Capturing Spatially Varying Anisotropic Reflectance Parameters using Fourier Analysis

International audienceReflectance parameters condition the appearance of objects in photorealistic rendering. Practical acquisition of reflectance parameters is still a difficult problem. Even more so for spatially varying or anisotropic materials, which increase the number of samples required. In this paper, we present an algorithm for acquisition of spatially varying anisotropic materials, sampling only a small number of directions. Our algorithm uses Fourier analysis to extract the material parameters from a sub-sampled signal. We are able to extract diffuse and specular reflectance, direction of anisotropy, surface normal and reflectance parameters from as little as 20 sample directions. Our system makes no assumption about the stationarity or regularity of the materials, and can recover anisotropic effects at the pixel level

Realistic Visualization of Animated Virtual Cloth

Photo-realistic rendering of real-world objects is a broad research area with applications in various different areas, such as computer generated films, entertainment, e-commerce and so on. Within photo-realistic rendering, the rendering of cloth is a subarea which involves many important aspects, ranging from material surface reflection properties and macroscopic self-shadowing to animation sequence generation and compression. In this thesis, besides an introduction to the topic plus a broad overview of related work, different methods to handle major aspects of cloth rendering are described. Material surface reflection properties play an important part to reproduce the look & feel of materials, that is, to identify a material only by looking at it. The BTF (bidirectional texture function), as a function of viewing and illumination direction, is an appropriate representation of reflection properties. It captures effects caused by the mesostructure of a surface, like roughness, self-shadowing, occlusion, inter-reflections, subsurface scattering and color bleeding. Unfortunately a BTF data set of a material consists of hundreds to thousands of images, which exceeds current memory size of personal computers by far. This work describes the first usable method to efficiently compress and decompress a BTF data for rendering at interactive to real-time frame rates. It is based on PCA (principal component analysis) of the BTF data set. While preserving the important visual aspects of the BTF, the achieved compression rates allow the storage of several different data sets in main memory of consumer hardware, while maintaining a high rendering quality. Correct handling of complex illumination conditions plays another key role for the realistic appearance of cloth. Therefore, an upgrade of the BTF compression and rendering algorithm is described, which allows the support of distant direct HDR (high-dynamic-range) illumination stored in environment maps. To further enhance the appearance, macroscopic self-shadowing has to be taken into account. For the visualization of folds and the life-like 3D impression, these kind of shadows are absolutely necessary. This work describes two methods to compute these shadows. The first is seamlessly integrated into the illumination part of the rendering algorithm and optimized for static meshes. Furthermore, another method is proposed, which allows the handling of dynamic objects. It uses hardware-accelerated occlusion queries for the visibility determination. In contrast to other algorithms, the presented algorithm, despite its simplicity, is fast and produces less artifacts than other methods. As a plus, it incorporates changeable distant direct high-dynamic-range illumination. The human perception system is the main target of any computer graphics application and can also be treated as part of the rendering pipeline. Therefore, optimization of the rendering itself can be achieved by analyzing human perception of certain visual aspects in the image. As a part of this thesis, an experiment is introduced that evaluates human shadow perception to speedup shadow rendering and provides optimization approaches. Another subarea of cloth visualization in computer graphics is the animation of the cloth and avatars for presentations. This work also describes two new methods for automatic generation and compression of animation sequences. The first method to generate completely new, customizable animation sequences, is based on the concept of finding similarities in animation frames of a given basis sequence. Identifying these similarities allows jumps within the basis sequence to generate endless new sequences. Transmission of any animated 3D data over bandwidth-limited channels, like extended networks or to less powerful clients requires efficient compression schemes. The second method included in this thesis in the animation field is a geometry data compression scheme. Similar to the BTF compression, it uses PCA in combination with clustering algorithms to segment similar moving parts of the animated objects to achieve high compression rates in combination with a very exact reconstruction quality.Realistische Visualisierung von animierter virtueller Kleidung Das photorealistisches Rendering