Poisson Disk Research Articles

Flexible 3D printing of the mitral valve apparatus and left coronary artery for patients with complex anatomical variations in mitral valve surgery

Abstract Funding Acknowledgements Type of funding sources: None. Introduction Injury to the left circumflex artery (LCA) occurs in an estimated 2.7% of patients undergoing mitral valve (MV) surgery. The average distance from the LCA to the MV varies substantially between patients but is on average 3.1 ± 1.3mm. In unfavorable anatomical variations, a 3D print of relevant anatomical structures could be helpful for a surgeon to be aware of the situation and determine a surgical strategy. In this case such a 3D print is made of a 66 year old patient with mitral valve regurgitation and a P2 prolapse assessed in the heart team for MVS. Purpose To create a flexible heart model using Computed tomography (CT) and Transesophageal echocardiography (TEE) scans of this patient that utilizes the synergistic information derived from both modalities and provides an improved method for surgical preparation in cases with unfavorable anatomical variations. Method CT and TEE scans of the heart and mitral valve are acquired and fused using Mutual information registration. Both modalities are used in the print as TEE is the gold standard for evaluating the MV prior to surgery while on CT the LCA can be visualized and the ventricle can be imaged with a higher spatial resolution. The combined reconstructions are hollowed and smoothed using Meshmixer and the Poisson disk sampling tool of Meshlab to make the reconstruction suitable for 3D printing, enhance visibility of the relevant anatomy and achieve the desired flexibility of the model. Results A flexible 3D model of the left side of the heart of a patient is created. The model consists of reconstructions of the left coronary artery (CT), the left side of the heart (CT), and the mitral valve (TEE). To expose the LCA, an indent in the tissue surrounding the LCA was made. At the apex of the heart and at the left lateral side a small window in the ventricle was created for visibility. A flexibility resembling the flexibility of tissue was created by hollowing a with walls of 1.2mm thickness and printing with Agilus 30 Clear (with a shore A value of 30) . Conclusion To our knowledge this is the first 3D print for the planning of mitral valve surgery in which CT and TEE scans are combined into one flexible print. The flexible 3D print with exposed coronary arteries allows for assessment of the mitral valve regurgitation deficit and determine a surgical strategy because of the flexibility of the model, and as the LCA is exposed in this model, the surgeon can adapt his surgical approach based on the location of the LCA.

Sparse sampled visualization of ultrasonic guided waves for defect identification in plate structures

Ultrasonic wave visualization is an effective tool to identify defects along with their location and topology in guided wave structural health monitoring applications. However, conventional imaging techniques require relatively longer data acquisition time and large storage space. Reconstructing waves from sparse sampled images can potentially overcome such difficulties. In this regard, sparse sampling techniques based on random sampling and uniform sampling are explored in this paper. Specifically random sparse sampling using Poisson disk with biharmonic interpolation (PDS-BI) technique is shown to achieve defect identification with an image sparsity of 95% and a sensor density of 5λ2. On the other hand, a novel technique based on uniform sparse sampling with carrier multiplication (US-CM) is demonstrated to reconstruct the image with a sparsity of greater than 98% and a sensor density less than 2λ2. The performance of the proposed techniques has been quantified using Structural Similarity (SSIM) metric and validated through experiments. The reconstructed images are found to be in good agreement with those obtained by a dense array with much larger number of receivers. We also experimentally demonstrate the visualization of ultrasonic wave propagation in a metallic plate using a surface-bonded fiber Bragg grating sensor as an alternative to the conventional sensor.

