Phenomenological modeling of image irradiance for non-Lambertian surfaces under natural illumination.

Various vision tasks are usually confronted by appearance variations due to changes of illumination. For instance, in a recognition system, it has been shown that the variability in human face appearance is owed to changes to lighting conditions rather than person\u27s identity. Theoretically, due to the arbitrariness of the lighting function, the space of all possible images of a fixed-pose object under all possible illumination conditions is infinite dimensional. Nonetheless, it has been proven that the set of images of a convex Lambertian surface under distant illumination lies near a low dimensional linear subspace. This result was also extended to include non-Lambertian objects with non-convex geometry. As such, vision applications, concerned with the recovery of illumination, reflectance or surface geometry from images, would benefit from a low-dimensional generative model which captures appearance variations w.r.t. illumination conditions and surface reflectance properties. This enables the formulation of such inverse problems as parameter estimation. Typically, subspace construction boils to performing a dimensionality reduction scheme, e.g. Principal Component Analysis (PCA), on a large set of (real/synthesized) images of object(s) of interest with fixed pose but different illumination conditions. However, this approach has two major problems. First, the acquired/rendered image ensemble should be statistically significant vis-a-vis capturing the full behavior of the sources of variations that is of interest, in particular illumination and reflectance. Second, the curse of dimensionality hinders numerical methods such as Singular Value Decomposition (SVD) which becomes intractable especially with large number of large-sized realizations in the image ensemble. One way to bypass the need of large image ensemble is to construct appearance subspaces using phenomenological models which capture appearance variations through mathematical abstraction of the reflection process. In particular, the harmonic expansion of the image irradiance equation can be used to derive an analytic subspace to represent images under fixed pose but different illumination conditions where the image irradiance equation has been formulated in a convolution framework. Due to their low-frequency nature, irradiance signals can be represented using low-order basis functions, where Spherical Harmonics (SH) has been extensively adopted. Typically, an ideal solution to the image irradiance (appearance) modeling problem should be able to incorporate complex illumination, cast shadows as well as realistic surface reflectance properties, while moving away from the simplifying assumptions of Lambertian reflectance and single-source distant illumination. By handling arbitrary complex illumination and non-Lambertian reflectance, the appearance model proposed in this dissertation moves the state of the art closer to the ideal solution. This work primarily addresses the geometrical compliance of the hemispherical basis for representing surface reflectance while presenting a compact, yet accurate representation for arbitrary materials. To maintain the plausibility of the resulting appearance, the proposed basis is constructed in a manner that satisfies the Helmholtz reciprocity property while avoiding high computational complexity. It is believed that having the illumination and surface reflectance represented in the spherical and hemispherical domains respectively, while complying with the physical properties of the surface reflectance would provide better approximation accuracy of image irradiance when compared to the representation in the spherical domain. Discounting subsurface scattering and surface emittance, this work proposes a surface reflectance basis, based on hemispherical harmonics (HSH), defined on the Cartesian product of the incoming and outgoing local hemispheres (i.e. w.r.t. surface points). This basis obeys physical properties of surface reflectance involving reciprocity and energy conservation. The basis functions are validated using analytical reflectance models as well as scattered reflectance measurements which might violate the Helmholtz reciprocity property (this can be filtered out through the process of projecting them on the subspace spanned by the proposed basis, where the reciprocity property is preserved in the least-squares sense). The image formation process of isotropic surfaces under arbitrary distant illumination is also formulated in the frequency space where the orthogonality relation between illumination and reflectance bases is encoded in what is termed as irradiance harmonics. Such harmonics decouple the effect of illumination and reflectance from the underlying pose and geometry. Further, a bilinear approach to analytically construct irradiance subspace is proposed in order to tackle the inherent problem of small-sample-size and curse of dimensionality. The process of finding the analytic subspace is posed as establishing a relation between its principal components and that of the irradiance harmonics basis functions. It is also shown how to incorporate prior information about natural illumination and real-world surface reflectance characteristics in order to capture the full behavior of complex illumination and non-Lambertian reflectance. The use of the presented theoretical framework to develop practical algorithms for shape recovery is further presented where the hitherto assumed Lambertian assumption is relaxed. With a single image of unknown general illumination, the underlying geometrical structure can be recovered while accounting explicitly for object reflectance characteristics (e.g. human skin types for facial images and teeth reflectance for human jaw reconstruction) as well as complex illumination conditions. Experiments on synthetic and real images illustrate the robustness of the proposed appearance model vis-a-vis illumination variation. Keywords: computer vision, computer graphics, shading, illumination modeling, reflectance representation, image irradiance, frequency space representations, {hemi)spherical harmonics, analytic bilinear PCA, model-based bilinear PCA, 3D shape reconstruction, statistical shape from shading

Sampling and Exact Reconstruction of Pulses with Variable Width

Recent sampling results enable the reconstruction of signals composed of streams of fixed-shaped pulses. These results have found applications in topics as varied as channel estimation, biomedical imaging and radio astronomy. However, in many real signals, the pulse shapes vary throughout the signal. In this paper, we show how to sample and perfectly reconstruct Lorentzian pulses with variable width. Since a stream of Lorentzian pulses has a finite number of degrees of freedom per unit time, it belongs to the class of signals with finite rate of innovation (FRI). In the noiseless case, perfect recovery is guaranteed by a set of theorems. In addition, we verify that our algorithm is robust to model-mismatch and noise. This allows us to apply the technique to two practical applications: electrocardiogram (ECG) compression and bidirectional reflectance distribution function (BRDF) sampling. ECG signals are one dimensional, but the BRDF is a higher dimensional signal, which is more naturally expressed in a spherical coordinate system; this motivated us to extend the theory to the 2D and spherical cases. Experiments on real data demonstrate the viability of the proposed model for ECG acquisition and compression, as well as the efficient representation and low-rate sampling of specular BRDFs

An Overview of BRDF Models

This paper is focused on the Bidirectional Reflectance Distribution Function (BRDF) in the context of algorithms for computational production of realistic synthetic images. We provide a review of most relevant analytical BRDF models proposed in the literature which have been used for realistic rendering. We also show different approaches used for obtaining efficient models from acquired reflectance data, and the related function fitting techniques, suitable for using that data in efficient rendering algorithms. We consider algorithms for computation of BRDF integrals, by using Monte-Carlo based numerical integration. In this context, we review known techniques to design efficient BRDF sampling schemes for both analytical and measured BRDF models.The authors have been partially supported by the Spanish Research Program under project TIN2004-07672-C03-02 and the Andalusian Research Program under project P08-TIC-03717

BRDF representation and acquisition

Photorealistic rendering of real world environments is important in a range of different areas; including Visual Special effects, Interior/Exterior Modelling, Architectural Modelling, Cultural Heritage, Computer Games and Automotive Design. Currently, rendering systems are able to produce photorealistic simulations of the appearance of many real-world materials. In the real world, viewer perception of objects depends on the lighting and object/material/surface characteristics, the way a surface interacts with the light and on how the light is reflected, scattered, absorbed by the surface and the impact these characteristics have on material appearance. In order to re-produce this, it is necessary to understand how materials interact with light. Thus the representation and acquisition of material models has become such an active research area. This survey of the state-of-the-art of BRDF Representation and Acquisition presents an overview of BRDF (Bidirectional Reflectance Distribution Function) models used to represent surface/material reflection characteristics, and describes current acquisition methods for the capture and rendering of photorealistic materials

BRDF Representation and Acquisition

Photorealistic rendering of real world environments is important in a range of different areas; including Visual Special effects, Interior/Exterior Modelling, Architectural Modelling, Cultural Heritage, Computer Games and Automotive Design. Currently, rendering systems are able to produce photorealistic simulations of the appearance of many real-world materials. In the real world, viewer perception of objects depends on the lighting and object/material/surface characteristics, the way a surface interacts with the light and on how the light is reflected, scattered, absorbed by the surface and the impact these characteristics have on material appearance. In order to re-produce this, it is necessary to understand how materials interact with light. Thus the representation and acquisition of material models has become such an active research area. This survey of the state-of-the-art of BRDF Representation and Acquisition presents an overview of BRDF (Bidirectional Reflectance Distribution Function) models used to represent surface/material reflection characteristics, and describes current acquisition methods for the capture and rendering of photorealistic materials

