Extending stochastic resonance for neuron models to general Levy noise

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Levy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general Levy noise models. We achieve this by showing that �¿large jump�¿ discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero. SR then follows by a �¿forbidden intervals�¿ theorem as in Patel and Kosko's paper

Wavelets In Real-time Rendering

Interactively simulating visual appearance of natural objects under natural illumination is a fundamental problem in computer graphics. 3D computer games, geometry modeling, training and simulation, electronic commerce, visualization, lighting design, digital libraries, geographical information systems, economic and medical image processing are typical candidate applications. Recent advances in graphics hardware have enabled real-time rasterization of complex scenes under artificial lighting environment. Meanwhile, pre-computation based soft shadow algorithms are proven effective under low-frequency lighting environment. Under the most practical yet popular all-frequency natural lighting environment, however, real-time rendering of dynamic scenes still remains a challenging problem. In this dissertation, we propose a systematic approach to render dynamic glossy objects under the general all-frequency lighting environment. In our framework, lighting integration is reduced to two rather basic mathematical operations, efficiently computing multi-function product and product integral. The main contribution of our work is a novel mathematical representation and analysis of multi-function product and product integral in the wavelet domain. We show that, multi-function product integral in the primal is equivalent to summation of the product of basis coefficients and integral coefficients. In the dissertation, we give a novel Generalized Haar Integral Coefficient Theorem. We also present a set of efficient algorithms to compute multi-function product and product integral. In the dissertation, we demonstrate practical applications of these algorithms in the interactive rendering of dynamic glossy objects under distant time-variant all-frequency environment lighting with arbitrary view conditions. At each vertex, the shading integral is formulated as the product integral of multiple operand functions. By approximating operand functions in the wavelet domain, we demonstrate rendering dynamic glossy scenes interactively, which is orders of magnitude faster than previous work. As an important enhancement to the popular Pre-computation Based Radiance Transfer (PRT) approach, we present a novel Just-in-time Radiance Transfer (JRT) technique, and demonstrate its application in real-time realistic rendering of dynamic all-frequency shadows under general lighting environment. Our work is a significant step towards real-time rendering of arbitrary scenes under general lighting environment. It is also of great importance to general numerical analysis and signal processing

Systems and Methods for Graphical Rendering

A computer readable medium configured to determine the integral of the product of a plurality of functions. The computer readable medium includes logic configured to project each function of the plurality of functions into the wavelet domain, logic configured to encode basis coefficients of each function in a wavelet tree, each function being encoded in at least one wavelet tree such that the plurality of functions are represented in the wavelet domain by a plurality of wavelet trees, and logic configured to traverse direct paths through the plurality of wavelet trees to determine the integral of the product of the function represented by the wavelet trees, along which direct paths an integral coefficient may be nonzero

Systems and Methods for Graphical Rendering.

A method of rendering a graphical scene includes determining a plurality of functions that contribute to a light transport model of the scene, projecting each function of the plurality of functions into the wavelet domain, encoding basis coefficients of each function in a wavelet tree, each function being encoded in at least one wavelet tree such that the plurality of functions are represented in the wavelet domain by a plurality of wavelet trees, traversing direct paths through the plurality of wavelet trees, along which direct paths an integral coefficient may be nonzero, to determine the radiance of a point in the scene, and rendering the scene

Systems and Methods for Graphical Rendering.

A computer readable medium configured to approximate the integral of the product of a plurality of functions includes logic configured to factor the plurality of functions into a set of fixed functions and one varying function, logic configured to determine a first vector that represents the product of the fixed functions in the wavelet domain, logic configured to determine a second vector that represents the one varying function in the wavelet domain, and logic configured to determine an inner product of the first vector and the second vector

Real-time Cinematic Design Of Visual Aspects In Computer-generated Images

Creation of visually-pleasing images has always been one of the main goals of computer graphics. Two important components are necessary to achieve this goal --- artists who design visual aspects of an image (such as materials or lighting) and sophisticated algorithms that render the image. Traditionally, rendering has been of greater interest to researchers, while the design part has always been deemed as secondary. This has led to many inefficiencies, as artists, in order to create a stunning image, are often forced to resort to the traditional, creativity-baring, pipelines consisting of repeated rendering and parameter tweaking. Our work shifts the attention away from the rendering problem and focuses on the design. We propose to combine non-physical editing with real-time feedback and provide artists with efficient ways of designing complex visual aspects such as global illumination or all-frequency shadows. We conform to existing pipelines by inserting our editing components into existing stages, hereby making editing of visual aspects an inherent part of the design process. Many of the examples showed in this work have been, until now, extremely hard to achieve. The non-physical aspect of our work enables artists to express themselves in more creative ways, not limited by the physical parameters of current renderers. Real-time feedback allows artists to immediately see the effects of applied modifications and compatibility with existing workflows enables easy integration of our algorithms into production pipelines

