisy reverberant environments. The proposed approach is based on using a beamformer with a large number of virtual microphones with the suggested arrangement on an open sphere. Our method takes into account virtual microphone signal synthesizing using the non-parametric sound field reproduction in the spherical harmonics domain and the popular weighted prediction error method. We obtain entirely accurate beam steering towards a known source location with more directivity. The suggested approach is proven to perform effectively not just in boosting the directivity factor but also in terms of improving speech quality as measured by subjective metrics like the PESQ. In comparison to current research in the area of speech enhancement by beamformer, our experiments reveal more noise and reverberation suppression as well as improved quality in the enhanced speech samples due to the usage of virtual beam rotation in the fixed beamformer. Text for this section.

Modelling 3D force-free neutron star magnetospheres

ABSTRACT Magnetars exhibit a variety of transient high-energy phenomena in the form of bursts, outbursts, and giant flares. It is a common belief that these events originate in the sudden release of magnetic energy due to the rearrangement of a twisted magnetic field. We present global models of a 3D force-free (FF) non-linear twisted magnetar magnetosphere. We solve the FF equations following the Grad–Rubin approach in a compactified spherical domain. Appropriate boundary conditions are imposed at the surface of the star for the current distribution and the magnetic field. Our implementation is tested by reproducing various known analytical as well as axisymmetric numerical results. We then proceed to study general 3D models with non-axisymmetric current distributions, such as fields with localized twists that resemble hotspots at the surface of the star, and we examine characteristic quantities such as energy, helicity, and twist. Finally, we discuss implications on the available energy budget, the surface temperature, and the diffusion time-scale, which can be associated with observations.

Acoustic reciprocity in the spherical harmonic domain: A formulation for directional sources and receivers

Acoustic reciprocity states that the transfer function between a source and a receiver remains unchanged if the two are interchanged. An extension of acoustic reciprocity to the spherical harmonic domain has been derived in the literature between a directional source and a directional receiver. The present letter derives a reciprocal relation between source and receiver directivity coefficients, which facilitates the derivation of a transfer function in the spherical harmonic domain using directivity coefficients obtained via reciprocity. Additionally, reciprocity between transfer functions is extended for more general source and receiver directivities, which include acoustic scattering effects.

3D Scene Geometry Estimation from 360° Imagery: A Survey

This article provides a comprehensive survey on pioneer and state-of-the-art 3D scene geometry estimation methodologies based on single, two, or multiple images captured under omnidirectional optics. We first revisit the basic concepts of the spherical camera model and review the most common acquisition technologies and representation formats suitable for omnidirectional (also called 360°, spherical or panoramic) images and videos. We then survey monocular layout and depth inference approaches, highlighting the recent advances in learning-based solutions suited for spherical data. The classical stereo matching is then revised on the spherical domain, where methodologies for detecting and describing sparse and dense features become crucial. The stereo matching concepts are then extrapolated for multiple view camera setups, categorizing them among light fields, multi-view stereo, and structure from motion (or visual simultaneous localization and mapping). We also compile and discuss commonly adopted datasets and figures of merit indicated for each purpose and list recent results for completeness. We conclude this article by pointing out current and future trends.

Global Moho Gravity Inversion from GOCE Data: Updates and Convergence Assessment of the GEMMA Model Algorithm

Since its discovery in 1909, the Moho was routinely studied by seismological methods. However, from the 1950s, a possible alternative was introduced by gravimetric inversion. Thanks to satellite gravity missions launched from the beginning of the 21st century, a global inversion became feasible, e.g., leading to the computation of the GEMMA model in 2012. This model was computed inverting the GOCE second radial derivatives of the anomalous potential by a Wiener filter, which was applied in the spherical harmonic domain, considering a two-layer model with lateral and vertical density variations. Moreover, seismic information was introduced in the inversion to deal with the joint estimation/correction of both density and geometry of the crustal model. This study aims at revising the GEMMA algorithm from the theoretical point of view, introducing a cleaner formalization and studying the used approximations more thoroughly. The updates are on: (1) the management of the approximations due to the forward operator linearization required for the inversion; (2) the regularization of spherical harmonic coefficients in the inversion by proper modelling the Moho signal and the gravity error covariances; (3) the inclusion of additional parameters and their regularization in the Least Squares adjustment to correct the density model by exploiting seismic information. Thanks to these updates, a significant improvement from the computational point of view is achieved too, thus the convergence of the iterative solution and the differences with respect to the previous algorithm can be assessed by closed-loop tests, showing the algorithm performance in retrieving the simulated “true” Moho.

Optimal beamformer design in spherical sector harmonics domain

Beamforming using spherical microphone arrays (SMAs) with processing in spherical harmonics (SH) domain is widely being studied. This is due to the ease of array processing in SH domain with no spatial ambiguity. Despite the widespread applications of SMA in beamforming, its size makes it inconvenient for practical or commercial use. Building of SMA over a rigid sphere is also a challenging task. Additionally, use of the entire sphere comes at the cost of more microphones and signals to process. Hence, it is uneconomic to use full SMA when sources are only present in restricted regions of the environment. Attempts have been made in literature to use hemispherical microphone array for beamforming. Acoustic image principle was utilized to enable application of SH but with greater computational complexity. In this paper, the use of a spherical sector microphone array is proposed for beamforming. An orthonormal spherical sector harmonics (S2H) basis function is used for data model development. An ideal direction-invariant beampattern using S2H basis function is utilized. Subsequently, to make the beamformer robust against sensor noise with a sharp directivity pattern at the direction of arrival and zero elsewhere, a new maximum directivity and white noise gain (MD-WNG) beamformer is designed for a spherical sector microphone array. Performance analysis of the proposed beamformer is presented using various experiments on directivity pattern and array gain. The proposed method is additionally compared with several existing beamforming techniques. The comparison reveals that the S2H based beamforming provides reasonably better results compared to the existing methods.

How Slab Age and Width Combine to Dictate the Dynamics and Evolution of Subduction Systems: A 3‐D Spherical Study

AbstractMany of the factors expected to control the dynamics and evolution of Earth's subduction zones are under‐explored in an Earth‐like spherical geometry. Here, we simulate multi‐material free‐subduction of a complex rheology slab in a 3‐D spherical shell domain, to investigate the effect of plate age (simulated by covarying plate thickness and density) and width on the evolution of subduction systems. We find that the first‐order predictions of our spherical cases are generally consistent with existing Cartesian studies: (a) as subducting plate age increases, slabs retreat more and subduct at a shallower dip angle, due to increased bending resistance and sinking rates; and (b) wider slabs can develop along‐strike variations in trench curvature due to toroidal flow at slab edges, trending toward a “W”‐shaped trench with increasing slab width. We find, however, that these along‐strike variations are restricted to older, stronger, retreating slabs: Younger slabs that drive minimal trench motion remain relatively straight along the length of the subduction zone. We summarize our results into a regime diagram, which highlights how slab age modulates the effect of slab width, and present examples of the evolutionary history of subduction zones that are consistent with our model predictions.

Topological Data Analysis of m-Polar Spherical Fuzzy Information with LAM and SIR Models

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods.

Film thickness and strain rate dependences of the mechanical properties of polystyrene-b-polyisoprene-b-polystyrene block copolymer ultrathin films forming a spherical domain

While the mechanical properties of ultrathin polymer films have been extensively studied, only few studies have focused on the ultrathin block copolymer films with complex topologies. The structure-property relationship of ultrathin films (thickness = 35–1000 nm) of polystyrene- b -polyisoprene- b -polystyrene (SIS) containing 14 wt% polystyrene (PS) is established in this study. Grazing-incidence small-angle X-ray scattering, dynamic secondary ion mass spectrometry, and atomic force microscopy were used to characterize the film structure. The difference in surface energy and interfacial energy of the domains resulted in the SIS thin films to primarily consist of three layers: a PS-rich subsurface layer (30 wt%), a spherical PS bulk layer (14 wt%), and a PS-rich interface layer (20 wt%). The film-on-water tensile test was used to investigate both the film thickness and strain rate dependences of mechanical properties. We found that the Young's modulus increased dramatically as film thickness decreased, although only few PS-rich layers consisting of disperse cylindrical and spherical PS domains existed at the surface and interface. Furthermore, the strain rate dependence of the modulus and stress relaxation was more significant for thinner films than for thicker films. The increase in modulus and unusual relaxation behavior are hypothesized to be the result of a combination of different factors, including PS domain alignment, confinement effects, and surface and interface interactions. • The structure-property relationship of ultrathin SIS films is analyzed. • Young's modulus increases upon decreasing thickness. • The extent of stress relaxation is larger for thinner films. • The stiffening may result from PS domain alignment.

DOA estimation using two independent convolutional neural networks with residual blocks

Acoustic source localization in the spherical harmonic domain with reverberation has hitherto not been investigated extensively. When the joint direction-of-arrival (DOA) estimation is treated as a classification task, it needs a lot of different classes and large-scale dataset, which is time-consuming and less cost-effective. Thus, a novel learning-based method is proposed in this paper, which separately estimates azimuths and elevations by two independent convolution neural networks (CNNs) with residual blocks. First, a mapping matrix is adopted to transform the spherical harmonic function into the Kronecker product of two Vandermonde vectors. Based on the special structure, features dependent on azimuth and elevation, respectively, are extracted as inputs to neural networks. This can divide the joint DOA estimation into two sub-tasks completed by two independent CNNs with residual blocks, which can be realized in parallel. Furthermore, the performance of the model learned by CNNs with residual blocks is better than ordinary CNNs. Simulations are conducted both on the simulated and real speech data for evaluating the performance of the proposed method. The results show that the method has higher accuracy. Moreover, the method is time-saving and effectively reduces the computational complexity.