Probability propagation for faster and efficient point cloud segmentation using a neural network

Neural networks (NN) have shown promising performance in point cloud segmentation (PCS). However, the measured points are too numerous to be used as model input at once. It results in a long inference time and high computational cost due to iterative sampling and inference. This study proposes Probability Propagation (PP) as a stochastic upsampling method. PP propagates the predicted probability of a sampled part of a point cloud into the other unpredicted points by considering proximity. By replacing the iterative inference of NN with PP, large point clouds can be dealt with quickly and efficiently. We investigated the effectiveness of PP using the ShapeNet benchmark on various settings: sampling methods (random, farthest point, and Poisson disk sampling) with sampling ratios (5%, 10%, 20%, 39%, and 78%) for NN and the stochastic mapping conditions (uniform, linear, cosine, Gaussian, and exponential distributions) for PP. Using NN with PP achieved higher performance and faster inference speed than when using NN alone. For the farthest point sampling method of 5% sampling ratio, NN+PP improved the instance mIoU by 2.457%p with 102 times faster speed compared to that when using NN alone. The result indicates that PP can significantly contribute to the improvement of performance and efficiency in PCS when used in edge AI systems.

Highly accelerated intracranial time-of-flight magnetic resonance angiography using wave-encoding.

To develop an accelerated 3D intracranial time-of-flight (TOF) magnetic resonance angiography (MRA) sequence with wave-encoding (referred to as 3D wave-TOF) and to evaluate two variants: wave-controlled aliasing in parallel imaging (CAIPI) and compressed-sensing wave (CS-wave). A wave-TOF sequence was implemented on a 3 T clinical scanner. Wave-encoded and Cartesian k-space datasets from six healthy volunteers were retrospectively and prospectively undersampled with 2D-CAIPI sampling and variable-density Poisson disk sampling. 2D-CAIPI, wave-CAIPI, standard CS, and CS-wave schemes were compared at various acceleration factors. Flow-related artifacts in wave-TOF were investigated, and a set of practicable wave parameters was developed. Quantitative analysis of wave-TOF and traditional Cartesian TOF MRA was performed by comparing the contrast-to-background ratio between the vessel and background tissue in source images, and the structural similarity index measure (SSIM) between the maximum intensity projection images from accelerated acquisitions and their respective fully sampled references. Flow-related artifacts caused by the wave-encoding gradients in wave-TOF were eliminated by properly chosen parameters. Images from wave-CAIPI and CS-wave acquisitions had a higher SNR and better-preserved contrast than traditional parallel imaging (PI) and CS methods. Maximum intensity projection images from wave-CAIPI and CS-wave acquisitions had a cleaner background, with vessels that were better depicted. Quantitative analyses indicated that wave-CAIPI had the highest contrast-to-background ratio, SSIM, and vessel-masked SSIM among the sampling schemes studied, followed by the CS-wave acquisition. 3D wave-TOF improves the capability of accelerated MRA and provides better image quality at higher acceleration factors compared to traditional PI- or CS-accelerated TOF, suggesting the potential use of wave-TOF in cerebrovascular disease.

MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces

We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening the point clouds and new meshfree restriction/interpolation operators based on polyharmonic splines for transferring information between the coarsened point clouds. These are then combined with standard smoothing and operator coarsening methods in a V-cycle iteration. MGM is applicable to discretizations of elliptic PDEs based on various localized meshfree methods, including RBF finite differences (RBF-FD) and generalized finite differences (GFD). We test MGM both as a standalone solver and preconditioner for Krylov subspace methods on several test problems using RBF-FD and GFD and numerically analyze convergence rates, efficiency, and scaling with increasing point cloud sizes. We also perform a side-by-side comparison to algebraic multigrid methods for solving the same systems. Finally, we further demonstrate the effectiveness of MGM by applying it to three challenging applications on complicated surfaces: pattern formation, surface harmonics, and geodesic distance.

Modeling method for rock heterogeneities and multiple hydraulic fractures propagation based on homogenization approach and PHF-LSM

Hydraulic fracturing is an important technique to enhance the production rate of oil and gas. We extend the functions of Permeability-based Hydraulic Fracture, Level Set Method (PHF-LSM) by including homogenization approaches to take into account the influence of the heterogeneities of rock media at both mesoscale and macroscale during hydraulic fracture propagation. The center position pattern of mesoscale heterogeneities is generated by introducing the Fast Poisson Disk (FPD) approach with an inherent parameter controlling the randomly distributed inclusions, and we developed an algorithm to detect inclusion collision by binary image matrix calculation. The level set function is used to describe the distributed joints at the macroscale. Both numerical and theoretical homogenization approaches are applied to study the characteristics of the material properties of rock matrices with randomly distributed hard inclusions at the mesoscale. Based on these results, we adopt the Mori–Tanaka (MT) and the Halpin–Tsai (HT) methods to homogenize the elasticity parameters (elastic modulus and Poisson’s ratio) and the hydraulic conductivity of the rock material, respectively. The Voigt upper bound is applied to estimate the tensile strength of the rock material at the integration points. A series of numerical simulations first indicated that the proposed method can model multi-scale heterogeneous rock that contains both the influences of macro-heterogeneities, e.g., distributed joints, and meso-heterogeneities, e.g., randomly distributed inclusions. Second, the development of pore pressure and stress path varied at the injection point, on the fracture path and on a joint. Finally, both the macro- and meso- heterogeneities influenced the propagation of multiple hydraulic fractures with joints significantly influenced the propagation path of the fractures, and increased injection number Np enhanced the height of the equivalent fracture zone when Np<5.

Simulation of Elastic Wave Propagation Based on Meshless Generalized Finite Difference Method with Uniform Random Nodes and Damping Boundary Condition

When the grid-based finite difference (FD) method is used for elastic wavefield forward modeling, it is inevitable that the grid divisions will be inconsistent with the actual velocity interface, resulting in problems related to the stepped grid diffraction and inaccurate travel time of reflected waves. The generalized finite difference method (GFDM), which is based on the Taylor series expansion and weighted least square fitting, solves these problems. The partial derivative of the unknown parameters in the differential equation is represented by the linear combination of the function values of adjacent nodes. In this study, the Poisson disk node generation algorithm and the centroid Voronoi node adjustment algorithm were combined to obtain an even and random node distribution. The generated nodes fit the internal boundary more accurately for model discretization, without the presence of diffracted waves caused by the stepped grid. To avoid the instability caused by the introduction of boundary conditions, a Cerjan damping boundary condition was proposed for boundary reflection processing. The test results generated by the different models showed that the generalized finite difference method can effectively solve the problems related to inaccurate travel time of reflection waves and stepped grid diffraction.

Variable Density Filling Algorithm Based on Delaunay Triangulation.

The quality of the filling algorithm in additive manufacturing directly affects the strength of the part. The commonly used 3D printing filling algorithm at this stage is the classic filling algorithm. The density of each part in the filling region is the same, and there is a cavity structure in the transverse direction, which makes the strength of the part in the transverse direction lower. Therefore, this paper proposed a new filling algorithm—variable density filling algorithm based on Delaunay triangulation. First, we performed concave-polygon-convex decomposition on the filling area to form printing sub-regions; then, the filling density value was set according to the required intensity of each region, and we used the Poisson disk sampling algorithm to generate the filling point set. Finally, Delaunay triangulation was performed on the generated point set to generate filled traces. The comparison with the two commonly used classical filling algorithms proves that the algorithm can improve the strength of the part to a certain extent, and the printing time and the consumption of consumables will not increase significantly.

Poisson disk sampling with randomized satellite points for projected texture stereo

A stereo camera is fundamental for 3D sensing. We can only use simple stereo algorithms for real-time applications; however, it has low accuracy. Adding texture by projection is a solution to the problem. The system is called projected texture stereo. Projecting light patterns is essential and deeply related to the matching algorithm in the system. This article proposes a projected pattern and a new texture stereo camera system with a suitable stereo matching algorithm. Experimental results show that our system is superior to Intel RealSense, the commercially successful projected texture stereo camera.

Optimization of undersampling parameters for 3D intracranial compressed sensing MR angiography at 7 T.

