Poisson Disk Research Articles

Surface reconstruction through poisson disk sampling.

This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points are sensitive to nearest neighbor definition. It is obvious that the reconstructed model is the level of detail of original points. Hence, our main motivation is to deal with the redundant scattered points. In implementation, Poisson disk sampling is taken to select seeds and helps to produce the Voronoi diagram. Adaptive reconstructions can be achieved by slightly changing the uniform strategy in selecting seeds. Behaviors of this method are investigated and accuracy evaluations are done. Experimental results show the proposed method is reliable and effective.

Poisson disk sampling through disk packing

Poisson disk sampling is an important problem in computer graphics and has a wide variety of applications in imaging, geometry, rendering, etc. In this paper, we propose a novel Poisson disk sampling algorithm based on disk packing. The key idea uses the observation that a relatively dense disk packing layout naturally satisfies the Poisson disk distribution property that each point is no closer to the others than a specified minimum distance, i.e., the Poisson disk radius. We use this property to propose a relaxation algorithm that achieves a good balance between the random and uniform properties needed for Poisson disk distributions. Our algorithm is easily adapted to image stippling by extending identical disk packing to unequal disks. Experimental results demonstrate the efficacy of our approaches.

Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated cardiac MRI.

For the application of compressive sensing to parallel MRI, Poisson disk sampling (PDS) has been shown to generate superior results compared with random sampling methods. However, due to its limited flexibility to incorporate additional constraints, PDS is not readily extendible to dynamic applications. Here, we propose and validate a pseudo-random sampling technique that allows incorporating constraints specific to dynamic imaging. The proposed sampling scheme, called variable density incoherent spatiotemporal acquisition (VISTA), is based on constrained minimization of Riesz energy on a spatiotemporal grid. Data from both a digital phantom and real-time cine were used to compare VISTA with uniform interleaved sampling (UIS) and variable density random sampling (VRS). The image quality was assessed qualitatively and quantitatively. VISTA improved the trade-off between noise and sharpness. Also, VISTA produced diagnostic quality images at an acceleration rate of 15, whereas UIS and VRS images degraded below the diagnostic threshold at lower acceleration rates. VISTA generates spatiotemporal sampling patterns with high levels of uniformity and incoherence, while maintaining a constant temporal resolution. Using a small pilot study, VISTA was shown to produce diagnostic quality images at acceleration rates up to 15.

Four-dimensional SAR imaging algorithm using Bayesian compressive sensing

The compressive sensing (CS) based 4-D synthetic aperture radar (SAR) imaging method performs well in the case of high signal-to-noise ratios (SNR). However, in the presence of strong noises, the performance of CS-based method degrades and the number of false targets increases rapidly. In this paper, a novel 4-D SAR imaging method is proposed based on Bayesian compressive sensing (BCS). Assume that the target scattering field follows the Cauchy distribution, the 4-D SAR imaging is transformed into signal reconstruction via maximum a posteriori estimation. In addition, Poisson disk sampling is utilized to generate the radar positions of 4-D SAR in the baseline-time plane. Experimental results show that the proposed method is capable of effective suppression of the noise by exploiting the sparseness prior distribution of the image scene, and a well-focused image could also be achieved even under the condition of low SNR.

Adaptive image sampling through establishing 3D geometrical model

Adaptive sampling for high dimensional manifold attracts much attention from related fields. The principal curvature based strategy is one of the popular methods. However, principal curvature estimation remains an open problem. Considering the relationship between geodesics and the principal curvatures of manifold, we transform the optimized sampling density computation into the problem of uniform sampling in the geodesic metric of manifold. Therefore, two well studied uniform sampling methods such as Poisson disk and farthest point strategy are used. For image sampling, a 3D geometrical metric model is built based on mean shift. Mean shift value is applied to describe the image grey information and taken as the height of this model. Uniform sampling is implemented to generate samples with blue noise properties on the 3D model surface. Then, adaptive results are obtained when these samples are projected back to the original 2D image. In contrast to previous methods, this strategy is flexible and can be easily extended to unorganized points simplification or mesh coarsening. Extensive experiments demonstrated the effectiveness of the proposed method.

3D ear recognition using local salience and principal manifold

As an emerging class of biometrics, human ear has drawn significant attention in recent years. In this paper, we propose a novel 3D ear shape matching and recognition system. First, we propose a novel method for computing saliency value of each point on 3D ear point clouds, which is based on the Gaussian-weighted average of the mean curvature and can be used to sort the keypoints accordingly. Then we propose the optimal selection of the salient key points using the Poisson Disk Sampling. Finally, we fit a surface to the neighborhood of each salient keypoint using the quadratic principal manifold method, establishing the local feature descriptor of each salient keypoint. The experimental results on ear shape matching show that, compared with other similar methods, the proposed system has higher approximation precision on shape feature detection and higher matching accuracy on the ear recognition.

Fast adaptive blue noise on polygonal surfaces

This paper proposes a novel method for the computation of hierarchical Poisson disk samplings on polygonal surfaces. The algorithm generates a pointerless hierarchical structure such that each level is a uniform Poisson disk sampling and a subset of the next level. As the main result, given a dynamically-varying importance sampling function defined over a surface, the hierarchy is capable of generating adaptive samplings with blue noise characteristics, temporal-coherence and real-time computation. Classical algorithms produce hierarchies in tight ratios, which is a serious bottleneck specially for a large number of samples. Instead, our method uses sparse ratios and decreases the adaptation error of the hierarchy through a fast optimization process. Therefore, we save a considerable amount of time (up to 74% in our experiments) while preserving the good blue noise properties. We present applications on Non-Photo Realistic rendering (NPR), more specifically, on surface stippling effects. First, we apply our method by taking illumination to be the importance sampling to shade the surface, and second, we dynamically deform a surface with a predefined stippled texture.

An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces

Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in IR(n). To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

A parallel algorithm for improving the maximal property of Poisson disk sampling

This paper presents a simple yet effective algorithm to improve an arbitrary Poisson disk sampling to reach the maximal property, i.e., no more Poisson disk can be inserted. Taking a non-maximal Poisson disk sampling as input, our algorithm efficiently detects the regions allowing additional samples and then generates Poisson disks in these regions. The key idea is to convert the complicated plane or space searching problem into a simple searching on circles or spheres, which is one dimensional lower than the original sampling domain. Our algorithm is memory efficient and flexible, which generates maximal Poisson disk sampling in an arbitrary 2D polygon or 3D polyhedron. Moreover, our parallel algorithm can be extended from the Euclidean space to curved surfaces in an intrinsic manner. Thanks to its parallel structure, our method can be implemented easily on modern graphics hardware. We have observed significance performance improvement compared to the existing techniques.

Application of randomized sampling schemes to curvelet‐based sparsity‐promoting seismic data recovery

ABSTRACTReconstruction of seismic data is routinely used to improve the quality and resolution of seismic data from incomplete acquired seismic recordings. Curvelet‐based Recovery by Sparsity‐promoting Inversion, adapted from the recently‐developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampled seismic data. Like traditional Fourier‐based methods, it performs best when used in conjunction with randomized subsampling, which converts aliases from the usual regular periodic subsampling into easy‐to‐eliminate noise. By virtue of its ability to control gap size, along with the random and irregular nature of its sampling pattern, jittered (sub)sampling is one proven method that has been used successfully for the determination of geophone positions along a seismic line. In this paper, we extend jittered sampling to two‐dimensional acquisition design, a more difficult problem, with both underlying Cartesian and hexagonal grids. We also study what we term separable and non‐separable two‐dimensional jittered samplings. We find hexagonal jittered sampling performs better than Cartesian jittered sampling, while fully non‐separable jittered sampling performs better than separable jittered sampling. Two other 2D randomized sampling methods, Poisson Disk sampling and Farthest Point sampling, both known to possess blue‐noise spectra, are also shown to perform well.

Surrogate modeling for the fast optimization of energy systems

While software simulations in the building technology field are essential for designing efficient systems, for specific applications, the tools currently available are computationally too expensive. This paper presents a novel approach for the fast computation of accurate simulation results and demonstrates its efficacy for solving a multiobjective optimization problem.A surrogate modeling approach is proposed, which is based on an effective interpolation algorithm and an optimal distribution of sampling nodes. The highest accuracy is shown to be achieved by a Poisson disk node distribution and an interpolation function developed from a cubic radial basis function. Furthermore, since global interpolation algorithms in high-dimensional spaces are fundamentally inefficient, a local adaptation is developed. The fidelity of the surrogate model is shown to generalize to higher dimensions with respect to the average number of nodes per dimension ηs.The application potential is tested on a case study consisting of a multiobjective design optimization problem. The results show that the surrogate and the fine model converge to the same solution. Being 150 times faster than the original model, the surrogate model is thus a valid choice for computationally demanding applications.

Three stochastic measurement schemes for direction-of-arrival estimation using compressed sensing method

We focus on the design of the measurement schemes in the compressed sensing (CS) method for direction-of-arrival estimation, and three stochastic measurement schemes are considered. In the perspectives of average apertures and incoherences, we give a detailed mathematical analysis for these schemes. The superiorities in incoherences for these schemes are illustrated, compared with the popularly used random Gaussian measurement scheme. Then we demonstrate that the newly used Poisson disk sampling scheme and uniform jittered sampling scheme can obtain relatively large average apertures by using a proposed computational method. Finally, several simulations are implemented to evaluate the performances of the CS methods with these stochastic measurement schemes.

Anisotropic Lp Poisson Disk Sampling for NPR Image with Adaptively Shaped Pieces

Anisotropic Lp Poisson Disk Sampling for NPR Image with Adaptively Shaped Pieces

Accelerated 4D flow imaging with variable-density cartesian undersampling and parallel imaging reconstruction

Background 4D flow CMR is hampered by long scan times. We investigated an effective undersampling scheme and an efficient parallel image reconstruction method to achieve highly accelerated 4D flow CMR with high reconstruction accuracy. Methods Variable-density Poisson Disk Distribution (VD-PDD) undersampling was applied for 4D flow imaging. By applying VD-PDD independently at each time frame (Figure 1a), we achieved random undersampling in both the ky-kz plane and temporal domains. In addition, we applied an improved initial solution for SPIRIT to significantly improve reconstruction accuracy and robustness. We explored the different undersampling and reconstruction algorithms on fully sampled 4D flow CMR data acquired on a 1.5T Siemens Avanto scanner with a 5-ch coil in 3 volunteers (venc=200 cm/s, FOV=320x240x55 mm 3 , matrix=128x96x22, ~18 time frames of 35 ms temporal resolution, ~25 mins scan time). VD-PDD (center 12x12 fully sampled; R=6) was retrospectively applied to the full data. Composite data was generated by sharing data from other frames based on the temporal distance to the time frame of interest (Figure 1b). k-space was filled to the extent possible from selected adjacent time frames. The images reconstructed from the composite data through time (Figure 1c) were used as initial solutions for SPIRIT. This is denoted as method “M1”. We also generated composite data that shared limited data from other frames (Figure 1d) to mitigate undersampling of the data. Then SPIRIT with the proposed initial solutions was applied to this new composite data through time (Figure 1e), referred to as “M2”. Flow-waveforms in the ascending (AA) and descending aorta (DA) were measured in 5 locations in each subject (Figure 2d-e). Relative error was calculated with the fully sampled data as reference. Results Both reconstruction methods were successfully applied to all subjects. Velocity images compared favorably to the fully sampled velocity image (Figure 2a-c). The relative error in flow measurement was 0.05±0.01 (AA, M1), 0.04 ±0.01 (AA, M2), 0.09±0.05 (DA, M1), and 0.07±0.02 (DA, M2). Both proposed methods achieved outstanding performance with 6-fold acceleration. Of the two, M2 had smaller errors, indicating that an effective temporal sharing scheme combined with VD-PDD and SPIRIT could be a potential way of improving image quality without sacrificing temporal resolution. Conclusions We employed undersampling patterns based on VD-PDD, parallel imaging method SPIRIT, and a temporal sharing scheme to achieve 6-fold accelerated 4D flow CMR with a small number of coils. The qualitative and quantitative comparisons indicate the potential of our methods to achieve highly accelerated flow imaging with maintained accuracy. Future work includes implementation of prospective undersampling.

Poisson disk sampling in geodesic metric for DEM simplification

To generate highly compressed digital elevation models (DEMs) with fine details, the method of Poisson disk sampling in geodesic metric is proposed. The main idea is to uniformly pick points from DEM nodes in geodesic metric, resulting in terrain-adaptive samples in Euclidean metric. This method randomly selects point from mesh nodes and then judges whether this point can be accepted in accordance with the related geodesic distances from the sampled points. The whole process is repeated until no more points can be selected. To further adjust the sampling ratios in different areas, weighted geodesic distance, which is in relation to terrain characteristics, are introduced. In addition to adaptability, sample distributions are well visualised. This method is simple and easy to implement. Cases are provided to illustrate the feasibility and superiority of the proposed method.