realer Gegenstände ist ein weites Forschungsfeld und hat Anwendungen in vielen Bereichen. Dazu zählen Computer generierte Filme (CGI), die Unterhaltungsindustrie und E-Commerce. Innerhalb dieses Forschungsbereiches ist das Rendern von photorealistischer Kleidung ein wichtiger Bestandteil. Hier reichen die wichtigen Aspekte, die es zu berücksichtigen gilt, von optischen Materialeigenschaften über makroskopische Selbstabschattung bis zur Animationsgenerierung und -kompression. In dieser Arbeit wird, neben der Einführung in das Thema, ein weiter Überblick über ähnlich gelagerte Arbeiten gegeben. Der Schwerpunkt der Arbeit liegt auf den wichtigen Aspekten der virtuellen Kleidungsvisualisierung, die oben beschrieben wurden. Die optischen Reflektionseigenschaften von Materialoberflächen spielen eine wichtige Rolle, um das so genannte look & feel von Materialien zu charakterisieren. Hierbei kann ein Material vom Nutzer identifiziert werden, ohne dass er es direkt anfassen muss. Die BTF (bidirektionale Texturfunktion)ist eine Funktion die abhängig von der Blick- und Beleuchtungsrichtung ist. Daher ist sie eine angemessene Repräsentation von Reflektionseigenschaften. Sie enthält Effekte wie Rauheit, Selbstabschattungen, Verdeckungen, Interreflektionen, Streuung und Farbbluten, die durch die Mesostruktur der Oberfläche hervorgerufen werden. Leider besteht ein BTF Datensatz eines Materials aus hunderten oder tausenden von Bildern und sprengt damit herkömmliche Hauptspeicher in Computern bei weitem. Diese Arbeit beschreibt die erste praktikable Methode, um BTF Daten effizient zu komprimieren, zu speichern und für Echtzeitanwendungen zum Visualisieren wieder zu dekomprimieren. Die Methode basiert auf der Principal Component Analysis (PCA), die Daten nach Signifikanz ordnet. Während die PCA die entscheidenen visuellen Aspekte der BTF erhält, können mit ihrer Hilfe Kompressionsraten erzielt werden, die es erlauben mehrere BTF Materialien im Hauptspeicher eines Consumer PC zu verwalten. Dies erlaubt ein High-Quality Rendering. Korrektes Verwenden von komplexen Beleuchtungssituationen spielt eine weitere, wichtige Rolle, um Kleidung realistisch erscheinen zu lassen. Daher wird zudem eine Erweiterung des BTF Kompressions- und Renderingalgorithmuses erläutert, die den Einsatz von High-Dynamic Range (HDR) Beleuchtung erlaubt, die in environment maps gespeichert wird. Um die realistische Erscheinung der Kleidung weiter zu unterstützen, muss die makroskopische Selbstabschattung integriert werden. Für die Visualisierung von Falten und den lebensechten 3D Eindruck ist diese Art von Schatten absolut notwendig. Diese Arbeit beschreibt daher auch zwei Methoden, diese Schatten schnell und effizient zu berechnen. Die erste ist nahtlos in den Beleuchtungspart des obigen BTF Renderingalgorithmuses integriert und für statische Geometrien optimiert. Die zweite Methode behandelt dynamische Objekte. Dazu werden hardwarebeschleunigte Occlusion Queries verwendet, um die Sichtbarkeitsberechnung durchzuführen. Diese Methode ist einerseits simpel und leicht zu implementieren, anderseits ist sie schnell und produziert weniger Artefakte, als vergleichbare Methoden. Zusätzlich ist die Verwendung von veränderbarer, entfernter HDR Beleuchtung integriert. Das menschliche Wahrnehmungssystem ist das eigentliche Ziel jeglicher Anwendung in der Computergrafik und kann daher selbst als Teil einer erweiterten Rendering Pipeline gesehen werden. Daher kann das Rendering selbst optimiert werden, wenn man die menschliche Wahrnehmung verschiedener visueller Aspekte der berechneten Bilder analysiert. Teil der vorliegenden Arbeit ist die Beschreibung eines Experimentes, das menschliche Schattenwahrnehmung untersucht, um das Rendern der Schatten zu beschleunigen. Ein weiteres Teilgebiet der Kleidungsvisualisierung in der Computergrafik ist die Animation der Kleidung und von Avataren für Präsentationen. Diese Arbeit beschreibt zwei neue Methoden auf diesem Teilgebiet. Einmal ein Algorithmus, der für die automatische Generierung neuer Animationssequenzen verwendet werden kann und zum anderen einen Kompressionsalgorithmus für eben diese Sequenzen. Die automatische Generierung von völlig neuen, anpassbaren Animationen basiert auf dem Konzept der Ähnlichkeitssuche. Hierbei werden die einzelnen Schritte von gegebenen Basisanimationen auf Ähnlichkeiten hin untersucht, die zum Beispiel die Geschwindigkeiten einzelner Objektteile sein können. Die Identifizierung dieser Ähnlichkeiten erlaubt dann Sprünge innerhalb der Basissequenz, die dazu benutzt werden können, endlose, neue Sequenzen zu erzeugen. Die Übertragung von animierten 3D Daten über bandbreitenlimitierte Kanäle wie ausgedehnte Netzwerke, Mobilfunk oder zu sogenannten thin clients erfordert eine effiziente Komprimierung. Die zweite, in dieser Arbeit vorgestellte Methode, ist ein Kompressionsschema für Geometriedaten. Ähnlich wie bei der Kompression von BTF Daten wird die PCA in Verbindung mit Clustering benutzt, um die animierte Geometrie zu analysieren und in sich ähnlich bewegende Teile zu segmentieren. Diese erkannten Segmente lassen sich dann hoch komprimieren. Der Algorithmus arbeitet automatisch und erlaubt zudem eine sehr exakte Rekonstruktionsqualität nach der Dekomprimierung