Purpose3D time‐of‐flight MRA can accurately visualize the intracranial vasculature but is limited by long acquisition times. Compressed sensing reconstruction can be used to substantially accelerate acquisitions. The quality of those reconstructions depends on the undersampling patterns used. In this work, we optimize sets of undersampling parameters for various acceleration factors of Cartesian 3D time‐of‐flight MRA.MethodsFully sampled datasets, acquired at 7 Tesla, were retrospectively undersampled using variable‐density Poisson disk sampling with various autocalibration region sizes, polynomial orders, and acceleration factors. The accuracy of reconstructions from the different undersampled datasets was assessed using the vessel‐masked structural similarity index. Identified optimal undersampling parameters were then evaluated in additional prospectively undersampled datasets. Compressed sensing reconstruction parameters were chosen based on a preliminary reconstruction parameter optimization.ResultsFor all acceleration factors, using a fully sampled calibration area of 12 × 12 k‐space lines and a polynomial order of 2 resulted in the highest image quality. The importance of parameter optimization of the sampling was found to increase for higher acceleration factors. The results were consistent across resolutions and regions of interest with vessels of varying sizes and tortuosity. The number of visible small vessels increased by 7.0% and 14.2% when compared to standard parameters for acceleration factors of 7.2 and 15, respectively.ConclusionThe image quality of compressed sensing time‐of‐flight MRA can be improved by appropriate choice of undersampling parameters. The optimized sets of parameters are independent of the acceleration factor and enable a larger number of vessels to be visualized.

Range Aliasing Elimination for FMICW Radar With Uniform Sampling Bursts and Poisson Disk Inter-Burst Delays

As an improvement of regular frequency-modulated continuous-wave (FMCW) radar in transmitter-receiver isolation, frequency-modulated interrupted continuous-wave (FMICW) radar has many advantages such as high range resolution, low peak power and high duty cycle. However, the false targets introduced by range aliasing may interfere with radar performance when it comes to long-range detection. In this paper, a range aliasing elimination method for FMICW radar is proposed based on batch Poisson disk sampling (BPDS) and sparse reconstruction. The received echoes are sampled by the newly developed BPDS pattern, which consists of uniform sampling bursts and Poisson disk inter-burst delays, so that the echoes from the maximum unambiguous range can be collected. Taking advantages of the excellent spectrum anti-aliasing performance of BPDS, the range aliasing phenomenon can be effectively eliminated and the range-Doppler spectrum containing multiple targets can be accurately reconstructed by the Iterative Soft Thresholding like (IST-like) algorithm. Compared with the existing signal processing methods for FMICW radar, the proposed method can obtain a larger maximum detection range without range aliasing. The effectiveness of the proposed method is verified by simulations and experiments on real FMICW radar data.

Unambiguous Doppler Extension for FMCW Radar via Poisson Disk Sampling

The maximum unambiguous Doppler in classical saw-tooth frequency-modulated continuous wave (FMCW) radar is inherently limited by the sweep repetition frequency (SRF). In this letter, an unambiguous Doppler extension method for FMCW radar is proposed, based on the combination of Poisson disk sampling (PDS) and sparse recovery. The PDS is adopted in the slow time domain such that there are random intervals between adjacent transmitted sweeps and no overlaps. Taking advantages of the excellent spectrum antialiasing performance of PDS, the maximum unambiguous Doppler of FMCW radar can be extended without reducing the range resolution. Then, the iterative soft thresholding-like (IST-like) algorithm is utilized to reconstruct the accurate range-Doppler spectrum. Compared with the existing unambiguous Doppler extension methods, the proposed method performs better in multitarget and low signal-to-noise ratio (SNR) scenarios. The effectiveness of the proposed method is verified by the experiments on real FMCW radar data.

Low Discrepancy Sparse Phased Array Antennas.