Coherent streamline generation for 2-D vector fields

Visualizing 2-D vector fields using streamlines is one popular flow visualization technique. Standard streamline generation algorithms compute the density of streamlines across the domain, detect features, and employ customized rules to emphasize features. In this process, feature characterization and visual clarity are heavily considered. Simultaneously preserving the temporal coherence for time-varying vector fields, however, remains a challenge. In this paper, we present a coherent and feature-aware streamline generation algorithm by employing a feature-guided streamline seeding technique and a coherent streamline placing scheme. For each frame, a feature map is first computed with critical points or the Finite-Time Lyapunov Exponent (FTLE) approach, and is used to initialize a set of seeds by leveraging the Poisson Disk distribution. These seeds are further optimized by using a deformation-driven moving mesh method. To preserve the temporal coherence, the streamlines generated from the seeds are individually checked subject to their correspondences to the ones in the previous frame. Subsequently, additional streamlines are sequentially inserted in low-density regions. We demonstrate our algorithm on both Computation Fluid Dynamics (CFD) and non-CFD datasets, and compare it with the recent literature.

KD-tree based parallel adaptive rendering

Multidimensional adaptive sampling technique is crucial for generating high quality images with effects such as motion blur, depth-of-field and soft shadows, but it costs a lot of memory and computation time. We propose a novel kd-tree based parallel adaptive rendering approach. First, a two-level framework for adaptive sampling in parallel is introduced to reduce the computation time and control the memory cost: in the prepare stage, we coarsely sample the entire multidimensional space and use kd-tree structure to separate it into several multidimensional subspaces; in the main stage, each subspace is refined by a sub kd-tree and rendered in parallel. Second, novel kd-tree based strategies are introduced to measure space’s error value and generate anisotropic Poisson disk samples. The experimental results show that our algorithm produces better quality images than previous ones.

Approximate Poisson disk sampling on mesh

Poisson disk sampling has been widely used in many applications such as remeshing, procedural texturing, object distribution, illumination, etc. While 2D Poisson disk sampling is intensively studied in recent years, direct Poisson disk sampling on 2-manifold surface is rarely covered. In this paper, we present a novel framework which generates approximate Poisson disk distribution directly on mesh, a discrete representation of 2-manifold surfaces. Our framework is easy to implement and provides extra flexibility to specified sampling issues like feature-preserving sampling and adaptive sampling. We integrate the tensor voting method into feature detection and adaptive sample radius calculation. Remeshing as a special downstream application is also addressed. According to our experiment results, our framework is efficient, robust, and widely applicable.

Efficient and good Delaunay meshes from random points

We present a Conforming Delaunay Triangulation (CDT) algorithm based on maximal Poisson disk sampling. Points are unbiased, meaning the probability of introducing a vertex in a disk-free subregion is proportional to its area, except in a neighborhood of the domain boundary. In contrast, Delaunay refinement CDT algorithms place points dependent on the geometry of empty circles in intermediate triangulations, usually near the circle centers. Unconstrained angles in our mesh are between 30° and 120°, matching some biased CDT methods. Points are placed on the boundary using a one-dimensional maximal Poisson disk sampling. Any triangulation method producing angles bounded away from 0° and 180° must have some bias near the domain boundary to avoid placing vertices infinitesimally close to the boundary.Random meshes are preferred for some simulations, such as fracture simulations where cracks must follow mesh edges, because deterministic meshes may introduce non-physical phenomena. An ensemble of random meshes aids simulation validation. Poisson-disk triangulations also avoid some graphics rendering artifacts, and have the blue-noise property.We mesh two-dimensional domains that may be non-convex with holes, required points, and multiple regions in contact. Our algorithm is also fast and uses little memory. We have recently developed a method for generating a maximal Poisson distribution of n output points, where n=Θ(Area/r2) and r is the sampling radius. It takes O(n) memory and O(nlogn) expected time; in practice the time is nearly linear. This, or a similar subroutine, generates our random points. Except for this subroutine, we provably use O(n) time and space. The subroutine gives the location of points in a square background mesh. Given this, the neighborhood of each point can be meshed independently in constant time. These features facilitate parallel and GPU implementations. Our implementation works well in practice as illustrated by several examples and comparison to Triangle.

階層的 Poisson Disk Sampling 法を用いた貼り絵風画像生成法

階層的 Poisson Disk Sampling 法を用いた貼り絵風画像生成法