A Precomputed Polynomial Representation for Interactive BRDF Editing with Global Illumination

The ability to interactively edit BRDFs in their final placement within a computer graphics scene is vital to making informed choices for material properties. We significantly extend previous work on BRDF editing for static scenes (with fixed lighting and view), by developing a precomputed polynomial representation that enables interactive BRDF editing with global illumination. Unlike previous recomputation based rendering techniques, the image is not linear in the BRDF when considering interreflections. We introduce a framework for precomputing a multi-bounce tensor of polynomial coefficients, that encapsulates the nonlinear nature of the task. Significant reductions in complexity are achieved by leveraging the low-frequency nature of indirect light. We use a high-quality representation for the BRDFs at the first bounce from the eye, and lower-frequency (often diffuse) versions for further bounces. This approximation correctly captures the general global illumination in a scene, including color-bleeding, near-field object reflections, and even caustics. We adapt Monte Carlo path tracing for precomputing the tensor of coefficients for BRDF basis functions. At runtime, the high-dimensional tensors can be reduced to a simple dot product at each pixel for rendering. We present a number of examples of editing BRDFs in complex scenes, with interactive feedback rendered with global illumination

Hierarchical Variance Reduction Techniques for Monte Carlo Rendering

Ever since the first three-dimensional computer graphics appeared half a century ago, the goal has been to model and simulate how light interacts with materials and objects to form an image. The ultimate goal is photorealistic rendering, where the created images reach a level of accuracy that makes them indistinguishable from photographs of the real world. There are many applications ñ visualization of products and architectural designs yet to be built, special effects, computer-generated films, virtual reality, and video games, to name a few. However, the problem has proven tremendously complex; the illumination at any point is described by a recursive integral to which a closed-form solution seldom exists. Instead, computer simulation and Monte Carlo methods are commonly used to statistically estimate the result. This introduces undesirable noise, or variance, and a large body of research has been devoted to finding ways to reduce the variance. I continue along this line of research, and present several novel techniques for variance reduction in Monte Carlo rendering, as well as a few related tools. The research in this dissertation focuses on using importance sampling to pick a small set of well-distributed point samples. As the primary contribution, I have developed the first methods to explicitly draw samples from the product of distant high-frequency lighting and complex reflectance functions. By sampling the product, low noise results can be achieved using a very small number of samples, which is important to minimize the rendering times. Several different hierarchical representations are explored to allow efficient product sampling. In the first publication, the key idea is to work in a compressed wavelet basis, which allows fast evaluation of the product. Many of the initial restrictions of this technique were removed in follow-up work, allowing higher-resolution uncompressed lighting and avoiding precomputation of reflectance functions. My second main contribution is to present one of the first techniques to take the triple product of lighting, visibility and reflectance into account to further reduce the variance in Monte Carlo rendering. For this purpose, control variates are combined with importance sampling to solve the problem in a novel way. A large part of the technique also focuses on analysis and approximation of the visibility function. To further refine the above techniques, several useful tools are introduced. These include a fast, low-distortion map to represent (hemi)spherical functions, a method to create high-quality quasi-random points, and an optimizing compiler for analyzing shaders using interval arithmetic. The latter automatically extracts bounds for importance sampling of arbitrary shaders, as opposed to using a priori known reflectance functions. In summary, the work presented here takes the field of computer graphics one step further towards making photorealistic rendering practical for a wide range of uses. By introducing several novel Monte Carlo methods, more sophisticated lighting and materials can be used without increasing the computation times. The research is aimed at domain-specific solutions to the rendering problem, but I believe that much of the new theory is applicable in other parts of computer graphics, as well as in other fields