Sampling the Multiple Facets of Light

The theme of this thesis revolves around three important manifestations of light, namely its corpuscular, wave and electromagnetic nature. Our goal is to exploit these principles to analyze, design and build imaging modalities by developing new signal processing and algorithmic tools, based in particular on sampling and sparsity concepts. First, we introduce a new sampling scheme called variable pulse width, which is based on the finite rate of innovation (FRI) sampling paradigm. This new framework enables to sample and perfectly reconstruct weighted sums of Lorentzians; perfect reconstruction from sampled signals is guaranteed by a set of theorems. Second, we turn to the context of light and study its reflection, which is based on the corpuscular model of light. More precisely, we propose to use our FRI-based model to represent bidirectional reflectance distribution functions. We develop dedicated light domes to acquire reflectance functions and use the measurements obtained to demonstrate the usefulness and versatility of our model. In particular, we concentrate on the representation of specularities, which are sharp and bright components generated by the direct reflection of light on surfaces. Third, we explore the wave nature of light through Lippmann photography, a century-old photography technique that acquires the entire spectrum of visible light. This fascinating process captures interferences patterns created by the exposed scene inside the depth of a photosensitive plate. By illuminating the developed plate with a neutral light source, the reflected spectrum corresponds to that of the exposed scene. We propose a mathematical model which precisely explains the technique and demonstrate that the spectrum reproduction suffers from a number of distortions due to the finite depth of the plate and the choice of reflector. In addition to describing these artifacts, we describe an algorithm to invert them, essentially recovering the original spectrum of the exposed scene. Next, the wave nature of light is further generalized to the electromagnetic theory, which we invoke to leverage the concept of polarization of light. We also return to the topic of the representation of reflectance functions and focus this time on the separation of the specular component from the other reflections. We exploit the fact that the polarization of light is preserved in specular reflections and investigate camera designs with polarizing micro-filters with different orientations placed just in front of the camera sensor; the different polarizations of the filters create a mosaic image, from which we propose to extract the specular component. We apply our demosaicing method to several scenes and additionally demonstrate that our approach improves photometric stereo. Finally, we delve into the problem of retrieving the phase information of a sparse signal from the magnitude of its Fourier transform. We propose an algorithm that resolves the phase retrieval problem for sparse signals in three stages. Unlike traditional approaches that recover a discrete approximation of the underlying signal, our algorithm estimates the signal on a continuous domain, which makes it the first of its kind. The concluding chapter outlines several avenues for future research, like new optical devices such as displays and digital cameras, inspired by the topic of Lippmann photography

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation

Interactive Sound Propagation using Precomputation and Statistical Approximations

Acoustic phenomena such as early reflections, diffraction, and reverberation have been shown to improve the user experience in interactive virtual environments and video games. These effects arise due to repeated interactions between sound waves and objects in the environment. In interactive applications, these effects must be simulated within a prescribed time budget. We present two complementary approaches for computing such acoustic effects in real time, with plausible variation in the sound field throughout the scene. The first approach, Precomputed Acoustic Radiance Transfer, precomputes a matrix that accounts for multiple acoustic interactions between all scene objects. The matrix is used at run time to provide sound propagation effects that vary smoothly as sources and listeners move. The second approach couples two techniques -- Ambient Reverberance, and Aural Proxies -- to provide approximate sound propagation effects in real time, based on only the portion of the environment immediately visible to the listener. These approaches lie at different ends of a space of interactive sound propagation techniques for modeling sound propagation effects in interactive applications. The first approach emphasizes accuracy by modeling acoustic interactions between all parts of the scene; the second approach emphasizes efficiency by only taking the local environment of the listener into account. These methods have been used to efficiently generate acoustic walkthroughs of architectural models. They have also been integrated into a modern game engine, and can enable realistic, interactive sound propagation on commodity desktop PCs.Doctor of Philosoph

