Bounds of star discrepancy for HSFC-based sampling

In this paper, we focus on estimating the probabilistic upper bounds of star discrepancy for Hilbert space filling curve (HSFC) sampling. The main idea is the stratified random sampling method, but the strict condition for sampling number $N=m^d$ of jittered sampling is removed. We inherit the advantages of this sampling and get better results than Monte Carlo (MC) sampling.Comment: 10 page

Distributing Monte Carlo Errors as a Blue Noise in Screen Space by Permuting Pixel Seeds Between Frames

International audienceRecent work has shown that distributing Monte Carlo errors as a blue noise in screen space improves the perceptual quality of rendered images. However, obtaining such distributions remains an open problem with high sample counts and high-dimensional rendering integrals. In this paper, we introduce a temporal algorithm that aims at overcoming these limitations. Our algorithm is applicable whenever multiple frames are rendered, typically for animated sequences or interactive applications. Our algorithm locally permutes the pixel sequences (represented by their seeds) to improve the error distribution across frames. Our approach works regardless of the sample count or the dimensionality and significantly improves the images in low-varying screen-space regions under coherent motion. Furthermore, it adds negligible overhead compared to the rendering times

End-to-end Sampling Patterns

Sample patterns have many uses in Computer Graphics, ranging from procedural object placement over Monte Carlo image synthesis to non-photorealistic depiction. Their properties such as discrepancy, spectra, anisotropy, or progressiveness have been analyzed extensively. However, designing methods to produce sampling patterns with certain properties can require substantial hand-crafting effort, both in coding, mathematical derivation and compute time. In particular, there is no systematic way to derive the best sampling algorithm for a specific end-task. Tackling this issue, we suggest another level of abstraction: a toolkit to end-to-end optimize over all sampling methods to find the one producing user-prescribed properties such as discrepancy or a spectrum that best fit the end-task. A user simply implements the forward losses and the sampling method is found automatically -- without coding or mathematical derivation -- by making use of back-propagation abilities of modern deep learning frameworks. While this optimization takes long, at deployment time the sampling method is quick to execute as iterated unstructured non-linear filtering using radial basis functions (RBFs) to represent high-dimensional kernels. Several important previous methods are special cases of this approach, which we compare to previous work and demonstrate its usefulness in several typical Computer Graphics applications. Finally, we propose sampling patterns with properties not shown before, such as high-dimensional blue noise with projective properties

Analysis of Sample Correlations for Monte Carlo Rendering

Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.publishe

TOWARDS A COMPUTATIONAL MODEL OF RETINAL STRUCTURE AND BEHAVIOR

Human vision is our most important sensory system, allowing us to perceive our surroundings. It is an extremely complex process that starts with light entering the eye and ends inside of the brain, with most of its mechanisms still to be explained. When we observe a scene, the optics of the eye focus an image on the retina, where light signals are processed and sent all the way to the visual cortex of the brain, enabling our visual sensation. The progress of retinal research, especially on the topography of photoreceptors, is often tied to the progress of retinal imaging systems. The latest adaptive optics techniques have been essential for the study of the photoreceptors and their spatial characteristics, leading to discoveries that challenge the existing theories on color sensation. The organization of the retina is associated with various perceptive phenomena, some of them are straightforward and strictly related to visual performance like visual acuity or contrast sensitivity, but some of them are more difficult to analyze and test and can be related to the submosaics of the three classes of cone photoreceptors, like how the huge interpersonal differences between the ratio of different cone classes result in negligible differences in color sensation, suggesting the presence of compensation mechanisms in some stage of the visual system. In this dissertation will be discussed and addressed issues regarding the spatial organization of the photoreceptors in the human retina. A computational model has been developed, organized into a modular pipeline of extensible methods each simulating a different stage of visual processing. It does so by creating a model of spatial distribution of cones inside of a retina, then applying descriptive statistics for each photoreceptor to contribute to the creation of a graphical representation, based on a behavioral model that determines the absorption of photoreceptors. These apparent color stimuli are reconstructed in a representation of the observed scene. The model allows the testing of different parameters regulating the photoreceptor's topography, in order to formulate hypothesis on the perceptual differences arising from variations in spatial organization