Sparse arrays have grating lobes in the far field pattern due to the large spacing of elements residing in a rectangular or triangular grid. Random element spacing removes the grating lobes but produces large variations in element density across the aperture. In fact, some areas are so dense that the elements overlap. This paper introduces a low discrepancy sequence (LDS) for generating the element locations in sparse planar arrays without grating lobes. This nonrandom alternative finds an element layout that reduces the grating lobes while keeping the elements far enough apart for practical construction. Our studies consider uniform sparse LDS arrays with 86% less elements than a fully populated array, and numerical results are presented that show these sampling techniques are capable of completely removing the grating lobes of sparse arrays. We present the mathematical formulation for implementing an LDS generated element lattice for sparse planar arrays, and present numerical results on their performance. Multiple array configurations are studied, and we show that these LDS techniques are not impacted by the type/shape of the planar array. Moreover, in comparison between the LDS techniques, we show that the Poisson disk sampling technique outperforms all other approaches and is the recommended LDS technique for sparse arrays.

Fast data-driven learning of parallel MRI sampling patterns for large scale problems

In this study, a fast data-driven optimization approach, named bias-accelerated subset selection (BASS), is proposed for learning efficacious sampling patterns (SPs) with the purpose of reducing scan time in large-dimensional parallel MRI. BASS is applicable when Cartesian fully-sampled k-space measurements of specific anatomy are available for training and the reconstruction method for undersampled measurements is specified; such information is used to define the efficacy of any SP for recovering the values at the non-sampled k-space points. BASS produces a sequence of SPs with the aim of finding one of a specified size with (near) optimal efficacy. BASS was tested with five reconstruction methods for parallel MRI based on low-rankness and sparsity that allow a free choice of the SP. Three datasets were used for testing, two of high-resolution brain images (text {T}_{2}-weighted images and, respectively, text {T}_{1rho }-weighted images) and another of knee images for quantitative mapping of the cartilage. The proposed approach has low computational cost and fast convergence; in the tested cases it obtained SPs up to 50 times faster than the currently best greedy approach. Reconstruction quality increased by up to 45% over that provided by variable density and Poisson disk SPs, for the same scan time. Optionally, the scan time can be nearly halved without loss of reconstruction quality. Quantitative MRI and prospective accelerated MRI results show improvements. Compared with greedy approaches, BASS rapidly learns effective SPs for various reconstruction methods, using larger SPs and larger datasets; enabling better selection of sampling-reconstruction pairs for specific MRI problems.

Fast 3D time-domain airborne EM forward modeling using random under-sampling

The high sampling rate of airborne electromagnetic (AEM) systems can create huge data volumes, causing major challenges for three-dimensional (3D) electromagnetic modeling and inversions and constraining the practical applicability of AEM. Rapid and accurate forward modeling is the key to efficient 3D inversion. Here a new strategy for improving the efficiency of 3D time-domain AEM forward modeling is presented, based on compressed-sensing theory combined with the finite-volume method. A Poisson disk random under-sampling method was used to obtain random survey stations and to calculate AEM responses via the finite-volume method at these sampling stations. Coefficients from the curvelet transform with anisotropic characteristics for sparse expression were used to analyze the sparsity of AEM data, with the AEM responses of all survey stations being obtained by reconstruction. Key factors influencing the accuracy of the reconstruction are also discussed, including the sampling method and rate, the sparse transformation, and the noise. To test the effectiveness of the method, reconstructed results were compared with those from traditional schemes for forward modeling using all stations. Results indicate that the new strategy requires only 20% ~ 50% of samples to achieve high-precision reconstruction of the AEM signal even for complex geoelectrical structures, and the efficiency of 3D forward modeling can be enhanced by a factor of two to five, laying a foundation for fast AEM inversions of large datasets and complex models.

