Efficient surface diffraction renderings with Chebyshev approximations

We propose an efficient method for reproducing diffraction colours on natural surfaces with complex nanostructures that can be represented as height-fields. Our method employs Chebyshev approximations to accurately model view-dependent iridescences for such a surface into its spectral bidirectional reflectance distribution function (BRDF). As main contribution, our method significantly reduces the runtime memory footprint from precomputed lookup tables without compromising photorealism. Our accuracy is comparable with current state-of-the-art methods and better at equal memory usage. Furthermore, a Chebyshev polynomial basis set with its near-best approximation properties allow for scalable memory-vs-performance trade-offs. We show realistic diffraction effects with just two lookup textures for natural, quasi-periodic surface nanostructures. Performance intensive applications like games and VR can benefit from our method, especially for low-end GPU or mobile platforms

Practical acquisition and rendering of diffraction effects in surface reflectance

We propose two novel contributions for measurement based rendering of diffraction effects in surface reflectance of planar homogeneous diffractive materials. As a general solution for commonly manufactured materials, we propose a practical data-driven rendering technique and a measurement approach to efficiently render complex diffraction effects in real-time. Our measurement step simply involves photographing a planar diffractive sam- ple illuminated with an LED flash. Here, we directly record the resultant diffraction pattern on the sample surface due to a narrow band point source illumination. Furthermore, we propose an efficient rendering method that exploits the measurement in conjunction with the Huygens-Fresnel principle to fit relevant diffraction parameters based on a first order approximation. Our proposed data-driven rendering method requires the precomputation of a single diffraction look up table for accurate spectral rendering of com- plex diffraction effects. Secondly, for sharp specular samples, we propose a novel method for practical measurement of the underlying diffraction grating using out-of-focus “bokeh” photography of the specular highlight. We demonstrate how the measured bokeh can be employed as a height field to drive a diffraction shader based on a first order approximation for efficient real-time rendering. Finally, we also drive analytic solutions for a few special cases of diffraction from our measurements and demonstrate realistic rendering results under complex light sources and environments

A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space

We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities

A 'Surface-based' Geometrical Acoustic formulation within a Galerkin Boundary Element framework

As sound propagates within a room, it experiences high-order reflection, diffraction, and scattering. This causes the reflection density to increase over time, such that the sound field becomes diffuse and chaotic. Under these conditions, there is little benefit in running a computationally costly full wave solver – if it is even feasible – so methods based on Geometrical models of acoustic propagation prevail. Raytracing is currently the de-facto method for this late-time, high-frequency regime in room acoustic modelling. It samples the propagating distributions of acoustic intensity by launching a set of rays and individually tracing their trajectories. This is computationally efficient when only specular reflections are present, but accurate inclusion of scattering or diffraction requires ‘ray-splitting’ to be introduced, causing an exponential increase in computational cost with reflection order, crippling the algorithm. Hence only crude Monte Carlo implantations of these processes are tractable with Raytracing.An emerging solution for modelling late-reflections is “Surface-Based” Geometrical Acoustics. These formulations map a distribution of rays arriving at a boundary onto a pre- defined ‘approximation space’ of basis functions spanning position and angle, so the sound field is represented by a vector of boundary coefficients. Re-radiation of subsequent reflections is thus reduced to a matrix multiplication, with the steady-state solvable via a Neumann series. As rays only propagate one reflection order before being collected, the multiple ‘child’ rays that would be produced by scattering or diffraction of a ‘parent’ ray at the boundary are absorbed into the ‘approximation’ space at each reflection order. This maintains a fixed number of degrees of freedom and a linear computational cost with reflection order. This thesis presents a Surface-Based Geometrical Acoustic formulation cast in a Galerkin Boundary Element framework.This thesis presents and implements the formulation in two dimensions and validates it against an Image Source Model for a rectangular room. The Galerkin Boundary Element scheme expediates comparison of different approximation schemes and their effect on convergence and accuracy can be easily studied. Examination of the resulting power distributions on the boundary for early reflections show power being smudged over a range of reflection angles, indicating approximation in the scheme. But this is perceptually appropriate for late-time diffuse fields as individual reflections will no longer be distinguishable, and late time energy decay rates are shown to be correct. Receiver responses for early reflections show very good agreement also, so long as angular resolution is set sufficiently high. The formulation is shown to converge with the number of angular degrees of freedom as well as smaller element sizes. The results show a high degree of accuracy and identical convergence trends when using continuous orthogonal polynomials, such as Legendre, Chebyshev or Lobatto, as angular basis. In contrast, other functions, such as continuous piecewise-linear, or discontinuous piecewise- constant, exhibit a significant degree of approximation for higher interpolation orders due to their discontinuous or non-smooth nature. Solutions in Geometrical Acoustics can be discontinuous. The ultimate ambition in formulating the model presented in this thesis is to include diffraction, and solutions when it is included will be continuous. This capability still remains as work for the future, but the choices made in this thesis were informed by that end goal

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

Methods for Automated Neuron Image Analysis

Knowledge of neuronal cell morphology is essential for performing specialized analyses in the endeavor to understand neuron behavior and unravel the underlying principles of brain function. Neurons can be captured with a high level of detail using modern microscopes, but many neuroscientific studies require a more explicit and accessible representation than offered by the resulting images, underscoring the need for digital reconstruction of neuronal morphology from the images into a tree-like graph structure. This thesis proposes new computational methods for automated detection and reconstruction of neurons from fluorescence microscopy images. Specifically, the successive chapters describe and evaluate original solutions to problems such as the detection of landmarks (critical points) of the neuronal tree, complete tracing and reconstruction of the tree, and the detection of regions containing neurons in high-content screens

Real-Time Physically Based Sound Synthesis and Application in Multimodal Interaction

An immersive experience in virtual environments requires realistic auditory feedback that is closely coupled with other modalities, such as vision and touch. This is particularly challenging for real-time applications due to its stringent computational requirement. In this dissertation, I present and evaluate effective real-time physically based sound synthesis models that integrate visual and touch data and apply them to create richly varying multimodal interaction. I first propose an efficient contact sound synthesis technique that accounts for texture information used for visual rendering and greatly reinforces cross-modal perception. Secondly, I present both empirical and psychoacoustic approaches that formally study the geometry-invariant property of the commonly used material model in real-time sound synthesis. Based on this property, I design a novel example-based material parameter estimation framework that automatically creates synthetic sound effects naturally controlled by complex geometry and dynamics in visual simulation. Lastly, I translate user touch input captured on commodity multi-touch devices to physical performance models that drive both visual and auditory rendering. This novel multimodal interaction is demonstrated in a virtual musical instrument application on both a large-size tabletop and mobile tablet devices, and evaluated through pilot studies. Such an application offers capabilities for intuitive and expressive music playing, rapid prototyping of virtual instruments, and active exploration of sound effects determined by various physical parameters.Doctor of Philosoph

Ray Tracing Gems

This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for: Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPU