Parallel Poisson disk sampling with spectrum analysis on surfaces

Bowers, John C.; Wang, Rui; Wei, Li-Yi; Maletz, David

doi:10.1145/1866158.1866188

Cited by 44 publications

(42 citation statements)

References 43 publications

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“…However, these methods need pre-computed parameterizations and are thus unsuitable for applications with dynamic geometry. The extensions of dart throwing method for surfaces are described in [26], [27], [28]. The computational complexity and the approximation of the geodesic metric are the major concerns in these extensions.…”

Section: Related Workmentioning

confidence: 99%

“…The density function is defined according to the curvature of the surface, so that regions of higher curvature are of higher density distribution. We compare our CapCVT method with other methods by the spectral analysis method proposed by Bowers et al [28] and the results are shown in Fig. 8.…”

Section: Extension To Surfacesmentioning

confidence: 99%

“…First, we introduce the generalized Leibniz rule [43], also called the LeibnizReynolds transport theorem, concerning the differentiation under the integral sign. CapCVT method using different λ's, the CVT method (which is equivalent to our method with λ = 0), the retiling method [42], and Bowers et al's method [28]. The radial means (dark) and anisotropy (orange) are generated using the method proposed by [28].…”

Section: Properties Of the Capcvt Energymentioning

confidence: 99%

“…CapCVT method using different λ's, the CVT method (which is equivalent to our method with λ = 0), the retiling method [42], and Bowers et al's method [28]. The radial means (dark) and anisotropy (orange) are generated using the method proposed by [28].…”

Section: Properties Of the Capcvt Energymentioning

confidence: 99%

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Variational Blue Noise Sampling

Chen

Yuan

Choi

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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Abstract-Blue noise point sampling is one of the core algorithms in computer graphics. In this paper we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including non-photorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces.

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Section: Related Workmentioning

confidence: 99%

Section: Extension To Surfacesmentioning

confidence: 99%

Section: Properties Of the Capcvt Energymentioning

confidence: 99%

Section: Properties Of the Capcvt Energymentioning

confidence: 99%

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Variational Blue Noise Sampling

Chen

Yuan

Choi

et al. 2012

IEEE Trans. Visual. Comput. Graphics

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“…This algorithm uses the voxelization of the model to generate random samples with controlled intra-distances. Other sampling strategies providing with uniform distribution of sample points on a surface are based on the farthest point [39] and Poisson disk sampling [40], which require the computation of geodesic distances.…”

Section: Point Sampling Approachesmentioning

confidence: 99%

Robust surface registration using N-points approximate congruent sets

Yao

Ruggeri

Taddei

et al. 2011

EURASIP J. Adv. Signal Process.

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Scans acquired by 3D sensors are typically represented in a local coordinate system. When multiple scans, taken from different locations, represent the same scene these must be registered to a common reference frame. We propose a fast and robust registration approach to automatically align two scans by finding two sets of N-points, that are approximately congruent under rigid transformation and leading to a good estimate of the transformation between their corresponding point clouds. Given two scans, our algorithm randomly searches for the best sets of congruent groups of points using a RANSAC-based approach. To successfully and reliably align two scans when there is only a small overlap, we improve the basic RANSAC random selection step by employing a weight function that approximates the probability of each pair of points in one scan to match one pair in the other. The search time to find pairs of congruent sets of N-points is greatly reduced by employing a fast search codebook based on both binary and multi-dimensional lookup tables. Moreover, we introduce a novel indicator of the overlapping region quality which is used to verify the estimated rigid transformation and to improve the alignment robustness. Our framework is general enough to incorporate and efficiently combine different point descriptors derived from geometric and texture-based feature points or scene geometrical characteristics. We also present a method to improve the matching effectiveness of texture feature descriptors by extracting them from an atlas of rectified images recovered from the scan reflectance image. Our algorithm is robust with respect to different sampling densities and also resilient to noise and outliers. We demonstrate its robustness and efficiency on several challenging scan datasets with varying degree of noise, outliers, extent of overlap, acquired from indoor and outdoor scenarios.

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Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

Ebeida

Mitchell

Patney

et al. 2014

Mathematics and Visualization

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We review our recent progress on efficient algorithms for generating wellspaced samples of high dimensional data, and for exploring and characterizing these data, the underlying domain, and functions over the domain. To our knowledge, these techniques have not yet been applied to computational topology, but the possible connections are worth considering. In particular, computational topology problems often have difficulty in scaling efficiently, and these sampling techniques have the potential to drastically reduce the size of the data over which these computational topology algorithms must operate. We summarize the definition of these sample distributions; algorithms for generating them in low, moderate, and high dimensions; and applications in mesh generation, rendering, motion planning and simulation.

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Parallel Poisson disk sampling with spectrum analysis on surfaces

Cited by 44 publications

References 43 publications

Variational Blue Noise Sampling

Variational Blue Noise Sampling

Robust surface registration using N-points approximate congruent sets

Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

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