PSE-Match: A Viewpoint-Free Place Recognition Method With Parallel Semantic Embedding

Accurate localization on the autonomous driving cars is essential for autonomy and driving safety, especially for complex urban streets and search-and-rescue subterranean environments where high-accurate GPS is not available. However current odometry estimation may introduce the drifting problems in long-term navigation without robust global localization. The main challenges involve scene divergence under the interference of dynamic environments and effective perception of observation and object layout variance from different viewpoints. To tackle these challenges, we present PSE-Match, a viewpoint-free place recognition method based on parallel semantic analysis of isolated semantic attributes from 3D point-cloud models. Compared with the original point cloud, the observed variance of semantic attributes is smaller. PSE-Match incorporates a divergence place learning network to capture different semantic attributes parallelly through the spherical harmonics domain. Using both existing benchmark datasets and two in-field collected datasets, our experiments show that the proposed method achieves above 70% average recall with top one retrieval and above 95% average recall with top ten retrieval cases. And PSE-Match has also demonstrated an obvious generalization ability with limited training dataset.

Combination of conformal mapping with variable discrete ordinates method for solving the radiation heat transfer in concentric spherical media

The radiation problem in one-dimensional participating media between two concentric spheres is solved by mapping the concentric spherical domain into the plane-parallel domain, where the radiative rays propagate along curved paths. The computational plane-parallel domain is discretized into slices with constant radiative properties and the angular domain for each control volume is discretized into variable polar angles. To validate the accuracy of the present method, comparisons are made with the previous studies in literature.

"General analytical solution of fractional Klein–Gordon equation in a spherical domain"

"Time-fractional Klein–Gordon equation in a sphere is considered for the case of central sym- metry under the time-variable Dirichlet condition. The time-fractional derivative with the power-law kernel is used. The Laplace transform and convenient transformations of the independent variable and unknown func- tion are used to determine the general analytical solution of the problem in the Laplace domain. In order to obtain the solution in the real domain, the inverse Laplace transforms of two functions of exponential type whose expressions are new in the literature have been determined. The similar solution for ordinary Klein– Gordon equation is a limiting case of general solution but a simpler form for this solution is provided. The convergence of general solution to the ordinary solution and the effects of fractional parameter on this solution are graphically underlined."

Geometrical deviation modeling and monitoring of 3D surface based on multi-output Gaussian process

Geometrical deviation is an important factor in determining the quality of a three-dimensional (3D) Surface. For 3D surfaces with complex shapes, the high-definition measurement (HDM) technology can provide detailed information on surface topography, which inspired new challenges in characterizing, modeling, and monitoring geometrical deviations. This paper proposes a spherical multi-output Gaussian process (S-MOGP) method to model and monitor 3D surfaces. Firstly, the surface in the 3D coordinate system is mapped to the spherical 2D parameter domain. Secondly, a state equation based on the multi-output Gaussian process is established to model the 3D surface. Finally, statistics are calculated and control charts are presented to monitor the geometrical deviation. The results of simulations and a case study show that the proposed method can effectively model 3D surfaces and monitor the geometrical deviations.

Adaptive area-preserving parameterization of open and closed anatomical surfaces

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape description. However, establishing a one-to-one correspondence between the object surface and the entire unit sphere may induce a large geometric distortion in case the shape of the surface is too different from a perfect sphere. In this work, we propose adaptive area-preserving parameterization methods for simply-connected open and closed surfaces with the target of the parameterization being a spherical cap. Our methods optimize the shape of the parameter domain along with the mapping from the object surface to the parameter domain. The object surface will be globally mapped to an optimal spherical cap region of the unit sphere in an area-preserving manner while also exhibiting low conformal distortion. We further develop a set of spherical harmonics-like basis functions defined over the adaptive spherical cap domain, which we call the adaptive harmonics. Experimental results show that the proposed parameterization methods outperform the existing methods for both open and closed anatomical surfaces in terms of area and angle distortion. Surface description of the object surfaces can be effectively achieved using a novel combination of the adaptive parameterization and the adaptive harmonics. Our work provides a novel way of mapping anatomical surfaces with improved accuracy and greater flexibility. More broadly, the idea of using an adaptive parameter domain allows easy handling of a wide range of biomedical shapes.

The Green’s Function-Based Thermal Analysis of a Spherical Geothermal Tank in a Semi-Infinite Domain

Abstract The Green’s function of a bimaterial infinite domain with a plane interface is applied to thermal analysis of a spherical underground heat storage tank. The heat transfer from a spherical source is derived from the integral of the Green’s function over the spherical domain. Because the thermal conductivity of the tank is generally different from soil, the Eshelby’s equivalent inclusion method (EIM) is used to simulate the thermal conductivity mismatch of the tank from the soil. For simplicity, the ground with an approximately uniform temperature on the surface is simulated by a bimaterial infinite domain, which is perfectly conductive above the ground. The heat conduction in the ground is investigated for two scenarios: First, a steady-state uniform heat flux from surface into the ground is considered, and the heat flux is disturbed by the existence of the tank due to the conductivity mismatch. A prescribed temperature gradient, or an eigen-temperature gradient, is introduced to investigate the local temperature field in the neighborhood of the tank. Second, when a temperature difference exists between the water in the tank and soil, the heat transfer between the tank and soil depends on the tank size, conductivity, and temperature difference, which provide a guideline for heat exchange design for the tank size. The modeling framework can be extended to two-dimensional cases, periodic, or transient heat transfer problems for geothermal well operations. The corresponding Green’s functions are provided for those applications.