Advanced methods for relightable scene representations in image space

The realistic reproduction of visual appearance of real-world objects requires accurate computer graphics models that describe the optical interaction of a scene with its surroundings. Data-driven approaches that model the scene globally as a reflectance field function in eight parameters deliver high quality and work for most material combinations, but are costly to acquire and store. Image-space relighting, which constrains the application to create photos with a virtual, fix camera in freely chosen illumination, requires only a 4D data structure to provide full fidelity. This thesis contributes to image-space relighting on four accounts: (1) We investigate the acquisition of 4D reflectance fields in the context of sampling and propose a practical setup for pre-filtering of reflectance data during recording, and apply it in an adaptive sampling scheme. (2) We introduce a feature-driven image synthesis algorithm for the interpolation of coarsely sampled reflectance data in software to achieve highly realistic images. (3) We propose an implicit reflectance data representation, which uses a Bayesian approach to relight complex scenes from the example of much simpler reference objects. (4) Finally, we construct novel, passive devices out of optical components that render reflectance field data in real-time, shaping the incident illumination into the desired imageDie realistische Wiedergabe der visuellen Erscheinung einer realen Szene setzt genaue Modelle aus der Computergraphik für die Interaktion der Szene mit ihrer Umgebung voraus. Globale Ansätze, die das Verhalten der Szene insgesamt als Reflektanzfeldfunktion in acht Parametern modellieren, liefern hohe Qualität für viele Materialtypen, sind aber teuer aufzuzeichnen und zu speichern. Verfahren zur Neubeleuchtung im Bildraum schränken die Anwendbarkeit auf fest gewählte Kameras ein, ermöglichen aber die freie Wahl der Beleuchtung, und erfordern dadurch lediglich eine 4D - Datenstruktur für volle Wiedergabetreue. Diese Arbeit enthält vier Beiträge zu diesem Thema: (1) wir untersuchen die Aufzeichnung von 4D Reflektanzfeldern im Kontext der Abtasttheorie und schlagen einen praktischen Aufbau vor, der Reflektanzdaten bereits während der Messung vorfiltert. Wir verwenden ihn in einem adaptiven Abtastschema. (2) Wir führen einen merkmalgesteuerten Bildsynthesealgorithmus für die Interpolation von grob abgetasteten Reflektanzdaten ein. (3) Wir schlagen eine implizite Beschreibung von Reflektanzdaten vor, die mit einem Bayesschen Ansatz komplexe Szenen anhand des Beispiels eines viel einfacheren Referenzobjektes neu beleuchtet. (4) Unter der Verwendung optischer Komponenten schaffen wir passive Aufbauten zur Darstellung von Reflektanzfeldern in Echtzeit, indem wir einfallende Beleuchtung direkt in das gewünschte Bild umwandeln

Perceptually-motivated, interactive rendering and editing of global illumination

This thesis proposes several new perceptually-motivated techniques to synthesize, edit and enhance depiction of three-dimensional virtual scenes. Finding algorithms that fit the perceptually economic middle ground between artistic depiction and full physical simulation is the challenge taken in this work. First, we will present three interactive global illumination rendering approaches that are inspired by perception to efficiently depict important light transport. Those methods have in common to compute global illumination in large and fully dynamic scenes allowing for light, geometry, and material changes at interactive or real-time rates. Further, this thesis proposes a tool to edit reflections, that allows to bend physical laws to match artistic goals by exploiting perception. Finally, this work contributes a post-processing operator that depicts high contrast scenes in the same way as artists do, by simulating it "seen'; through a dynamic virtual human eye in real-time.Diese Arbeit stellt eine Anzahl von Algorithmen zur Synthese, Bearbeitung und verbesserten Darstellung von virtuellen drei-dimensionalen Szenen vor. Die Herausforderung liegt dabei in der Suche nach Ausgewogenheit zwischen korrekter physikalischer Berechnung und der künstlerischen, durch die Gesetze der menschlichen Wahrnehmung motivierten Praxis. Zunächst werden drei Verfahren zur Bild-Synthese mit globaler Beleuchtung vorgestellt, deren Gemeinsamkeit in der effizienten Handhabung großer und dynamischer virtueller Szenen liegt, in denen sich Geometrie, Materialen und Licht frei verändern lassen. Darauffolgend wird ein Werkzeug zum Editieren von Reflektionen in virtuellen Szenen das die menschliche Wahrnehmung ausnutzt um künstlerische Vorgaben umzusetzen, vorgestellt. Die Arbeit schließt mit einem Filter am Ende der Verarbeitungskette, der den wahrgenommen Kontrast in einem Bild erhöht, indem er die Entstehung von Glanzeffekten im menschlichen Auge nachbildet