Effect of microstructure on dynamic compressive behavior of cellular materials

It is known that the microstructure of cellular materials has a significant impact on their compressive properties. To study these phenomena, a hierarchical Poisson disk sampling algorithm and Voronoi partitioning were used to create a 3D numerical analysis model of cellular materials. In this study, we prepared random, periodic, and ellipsoidal cell models to investigate the effects of cell shape randomness and oblateness. Numerical experiments were performed using the finite element method solver RADIOSS. In the numerical analysis, an object collided with the cellular materials at a velocity of 25 m/s. The results showed that the flow stress of the random cell model was higher than that of the periodic cell model. Further, it was found that the aspect ratio of the cell shape has a significant impact on the mechanical properties of cellular materials.

Unambiguous range extension for pulse‐Doppler radar via Poisson disk sampling

Unambiguous range extension for pulse‐Doppler radar via Poisson disk sampling

A Singular Value Decomposition based Maximal Poisson-disk Sampling for adaptive Digital Elevation Model simplification.

The proposed method is to do simplification for Digital Elevation Model (DEM), which uses a few of original nodes representing the terrain surface while maintaining the accuracy. The original DEM nodes are sampled using the Maximal Poisson-disk Sampling (MPS), in which, the disk’s size of each sample is computed on basis of the Singular Value Decomposition (SVD). MPS can generate the hyper-uniformly distributed samples and was taken to do DEM adaptive sampling by being combined with the geodesic metric. However, the geodesic distance computation is complex and the requirement for memory is high. As such, this paper proposes an extension of the classic MPS based method for selecting quasi-randomly distributed points from DEM nodes based on the distribution of eigenvalues, accounting for surface heterogeneity. To achieve this objective, uniform MPS is conducted to sample the DEM nodes by setting the related disk radius to be inversely proportional to the local terrain complexity, which is defined as an index expressing the local terrain variation. Then, the geodesic metric related parameters are implicitly contained in the defined index. As a result, more samples are concentrated in the rugged regions, and vice versa. The proposed method shows better perfermance, at least the results are comparable with the geodesic distance based Poisson disk sampling method. Meanwhile, it greatly accelerates the sampling process and reduces the memory cost.

Using Poisson Disk Sampling to Render Oil Particles at Sea

Fluid simulation is one of the most complex tasks in three-dimensional simulation. Specifically, in the case of oil spills at sea, the oil film constantly interacts and is influenced by the environment, thus making its composition and properties change over time. In this paper, we tackle this problem by using both Lehr's spreading model and Hoult's drifting model to build the oil spill physical model. Unlike previous studies that only applied the Poisson disk algorithm to static and solid objects, we applied it in a three-dimensional space to divide the oil film into fluid particles. The track of oil particles under the influence of waves, wind, and currents is rendered by the Unity3D tool with C# programming language, which vividly and realistically simulates the collision of oil particles on the ocean scene with obstacles such as buoys and small islands. The result of this research can be used to predict oil spill direction, thus providing the solution to respond and minimize the damage caused by oil spills at sea. We also discuss some improvements to our model by using the Marching cube algorithm to render the Metaball model.

A Tractable Model for Wirelessly Powered Networks With Energy Correlation

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored. While this leads to remarkably simple results for key performance metrics, it is typically not realistic and accurate. Considering the accuracy, tractability, and practicability tradeoffs, this paper introduces and promotes the Poisson disk process (PDP) as a model for the energized nodes that succeed in harvesting energy. To show that the model leads to analytically tractable results in several cases of interest, we derive its first and second moment densities, which fully characterize the PDP. Besides, we also provide tight bounds for its probability generating functional as well as its contact and nearest-neighbor distance distributions. Then, to show that the model is relevant for wirelessly powered networks-which all have positive energy correlation-we provide two approaches to fit the PDP to a given energized point process incorporating practical energy harvesting factors. Further, we derive the success probability in the information transmission phase, where the distribution of the active transmitters is modeled by a PDP. It turns out that the resulting PDP can closely model the distribution of actual energized nodes in terms of the success probability and other statistics while preserving analytical tractability.