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

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

On the well-posedness of uncalibrated photometric stereo under general lighting

Uncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem under directional lighting are well-established, there is a lack of mathematical evidence for the uniqueness of a solution under general lighting. On the other hand, stable and accurate heuristical solutions of uncalibrated photometric stereo under such general lighting have recently been proposed. The quality of the results demonstrated therein tends to indicate that the problem may actually be well-posed, but this still has to be established. The present paper addresses this theoretical issue, considering first-order spherical harmonics approximation of general lighting. Two important theoretical results are established. First, the orthographic integrability constraint ensures uniqueness of a solution up to a global concave-convex ambiguity , which had already been conjectured, yet not proven. Second, the perspective integrability constraint makes the problem well-posed, which generalizes a previous result limited to directional lighting. Eventually, a closed-form expression for the unique least-squares solution of the problem under perspective projection is provided , allowing numerical simulations on synthetic data to empirically validate our findings

Doctor of Philosophy

dissertationReal-time global illumination is the next frontier in real-time rendering. In an attempt to generate realistic images, games have followed the film industry into physically based shading and will soon begin integrating global illumination techniques. Traditional methods require too much memory and too much time to compute for real-time use. With Modular and Delta Radiance Transfer we precompute a scene-independent, low-frequency basis that allows us to calculate complex indirect lighting calculations in a much lower dimensional subspace with a reduced memory footprint and real-time execution. The results are then applied as a light map on many different scenes. To improve the low frequency results, we also introduce a novel screen space ambient occlusion technique that allows us to generate a smoother result with fewer samples. These three techniques, low and high frequency used together, provide a viable indirect lighting solution that can be run in milliseconds on today's hardware, providing a useful new technique for indirect lighting in real-time graphics

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

3D facial shape estimation from a single image under arbitrary pose and illumination.

Humans have the uncanny ability to perceive the world in three dimensions (3D), otherwise known as depth perception. The amazing thing about this ability to determine distances is that it depends only on a simple two-dimensional (2D) image in the retina. It is an interesting problem to explain and mimic this phenomenon of getting a three-dimensional perception of a scene from a flat 2D image of the retina. The main objective of this dissertation is the computational aspect of this human ability to reconstruct the world in 3D using only 2D images from the retina. Specifically, the goal of this work is to recover 3D facial shape information from a single image of unknown pose and illumination. Prior shape and texture models from real data, which are metric in nature, are incorporated into the 3D shape recovery framework. The output recovered shape, likewise, is metric, unlike previous shape-from-shading (SFS) approaches that only provide relative shape. This work starts first with the simpler case of general illumination and fixed frontal pose. Three optimization approaches were developed to solve this 3D shape recovery problem, starting from a brute-force iterative approach to a computationally efficient regression method (Method II-PCR), where the classical shape-from-shading equation is cast as a regression framework. Results show that the output of the regression-like approach is faster in timing and similar in error metrics when compared to its iterative counterpart. The best of the three algorithms above, Method II-PCR, is compared to its two predecessors, namely: (a) Castelan et al. [1] and (b) Ahmed et al. [2]. Experimental results show that the proposed method (Method II-PCR) is superior in all aspects compared to the previous state-of-the-art. Robust statistics was also incorporated into the shape recovery framework to deal with noise and occlusion. Using multiple-view geometry concepts [3], the fixed frontal pose was relaxed to arbitrary pose. The best of the three algorithms above, Method II-PCR, once again is used as the primary 3D shape recovery method. Results show that the pose-invariant 3D shape recovery version (for input with pose) has similar error values compared to the frontal-pose version (for input with frontal pose), for input images of the same subject. Sensitivity experiments indicate that the proposed method is, indeed, invariant to pose, at least for the pan angle range of (-50° to 50°). The next major part of this work is the development of 3D facial shape recovery methods, given only the input 2D shape information, instead of both texture and 2D shape. The simpler case of output 3D sparse shapes was dealt with, initially. The proposed method, which also use a regression-based optimization approach, was compared with state-of-the art algorithms, showing decent performance. There were five conclusions that drawn from the sparse experiments, namely, the proposed approach: (a) is competitive due to its linear and non-iterative nature, (b) does not need explicit training, as opposed to [4], (c) has comparable results to [4], at a shorter computational time, (d) better in all aspects than Zhang and Samaras [5], and (e) has the limitation, together with [4] and [5], in terms of the need to manually annotate the input 2D feature points. The proposed method was then extended to output 3D dense shapes simply by replacing the sparse model with its dense equivalent, in the regression framework inside the 3D face recovery approach. The numerical values of the mean height and surface orientation error indicate that even if shading information is unavailable, a decent 3D dense reconstruction is still possible

Radiometric Scene Decomposition: Estimating Complex Re ectance and Natural Illumination from Images

The phrase, "a picture is worth a thousand words," is often used to emphasize the wealth of information encoded into an image. While much of this information (e.g., the identities of people in an image, the type and number of objects in an image, etc.) is readily inferred by humans, fully understanding an image is still extremely difficult for computers. One important set of information encoded into images are radiometric scene properties---the properties of a scene related to light. Each pixel in an image indicates the amount of light received by the camera after being reflected, transmitted, or emitted by objects in a scene. It follows that we can learn about the objects of the scene and the scene itself through the image by thinking about the interaction between light and geometry in a scene. The appearance of objects in an image is primarily due to three factors: the geometry of the scene, the reflectance of the surfaces, and the incident illumination of the scene. Recovering these hidden properties of scenes can give us a deep understanding of a scene. For example, the reflectance of a surface can give a hint at the material properties of that surface. In this thesis, we address the question of how to recover complex, spatially-varying reflectance functions and natural illumination in real scenes from one or more images with known or approximately-known geometry. Recovering latent radiometric properties from images is difficult because of the severe underdetermined nature of the problem (i.e., there are many potential combinations of reflectance, light, and geometry that would produce identical input images) combined with the overwhelming dimensionality of the problem. In the real world, reflectance functions are complex, requiring many parameters to accurately model. An important aspect of solving this problem is to create a compact mathematical model to express a wide range of surface reflectance. We must also carefully model scene illumination, which typically exhibits complex behavior as well. Prior work has often simply assumed the light incident to a scene is made up of one or more infinitely-distant point lights. This assumption, however, rarely holds up in practice as not only are scenes illuminated by every possible direction, they are also illuminated by other objects interreflecting one another. To accurately infer reflectance and illumination of real-world scenes, we must account for the real-world behavior of reflectance and illumination. In this work, we develop a mathematical framework for the inference of complex, spatially-varying reflectance and natural illumination in real-world scenes. We use a Bayesian approach, where the radiometric properties (i.e., reflectance and illumination) to be inferred are modeled as random variables. We can then apply statistical priors to model how reflectance and illumination often exist in the real world to help combat the ambiguities created through the image formation process. We use our framework to infer the reflectance and illumination in a variety of scenes, ultimately using it in unrestricted real-world scenes. We show that the framework is capable of recovering complex reflectance and natural illumination in the real world.Ph.D., Computer Science -- Drexel University, 201