Real-time Modelling, Diagnostics and Optimised MPPT for Residential PV Systems

The work documented in the thesis has been focused into two main sections. The first part is centred around Maximum Power Point Tracking (MPPT) techniques for photovoltaic arrays, optimised for fast-changing environmental conditions, and is described in Chapter 2. The second part is dedicated to diagnostic functions as an additional tool to maximise the energy yield of photovoltaic arrays (Chapter 4). Furthermore, mathematical models of PV panels and arrays have been developed and built (detailed in Chapter 3) for testing MPPT algorithms, and for diagnostic purposes.In Chapter 2 an overview of the today’s most popular MPPT algorithms is given, and, considering their difficulty in tracking under variable conditions, a simple technique is proposed to overcome this drawback. The method separates the MPPT perturbation effects from environmental changes and provides correct information to the tracker, which is therefore not affected by the environmental fluctuations. The method has been implemented based on the Perturb and Observe (P&O), and the experimental results demonstrate that it preserves the advantages of the existing tracker in being highly efficient during stable conditions, having a simple and generic nature, and has the benefit of also being efficient in fast-changing conditions. Furthermore, the algorithm has been successfully implemented on a commercial PV inverter, currently on the market. In Chapter 3, an overview of the existing mathematical models used to describe the electrical behaviour of PV panels is given, followed by the parameter determination for the five-parameter single-exponential model based on datasheet values, which has been used for the implementation of a PV simulator taking in account the shape, size ant intensity of partial shadow in respect to bypass diodes.In order to eliminate the iterative calculations for parameter determinations, a simplified three-parameter model is used throughout Chapter 4, dedicated to diagnostic functions of PV panels. Simple analytic expressions for the model important parameters, which could reflect deviations from the normal (e.g. from datasheet or reference measurement) I −V characteristic, is proposed.A considerable part of the thesis is dedicated to the diagnostic functions of crystalline photovoltaic panels, aimed to detect failures related to increased series resistance and partial shadowing, the two major factors responsible for yield-reduction of residential photovoltaic systems.Combining the model calculations with measurements, a method to detect changes in the panels’ series resistance based on the slope of the I − V curve in the vicinity of open-circuit conditions and scaled to Standard Test Conditions (STC) , is proposed. The results confirm the benefits of the proposed method in terms of robustness to irradiance changes and to partial shadows.In order to detect partial shadows on PV panels, a method based on equivalent thermal voltage (Vt) monitoring is proposed. Vt is calculated using the simplified three-parameter model, based on experimental curve. The main advantages of the method are the simple expression for Vt, high sensitivity to even a relatively small area of partial shadow and very good robustness against changes in series resistance.Finally, in order to quantify power losses due to different failures, e.g. partial shadows or increased series resistance, a model based approach has been proposed to estimate the panel rated power (in STC). Although it is known that the single-exponential model has low approximation precision at low irradiation conditions, using the previously determined parameters it was possible to achieve relatively good accuracy. The main advantage of the method is that it relies on already determined parameters (Rsm, Vt) based on measurements, therefore reducing the errors introduced by the limitation of the single-exponential model especially at low irradiation conditions

