24 research outputs found
Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective
In this report, we revisit the work of Pilleboue et al. [2015], providing a
representation-theoretic derivation of the closed-form expression for the
expected value and variance in homogeneous Monte Carlo integration. We show
that the results obtained for the variance estimation of Monte Carlo
integration on the torus, the sphere, and Euclidean space can be formulated as
specific instances of a more general theory. We review the related
representation theory and show how it can be used to derive a closed-form
solution
How Different Materials are Carried on the Routes of India in Supply Chain.
In this research , it was presented that how there are different kind of materials which can be transported by commercial vehicle, various category of heavy vehicles, weight segments for carrying distinct product with safety, emission standard for vehicles and numerous challenges faced while transporting the goods. This study focusses on five category material, commercial vehicles, weight, new emission norms and challenges. For analysing this paper descriptive coding was used so that data can easily be divided into these categories. The result shows that for loading and unloading of materials documents, workforce, equipment and safety kit are needed, different type of commercial vehicle is needed for carrying distinct material like liquid in tankers, parcel in container and generic product in trailers, safety measures like plastic covers and straps for open body vehicles, SS tank for chemical products and
wooden or cardboard sheets in containers, the new norms has improved the engines, vehicles produce less pollution, better safety equipment, only improvement is done but no major changes has been noticed. Finally, the challenges faced in transit are theft, less margin, low infrastructure, harassment and corruption
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
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
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
Patternshop: Editing Point Patterns by Image Manipulation
Point patterns are characterized by their density and correlation. While
spatial variation of density is well-understood, analysis and synthesis of
spatially-varying correlation is an open challenge. No tools are available to
intuitively edit such point patterns, primarily due to the lack of a compact
representation for spatially varying correlation. We propose a low-dimensional
perceptual embedding for point correlations. This embedding can map point
patterns to common three-channel raster images, enabling manipulation with
off-the-shelf image editing software. To synthesize back point patterns, we
propose a novel edge-aware objective that carefully handles sharp variations in
density and correlation. The resulting framework allows intuitive and
backward-compatible manipulation of point patterns, such as recoloring,
relighting to even texture synthesis that have not been available to 2D point
pattern design before. Effectiveness of our approach is tested in several user
experiments.Comment: 14 pages, 16 figure
Efficient Gradient Estimation via Adaptive Sampling and Importance Sampling
Machine learning problems rely heavily on stochastic gradient descent (SGD)
for optimization. The effectiveness of SGD is contingent upon accurately
estimating gradients from a mini-batch of data samples. Instead of the commonly
used uniform sampling, adaptive or importance sampling reduces noise in
gradient estimation by forming mini-batches that prioritize crucial data
points. Previous research has suggested that data points should be selected
with probabilities proportional to their gradient norm. Nevertheless, existing
algorithms have struggled to efficiently integrate importance sampling into
machine learning frameworks. In this work, we make two contributions. First, we
present an algorithm that can incorporate existing importance functions into
our framework. Second, we propose a simplified importance function that relies
solely on the loss gradient of the output layer. By leveraging our proposed
gradient estimation techniques, we observe improved convergence in
classification and regression tasks with minimal computational overhead. We
validate the effectiveness of our adaptive and importance-sampling approach on
image and point-cloud datasets.Comment: 15 pages, 10 figure
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
Monte Carlo Convergence Analysis for Anisotropic Sampling Power Spectra
Traditional Monte Carlo (MC) integration methods use point samples to numerically approximate the underlying integral. This approximation introduces variance in the integrated result, and this error can depend critically on the sampling patterns used during integration. Most of the well known samplers used for MC integration in graphics, e.g. jitter, Latin hypercube (n-rooks), multi-jitter, are anisotropic in nature. However, there are currently no tools available to analyze the impact of such anisotropic samplers on the variance convergence behavior of Monte Carlo integration. In this work, we propose a mathematical tool in the Fourier domain that allows analyzing the variance, and subsequently the convergence rate, of Monte Carlo integration using any arbitrary (anisotropic) sampling power spectrum. We apply our analysis to common anisotropic point sampling strategies in Monte Carlo integration, and extend our analysis to recent Monte Carlo approaches relying on line samples which have inherently anisotropic power spectra. We validate our theoretical results with several experiments using both point and line samples