Prime gradient noise

Analytical approaches, based on digitised 2D texture models, for an automatic solid (3D) texture synthesis have been recently introduced to Computer Graphics. However, these approaches cannot provide satisfactory solutions in the usual case of natural anisotropic textures (wood grain for example). Indeed, solid texture synthesis requires particular care, and sometimes external knowledge to "guess" the internal structure of solid textures because only 2D texture models are used for analysis. By making some basic assumptions about the internal structure of solid textures, we propose a very efficient method based on a hybrid analysis (spectral and histogram) for an automatic synthesis of solid textures. This new method allows us to obtain high precision solid textures (closely resembling initial models) in a large number of cases, including the difficult case of anisotropic textures.

Fast display of realistic dynamic cloud scene is a challenging task for researchers in computer graphics. This paper describes a novel method of simulating animations of cloud. We first model the motion of cloud based on the physical theory of cloud formation. Then, the physical model of cloud is solved in discrete sparse grids. Thus, we can get approximate motion of cloud. Next, we advect texture image using the calculated velocity field to add the local detail of dynamic cloud scene. Here the texture image we used is Perlin noise map. The color of arbitrary point in the simulation space is got by calculating the product of the density texture and the regenerated Perlin noise texture. Finally, by changing different noise maps, realistic dynamic cloud scenes in different light environment are generated at high rendering rates.

Fibrosis, a pathological increase in extracellular matrix proteins, is a significant health issue that hinders the function of many organs in the body, in some cases fatally. In the heart, fibrosis impacts on electrical propagation in a complex and poorly predictable fashion, potentially serving as a substrate for dangerous arrhythmias. Individual risk depends on the spatial manifestation of fibrotic tissue, and learning the spatial arrangement on the fine scale in order to predict these impacts still relies upon invasive ex vivo procedures. As a result, the effects of spatial variability on the symptomatic impact of cardiac fibrosis remain poorly understood. In this work, we address the issue of availability of such imaging data via a computational methodology for generating new realisations of cardiac fibrosis microstructure. Using the Perlin noise technique from computer graphics, together with an automated calibration process that requires only a single training image, we demonstrate successful capture of collagen texturing in four types of fibrosis microstructure observed in histological sections. We then use this generator to quantitatively analyse the conductive properties of these different types of cardiac fibrosis, as well as produce three-dimensional realisations of histologically-observed patterning. Owing to the generator’s flexibility and automated calibration process, we also anticipate that it might be useful in producing additional realisations of other physiological structures.

This paper describes how evolutionary techniques of variation and selection can be used to create complex simulated structures, textures, and motions for use in computer graphics and animation. Interactive selection, based on visual perception of procedurally generated results, allows the user to direct simulated evolutions in preferred directions. Several examples using these methods have been implemented and are described. 3D plant structures are grown using fixed sets of genetic parameters. Images, solid textures, and animations are created using mutating symbolic lisp expressions. Genotypes consisting of symbolic expressions are presented as an attempt to surpass the limitations of fixed-length genotypes with predefined expression rules. It is proposed that artificial evolution has potential as a powerful tool for achieving flexible complexity with a minimum of user input and knowledge of details.

A Monte Carlo method for calculating strength functions in many-fermion systems

An adaptive approach for texture enhancement based on a fractional differential operator with non-integer step and order

In computer graphics, it is of interest to render a Beta-spline, that is, create a realistic two-dimensional image representing three-dimensional Beta-spline objects. This chapter shows several synthetic color images of Beta-spline objects including such features as specular highlights and texture patterns.

We present experimental findings on the decoding failure rate (DFR) of BIKE, a fourth-round candidate in the NIST Post-Quantum Standardization process, at the 20-bit security level. We select parameters according to BIKE design principles and conduct a series of experiments. We directly compute the average DFR on a range of BIKE block sizes and identify both the waterfall and error floor regions of the DFR curve. We then study the influence on the average DFR of three sets \(\mathcal {C}\), \(\mathcal {N}\), and \(2\mathcal {N}\) of near-codewords—vectors of low weight that induce syndromes of low weight—defined by Vasseur in 2021. We find that error vectors leading to decoding failures have small maximum support intersection with elements of these sets; further, the distribution of intersections is quite similar to that of sampling random error vectors and counting the intersections with \(\mathcal {C}\), \(\mathcal {N}\), and \(2\mathcal {N}\). Our results indicate that these three sets are not sufficient in classifying vectors expected to cause decoding failures. Finally, we study the role of syndrome weight on the decoding behavior and conclude that the set of error vectors that lead to decoding failures differ from random vectors by having low syndrome weight.KeywordsBIKEError-correcting codesMcEliecePQCQC-MDPC

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two approaches, the first based on a concentration principle (valid for a large class of resampling weights) and the second on a resampled quantile, specifically using Rademacher weights. Several intermediate results established in the approach based on concentration principles are of interest in their own right. We also discuss the question of accuracy when using Monte Carlo approximations of the resampled quantities.