Efficient algorithms for occlusion culling and shadows

The goal of this research is to develop more efficient techniques for computing the visibility and shadows in real-time rendering of three-dimensional scenes. Visibility algorithms determine what is visible from a camera, whereas shadow algorithms solve the same problem from the viewpoint of a light source. In rendering, a lot of computational resources are often spent on primitives that are not visible in the final image. One visibility algorithm for reducing the overhead is occlusion culling, which quickly discards the objects or primitives that are obstructed from the view by other primitives. A new method is presented for performing occlusion culling using silhouettes of meshes instead of triangles. Additionally, modifications are suggested to occlusion queries in order to reduce their computational overhead. The performance of currently available graphics hardware depends on the ordering of input primitives. A new technique, called delay streams, is proposed as a generic solution to order-dependent problems. The technique significantly reduces the pixel processing requirements by improving the efficiency of occlusion culling inside graphics hardware. Additionally, the memory requirements of order-independent transparency algorithms are reduced. A shadow map is a discretized representation of the scene geometry as seen by a light source. Typically the discretization causes difficult aliasing issues, such as jagged shadow boundaries and incorrect self-shadowing. A novel solution is presented for suppressing all types of aliasing artifacts by providing the correct sampling points for shadow maps, thus fully abandoning the previously used regular structures. Also, a simple technique is introduced for limiting the shadow map lookups to the pixels that get projected inside the shadow map. The fillrate problem of hardware-accelerated shadow volumes is greatly reduced with a new hierarchical rendering technique. The algorithm performs per-pixel shadow computations only at visible shadow boundaries, and uses lower resolution shadows for the parts of the screen that are guaranteed to be either fully lit or fully in shadow. The proposed techniques are expected to improve the rendering performance in most real-time applications that use 3D graphics, especially in computer games. More efficient algorithms for occlusion culling and shadows are important steps towards larger, more realistic virtual environments.reviewe

Linear Efficient Antialiased Displacement and Reflectance Mapping

International audienceWe present Linear Efficient Antialiased Displacement and Reflectance (LEADR) mapping, a reflectance filtering technique for displacement mapped surfaces. Similarly to LEAN mapping, it employs two mipmapped texture maps, which store the first two moments of the displacement gradients. During rendering, the projection of this data over a pixel is used to compute a noncentered anisotropic Beckmann distribution using only simple, linear filtering operations. The distribution is then injected in a new, physically based, rough surface microfacet BRDF model, that includes masking and shadowing effects for both diffuse and specular reflection under directional, point, and environment lighting. Furthermore, our method is compatible with animation and deformation, making it extremely general and flexible. Combined with an adaptive meshing scheme, LEADR mapping provides the very first seamless and hardware-accelerated multi-resolution representation for surfaces. In order to demonstrate its effectiveness, we render highly detailed production models in real time on a commodity GPU, with quality matching supersampled ground-truth images

