677 research outputs found
Fast Blue-Noise Generation via Unsupervised Learning
āBlue noise is known for its uniformity in the spatial
domain, avoiding the appearance of structures such as voids and
clusters. Because of this characteristic, it has been adopted in
a wide range of visual computing applications, such as image
dithering, rendering and visualisation. This has motivated the
development of a variety of generative methods for blue noise,
with different trade-offs in terms of accuracy and computational
performance. We propose a novel unsupervised learning approach that leverages a neural network architecture to generate
blue noise masks with high accuracy and real-time performance,
starting from a white noise input. We train our model by
combining three unsupervised losses that work by conditioning
the Fourier spectrum and intensity histogram of noise masks
predicted by the network. We evaluate our method by leveraging
the generated noise for two applications: grayscale blue noise
masks for image dithering, and blue noise samples for Monte
Carlo integration
Digital Color Imaging
This paper surveys current technology and research in the area of digital
color imaging. In order to establish the background and lay down terminology,
fundamental concepts of color perception and measurement are first presented
us-ing vector-space notation and terminology. Present-day color recording and
reproduction systems are reviewed along with the common mathematical models
used for representing these devices. Algorithms for processing color images for
display and communication are surveyed, and a forecast of research trends is
attempted. An extensive bibliography is provided
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
Deep Point Correlation Design
Designing point patterns with desired properties can require substantial
effort, both in hand-crafting coding and mathematical derivation. Retaining
these properties in multiple dimensions or for a substantial number of points
can be challenging and computationally expensive. Tackling those two issues,
we suggest to automatically generate scalable point patterns from design
goals using deep learning. We phrase pattern generation as a deep composition of weighted distance-based unstructured filters. Deep point pattern
design means to optimize over the space of all such compositions according to
a user-provided point correlation loss, a small program which measures a patternās fidelity in respect to its spatial or spectral statistics, linear or non-linear
(e. g., radial) projections, or any arbitrary combination thereof. Our analysis
shows that we can emulate a large set of existing patterns (blue, green, step,
projective, stair, etc.-noise), generalize them to countless new combinations
in a systematic way and leverage existing error estimation formulations to
generate novel point patterns for a user-provided class of integrand functions.
Our point patterns scale favorably to multiple dimensions and numbers of
points: we demonstrate nearly 10 k points in 10-D produced in one second
on one GPU. All the resources (source code and the pre-trained networks)
can be found at https://sampling.mpi-inf.mpg.de/deepsampling.html
Perceptual error optimization for Monte Carlo rendering
Realistic image synthesis involves computing high-dimensional light transport
integrals which in practice are numerically estimated using Monte Carlo
integration. The error of this estimation manifests itself in the image as
visually displeasing aliasing or noise. To ameliorate this, we develop a
theoretical framework for optimizing screen-space error distribution. Our model
is flexible and works for arbitrary target error power spectra. We focus on
perceptual error optimization by leveraging models of the human visual system's
(HVS) point spread function (PSF) from halftoning literature. This results in a
specific optimization problem whose solution distributes the error as visually
pleasing blue noise in image space. We develop a set of algorithms that provide
a trade-off between quality and speed, showing substantial improvements over
prior state of the art. We perform evaluations using both quantitative and
perceptual error metrics to support our analysis, and provide extensive
supplemental material to help evaluate the perceptual improvements achieved by
our methods
Dithering by Differences of Convex Functions
Motivated by a recent halftoning method which is based on electrostatic principles, we analyse a halftoning framework where one minimizes a functional consisting of the difference of two convex functions (DC). One of them describes attracting forces caused by the image gray values, the other one enforces repulsion between points. In one dimension, the minimizers of our functional can be computed analytically and have the following desired properties: the points are pairwise distinct, lie within the image frame and can be placed at grid points. In the two-dimensional setting, we prove some useful properties of our functional like its coercivity and suggest to compute a minimizer by a forward-backward splitting algorithm. We show that the sequence produced by such an algorithm converges to a critical point of our functional. Furthermore, we suggest to compute the special sums occurring in each iteration step by a fast summation technique based on the fast Fourier transform at non-equispaced knots which requires only Ο(m log(m)) arithmetic operations for m points. Finally, we present numerical results showing the excellent performance of our DC dithering method
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
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