Theory and algorithms for efficient physically-based illumination

Realistic image synthesis is one of the central fields of study within computer graphics. This thesis treats efficient methods for simulating light transport in situations where the incident illumination is produced by non-pointlike area light sources and distant illumination described by environment maps. We describe novel theory and algorithms for physically-based lighting computations, and expose the design choices and tradeoffs on which the techniques are based. Two publications included in this thesis deal with precomputed light transport. These techniques produce interactive renderings of static scenes under dynamic illumination and full global illumination effects. This is achieved through sacrificing the ability to freely deform and move the objects in the scene. We present a comprehensive mathematical framework for precomputed light transport. The framework, which is given as an abstract operator equation that extends the well-known rendering equation, encompasses a significant amount of prior work as its special cases. We also present a particular method for rendering objects in low-frequency lighting environments, where increased efficiency is gained through the use of compactly supported function bases. Physically-based shadows from area and environmental light sources are an important factor in perceived image realism. We present two algorithms for shadow computation. The first technique computes shadows cast by low-frequency environmental illumination on animated objects at interactive rates without requiring difficult precomputation or a priori knowledge of the animations. Here the capability to animate is gained by forfeiting indirect illumination. Another novel shadow algorithm for off-line rendering significantly enhances a previous physically-based soft shadow technique by introducing an improved spatial hierarchy that alleviates redundant computations at the cost of using more memory. This thesis advances the state of the art in realistic image synthesis by introducing several algorithms that are more efficient than their predecessors. Furthermore, the theoretical contributions should enable the transfer of ideas from one particular application to others through abstract generalization of the underlying mathematical concepts.Tämä tutkimus käsittelee realististen kuvien syntetisointia tietokoneella tilanteissa, jossa virtuaalisen ympäristön valonlähteet ovat fysikaalisesti mielekkäitä. Fysikaalisella mielekkyydellä tarkoitetaan sitä, että valonlähteet eivät ole idealisoituja eli pistemäisiä, vaan joko tavanomaisia pinta-alallisia valoja tai kaukaisia ympäristövalokenttiä (environment maps). Väitöskirjassa esitetään uusia algoritmeja, jotka soveltuvat matemaattisesti perusteltujen valaistusapproksimaatioiden laskentaan erilaisissa käyttötilanteissa. Esilaskettu valonkuljetus on yleisnimi reaaliaikaisille menetelmille, jotka tuottavat kuvia staattisista ympäristöistä siten, että valaistus voi muuttua ajon aikana vapaasti ennalta määrätyissä rajoissa. Tässä työssä esitetään esilasketulle valonkuljetukselle kattava matemaattinen kehys, joka selittää erikoistapauksinaan suuren määrän aiempaa tutkimusta. Kehys annetaan abstraktin lineaarisen operaattoriyhtälön muodossa, ja se yleistää tunnettua kuvanmuodostusyhtälöä (rendering equation). Työssä esitetään myös esilasketun valonkuljetuksen algoritmi, joka parantaa aiempien vastaavien menetelmien tehokkuutta esittämällä valaistuksen funktiokannassa, jonka ominaisuuksien vuoksi ajonaikainen laskenta vähenee huomattavasti. Fysikaalisesti mielekkäät valonlähteet tuottavat pehmeäreunaisia varjoja. Työssä esitetään uusi algoritmi pehmeiden varjojen laskemiseksi liikkuville ja muotoaan muuttaville kappaleille, joita valaisee matalataajuinen ympäristövalokenttä. Useimmista aiemmista menetelmistä poiketen algoritmi ei vaadi esitietoa siitä, kuinka kappale voi muuttaa muotoaan ajon aikana. Muodonmuutoksen aiheuttaman suuren laskentakuorman vuoksi epäsuoraa valaistusta ei huomioida. Työssä esitetään myös toinen uusi algoritmi pehmeiden varjojen laskemiseksi, jossa aiemman varjotilavuuksiin (shadow volumes) perustuvan algoritmin tehokkuutta parannetaan merkittävästi uuden hierarkkisen avaruudellisen hakurakenteen avulla. Uusi rakenne vähentää epäoleellista laskentaa muistinkulutuksen kustannuksella. Työssä esitetään aiempaa tehokkaampia algoritmeja fysikaalisesti perustellun valaistuksen laskentaan. Niiden lisäksi työn esilaskettua valonkuljetusta koskevat teoreettiset tulokset yleistävät suuren joukon aiempaa tutkimusta ja mahdollistavat näin ideoiden siirron erityisalalta toiselle.reviewe