Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Fourier Analysis of Stochastic Sampling Strategies for Assessing Bias and Variance in Integration

Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these high-dimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image. We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.</jats:p

ART-Owen Scrambling

We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols, and equip each symbol with a scrambling code that affects all descendant nodes. We nominate the grammar of adaptive regular tiles (ART) derived from the repetition-avoiding Thue-Morse word, and we discuss its potential advantages and shortcomings. Our algorithm has many advantages, including random access to samples, fixed time complexity, GPU friendliness, and scalability to any memory budget. Further, it provides two unique features over known methods: it admits optimization, and it is invertible, enabling screen-space scrambling of the high-dimensional Sobol sampler.Comment: To appear at SIGGRAPH Asia 202

Variational blue noise sampling

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 nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces. © 1995-2012 IEEE.published_or_final_versio

Scalable multi-class sampling via filtered sliced optimal transport

We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We demonstrate the effectiveness of our framework on various sampling applications like stippling, object placement, and Monte-Carlo integration. We a derive multi-class error bound for perceptual rendering error which can be minimized using our optimization. We provide source code at https://github.com/iribis/filtered-sliced-optimal-transport.Comment: 15 pages, 17 figures, ACM Trans. Graph., Vol. 41, No. 6, Article 261. Publication date: December 202

Efficient Product Importance Sampling using Hierarchical Thresholding

We present an efficient method for importance sampling the product of multiple functions. Our algorithm computes a quick approximation of the product on-the-fly, based on hierarchical representations of the Local maxima and averages of the individual terms. Samples are generated by exploiting the hierarchical properties of many low-discrepancy sequences, and thresholded against the estimated product. We evaluate direct illumination by sampling the triple product of environment map lighting, surface reflectance, and a visibility function estimated per pixel. Our results show considerable noise reduction compared to existing state-of-the-art methods using only the product of lighting and BRDF