Efektivní a expresivní mikrofasetové modely

Název: Efektivní a expresivní mikrofasetové modely Autor: Asen Atanasov Katedra: Katedra softwaru a výuky informatiky Vedoucí: doc. Dr. Alexander Wilkie, Katedra softwaru a výuky informatiky Abstrakt: V realistickém modelování vzhledu jsou drsné povrchy, které mají mikroskopické detaily, popsány pomocí tzv. mikrofazetových modelů. Mezi tyto modely patří analytické modely, které statisticky definují fyzikálně založený mikropovrch. Takové modely jsou široce používány v praxi, protože jsou nenáročné na výpočet a nabízejí značnou flexibilitu ve vzhledu, který s nimi lze docílit. Tyto modely mohou být rozšířené o viditelné povrchové prvky prostřednictvím normálové mapy. Stále však existují oblasti, ve kterých lze tento obecný typ modelu vylepšit: důležité funkce, jako je řízení anizotropie, někdy postrádají analytická řešení a účinné vykreslování normálových map vyžaduje přesné a obecné filtrovací algoritmy. Posunujeme předchozí práci v následujících oblastech: odvodíme analytické anizotropní modely, přeformulujeme problém filtrování a navrhneme efektivní filtrační algoritmus založený na nové datové struktuře filtračních dat. Konkrétně odvodíme obecný výsledek v mikrofazetové teorii: na základě libovolného mikropovrchu definovaného pomocí standardní mikrofazetové statistiky ukážeme, jak konstruovat statistiku...Title: Efficient and Expressive Microfacet Models Author: Asen Atanasov Department: Department of Software and Computer Science Education Supervisor: doc. Dr. Alexander Wilkie, Department of Software and Computer Science Education Abstract: In realistic appearance modeling, rough surfaces that have micro- scopic details are described using so-called microfacet models. These include analytical models that statistically define a physically-based microsurface. Such models are extensively used in practice because they are inexpensive to compute and offer considerable flexibility in terms of appearance control. Also, small but visible surface features can easily be added to them through the use of a normal map. However, there are still areas in which this general type of model can be improved: important features like anisotropy control sometimes lack analytic solutions, and the efficient rendering of normal maps requires accurate and general filtering algorithms. We advance the state of the art with regard to such models in these areas: we derive analytic anisotropic models, reformulate the filtering problem and propose an efficient filtering algorithm based on a novel filtering data structure. Specifically, we derive a general result in microfacet theory: given an arbitrary microsurface defined via standard...Katedra softwaru a výuky informatikyDepartment of Software and Computer Science EducationMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

BxDF material acquisition, representation, and rendering for VR and design

Photorealistic and physically-based rendering of real-world environments with high fidelity materials is important to a range of applications, including special effects, architectural modelling, cultural heritage, computer games, automotive design, and virtual reality (VR). Our perception of the world depends on lighting and surface material characteristics, which determine how the light is reflected, scattered, and absorbed. In order to reproduce appearance, we must therefore understand all the ways objects interact with light, and the acquisition and representation of materials has thus been an important part of computer graphics from early days. Nevertheless, no material model nor acquisition setup is without limitations in terms of the variety of materials represented, and different approaches vary widely in terms of compatibility and ease of use. In this course, we describe the state of the art in material appearance acquisition and modelling, ranging from mathematical BSDFs to data-driven capture and representation of anisotropic materials, and volumetric/thread models for patterned fabrics. We further address the problem of material appearance constancy across different rendering platforms. We present two case studies in architectural and interior design. The first study demonstrates Yulio, a new platform for the creation, delivery, and visualization of acquired material models and reverse engineered cloth models in immersive VR experiences. The second study shows an end-to-end process of capture and data-driven BSDF representation using the physically-based Radiance system for lighting simulation and rendering

Importance Sampling BRDF Derivatives

We propose a set of techniques to efficiently importance sample the derivatives of several BRDF models. In differentiable rendering, BRDFs are replaced by their differential BRDF counterparts which are real-valued and can have negative values. This leads to a new source of variance arising from their change in sign. Real-valued functions cannot be perfectly importance sampled by a positive-valued PDF and the direct application of BRDF sampling leads to high variance. Previous attempts at antithetic sampling only addressed the derivative with the roughness parameter of isotropic microfacet BRDFs. Our work generalizes BRDF derivative sampling to anisotropic microfacet models, mixture BRDFs, Oren-Nayar, Hanrahan-Krueger, among other analytic BRDFs. Our method first decomposes the real-valued differential BRDF into a sum of single-signed functions, eliminating variance from a change in sign. Next, we importance sample each of the resulting single-signed functions separately. The first decomposition, positivization, partitions the real-valued function based on its sign, and is effective at variance reduction when applicable. However, it requires analytic knowledge of the roots of the differential BRDF, and for it to be analytically integrable too. Our key insight is that the single-signed functions can have overlapping support, which significantly broadens the ways we can decompose a real-valued function. Our product and mixture decompositions exploit this property, and they allow us to support several BRDF derivatives that positivization could not handle. For a wide variety of BRDF derivatives, our method significantly reduces the variance (up to 58x in some cases) at equal computation cost and enables better recovery of spatially varying textures through gradient-descent-based inverse rendering

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