Brain-inspired high-dimensional (HD) computing represents and manipulates data using very long, random vectors with dimensionality in the thousands. This representation provides great robustness for various classification tasks where classifiers operate at low signal-to-noise ratio (SNR) conditions. Similarly, hyperdimensional modulation (HDM) leverages the robustness of complex-valued HD representations to reliably transmit information over a wireless channel, achieving a similar SNR gain compared to state-of-the-art codes. Here, we first propose methods to improve HDM in two ways: (1) reducing the complexity of encoding and decoding operations by generating, manipulating, and transmitting bipolar or integer vectors instead of complex vectors; (2) increasing the SNR gain by 0.2 dB using a new soft-feedback decoder; it can also increase the additive superposition capacity of HD vectors up to 1.7times in noise-free cases. Secondly, we propose to combine encoding/decoding aspects of communication with classification into a single framework by relying on multifaceted HD representations. This leads to a near-channel classification (NCC) approach that avoids transformations between different representations and the overhead of multiple layers of encoding/decoding, hence reducing latency and complexity of a wireless smart distributed system while providing robustness against noise and interference from other nodes. We provide a use-case for wearable hand gesture recognition with 5 classes from 64 EMG sensors, where the encoded vectors are transmitted to a remote node for either performing NCC, or reconstruction of the encoded data. In NCC mode, the original classification accuracy of 94% is maintained, even in the channel at SNR of 0 dB, by transmitting 10,000-bit vectors. We remove the redundancy by reducing the vector dimensionality to 2048-bit that still exhibits a graceful degradation: less than 6% accuracy loss is occurred in the channel at − 5 dB, and with the interference from 6 nodes that simultaneously transmit their encoded vectors. In the reconstruction mode, it improves the mean-squared error by up to 20 dB, compared to standard decoding, when transmitting 2048-dimensional vectors.

Many image acquisition techniques used in biomedical imaging, material analysis, and structural geology are capable of acquiring 3-D solid images. Computational analysis of these images is complex but necessary since it is difficult for humans to visualize and quantify their detailed 3-D content. One of the most common methods to analyze 3-D data is to characterize the volumetric texture patterns. Texture analysis generally consists of encoding the local organization of image scales and directions, which can be extremely diverse in 3-D. Current state-of-the- art techniques face many challenges when working with 3-D solid texture, where most approaches are not able to consistently characterize both scale and directional information. 3-D Riesz- wavelets can deal with both properties. One key property of Riesz filterbanks is steerability, which can be used to locally align the filters and compare textures with arbitrary (local) orientations. This paper proposes and compares three novel local alignment criteria for higher-order 3-D Riesz-wavelet transforms. The estimations of local texture orientations are based on higher- order extensions of regularized structure tensors. An experimental evaluation of the proposed methods for the classification of synthetic 3-D solid textures with alterations (such as rotations and noise) demonstrated the importance of local directional information for robust and accurate solid texture recognition. These alignment methods improved the accuracy of the unaligned Riesz descriptors up to 0.63, from 0.32 to 0.95 over 1 in the rotated data, which is better than all other techniques that are published and tested on the same database.

Rotational symmetry fields appear in a wide range of applications in computer graphics, such as quadrangular and triangular remeshing, texture and geometry pattern synthesis, painterly rendering, pen-and-ink sketching, street network modeling, and computer architecture. In all of these applications, an orientation field is needed to guide the tiling of the surface (remeshing) and placement of graphics primitives (e.g., painting strokes, hatches, street segments, texture and geometry patterns). The continuity and smoothness of the input rotational symmetry field as well as its topology of the rotational symmetry field (singularities), can greatly influence the quality of the application results. In this course note, we will start with vector fields, a special kind of rotational symmetry fields that are important in their own right. We will cover the topology as well as smoothness of vector fields and provide algorithms for vector field design and analsysi. Next, we will extend the work to the general N-way rotational symmetry fields and provide algorithms for the representation, analysis, design, processing, and visualization of such fields.

3D solid textures are important data for computer graphics applications because they are useful for synthesizing photo realistic patterns such as stone, smoke, water, clouds, fire, and wood. Unlike typical 2D textures, 3D solid textures are represented in voxel forms, which use three-dimensional coordinates. Various kinds of research have been conducted for pattern analysis of 2D textures to help development of computer applications. However, pattern analysis of 3D solid textures has not been investigated sufficiently even though 3D data related software is emerging. In this research, we have extended higher order local autocorrelation (HLAC) 2D mask patterns to 3D mask patterns so that pattern analysis software can handle not only 2D texture images but also 3D solid textures. Our experimental system can classify and look for 3D solid textures with similar patterns from a 3D solid texture database by using 3D HLAC masks. We have examined (1) similarity retrieval of 3D solid textures and (2) pattern classification of 3D solid textures by using the system.

Copulas are used in finance and insurance for modeling stochastic dependency. They comprehend the entire dependence structure, not only the correlations. Here they are estimated from measured samples of random vectors. The copula and the marginal distributions of the vector elements define a multivariate distribution of the sample which can be used to generate random vectors with this distribution. This can be applied as well to time series. A programmed algorithm is proposed. It is fast and allows for random vectors with high dimension, for example 100.

The multivariate normal is widely used as the expected distribution of face shape. It has been used for face detection and tracking in computer vision, as a prior for facial animation editing in computer graphics, and as a model in psychological theory. In this contribution we consider the character of the multivariate normal in high dimensions, and show that these applications are not justified. While we provide limited evidence that facial proportions are not Gaussian, this is tangential to our conclusion: even if faces are truly “Gaussian”, maximum a posteriori and other applications and conclusions that assume that typical faces lie near the mean are not valid.KeywordsPrincipal component analysis (PCA)Multivariate Gaussian (distribution)BlendshapesMahalanobis distanceCurse of dimensionalityActive appearance model (AAM)Maximum a posteriori (MAP)