Accurate and Efficient Filtering using Anisotropic Filter Decomposition

Efficient filtering remains an important challenge in computer graphics, particularly when filters are spatially-varying, have large extent, and/or exhibit complex anisotropic profiles. We present an efficient filtering approach for these difficult cases based on anisotropic filter decomposition (IFD). By decomposing complex filters into linear combinations of simpler, displaced isotropic kernels, and precomputing a compact prefiltered dataset, we are able to interactively apply any number of---potentially transformed---filters to a signal. Our performance scales linearly with the size of the decomposition, not the size nor the dimensionality of the filter, and our prefiltered data requires reasonnable storage, comparing favorably to the state-of-the-art. We apply IFD to interesting problems in image processing and realistic rendering.Les opérations de filtrage en synthèse/analyse d'images sont coûteuses à effectuer lorsque les filtres varient spatialement, sont très étendus et/ou très anisotropes. Nous présentons dans ce cas précis une méthode pour rendre le filtrage efficace, basée sur une décomposition du filtre en une combinaison linéaire de filtres isotropes, en translation. Le coût de notre méthode est linéaire par rapport au nombre de filtres utilisés dans la décomposition, et ne dépend pas de la taille des données filtrées. Nous en présentons différentes applications, en analyses d'images et en rendu

Locally Adaptive Products for Genuine Spherical Harmonic Lighting

Precomputed radiance transfer techniques have been broadly used for supporting complex illumination effects on diffuse and glossy objects. Although working with the wavelet domain is efficient in handling all-frequency illumination, the spherical harmonics domain is more convenient for interactively changing lights and views on the fly due to the rotational invariant nature of the spherical harmonic domain. For interactive lighting, however, the number of coefficients must be limited and the high orders of coefficients have to be eliminated. Therefore spherical harmonic lighting has been preferred and practiced only for interactive soft-diffuse lighting. In this paper, we propose a simple but practical filtering solution using locally adaptive products of high-order harmonic coefficients within the genuine spherical harmonic lighting framework. Our approach works out on the fly in two folds. We first conduct multi-level filtering on vertices in order to determine regions of interests, where the high orders of harmonics are necessary for high frequency lighting. The initially determined regions of interests are then refined through filling in the incomplete regions by traveling the neighboring vertices. Even not relying on graphics hardware, the proposed method allows to compute high order products of spherical harmonic lighting for both diffuse and specular lighting

A Wave Optics Propagation Code for Multi-Conjugate Adaptive Optics

We describe the purpose, theory, implementation and sample results of a wave optics propagation simulation developed to study multi-conjugate adaptive optics (MCAQ) for 4-10m class telescopes. This code was more specifically developed to assess the impact of diffraction effects and a variety of implementation error sources upon the performance of the Gemini-South MCAO system. These errors include: Hartmann sensing with extended and elongated laser guide stars, optical propagation effects through the optics and atmosphere, laser guide star (LGS) projection through the atmosphere, deformable mirror (DM) and wave front sensor (WFS) misregistration, and calibration for non-common path errors. The code may be run in either a wave optics or geometric propagation mode to allow the code to be anchored against linear analytical models and to explicitly evaluate the impact of diffraction effects. The code is written in MATLAB, and complete simulations of the Gemini-South MCAO design (including 3 deformable mirrors with 769 actuators, 5 LGS WFS with 1020 subapertures, 3 tip/tilt natural guide star (NGS) WFS, and 50 meter phase screens with 1/32nd meter resolution) are possible using a Pentium III but require 1 to 6 days. Sample results are presented for Gemini-South MCAO as well as simpler AO systems. Several possibilities for parallelizing the code for faster execution and the modeling of extremely large telescopes (ELT's) are discussed

View-dependent precomputed light transport using non-linear Gaussian function approximations

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 43-46).We propose a real-time method for rendering rigid objects with complex view-dependent effects under distant all-frequency lighting. Existing precomputed light transport approaches can render rich global illumination effects, but high-frequency view-dependent effects such as sharp highlights remain a challenge. We introduce a new representation of the light transport operator based on sums of Gaussians. The non-linear parameters of the representation allow for 1) arbitrary bandwidth because scale is encoded as a direct parameter; and 2) high-quality interpolation across view and mesh triangles because we interpolate the average direction of the incoming light, thereby preventing linear cross-fading artifacts. However, fitting the precomputed light transport data to this new representation requires solving a non-linear regression problem that is more involved than traditional linear and non-linear (truncation) approximation techniques. We present a new data fitting method based on optimization that includes energy terms aimed at enforcing good interpolation. We demonstrate that our method achieves high visual quality for a small storage cost and fast rendering time.by Paul Elijah Green.S.M

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

Continuous wavelet transforms on the unit sphere

Doutoramento em MatemáticaFCT - SFRH/BD/12744/200

ADVANCES IN SEQUENTIAL DATA ASSIMILATION AND NUMERICAL WEATHER FORECASTING: AN ENSEMBLE TRANSFORM KALMAN-BUCY FILTER, A STUDY ON CLUSTERING IN DETERMINISTIC ENSEMBLE SQUARE ROOT FILTERS, AND A TEST OF A NEW TIME STEPPING SCHEME IN AN ATMOSPHERIC MODEL

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn't represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter

Hessian-based occlusion-aware radiance caching

Simuler efficacement l'éclairage global est l'un des problèmes ouverts les plus importants en infographie. Calculer avec précision les effets de l'éclairage indirect, causés par des rebonds secondaires de la lumière sur des surfaces d'une scène 3D, est généralement un processus coûteux et souvent résolu en utilisant des algorithmes tels que le path tracing ou photon mapping. Ces techniquesrésolvent numériquement l'équation du rendu en utilisant un lancer de rayons Monte Carlo. Ward et al. ont proposé une technique nommée irradiance caching afin d'accélérer les techniques précédentes lors du calcul de la composante indirecte de l'éclairage global sur les surfaces diffuses. Krivanek a étendu l'approche de Ward et Heckbert pour traiter le cas plus complexe des surfaces spéculaires, en introduisant une approche nommée radiance caching. Jarosz et al. et Schwarzhaupt et al. ont proposé un modèle utilisant le hessien et l'information de visibilité pour raffiner le positionnement des points de la cache dans la scène, raffiner de manière significative la qualité et la performance des approches précédentes. Dans ce mémoire, nous avons étendu les approches introduites dans les travaux précédents au problème du radiance caching pour améliorer le positionnement des éléments de la cache. Nous avons aussi découvert un problème important négligé dans les travaux précédents en raison du choix des scènes de test. Nous avons fait une étude préliminaire sur ce problème et nous avons trouvé deux solutions potentielles qui méritent une recherche plus approfondie.Efficiently simulating global illumination is one of the most important open problems in computer graphics. Accurately computing the effects of indirect illumination, caused by secondary bounces of light off surfaces in a 3D scene, is generally an expensive process and often solved using algorithms such as path tracing or photon mapping. These approaches numerically solve the rendering equation using stochastic Monte Carlo ray tracing. Ward et al. proposed irradiance caching to accelerate these techniques when computing the indirect illumination component on diffuse surfaces. Krivanek extended the approach of Ward and Heckbert to handle the more complex case of glossy surfaces, introducing an approach referred to as radiance caching. Jarosz et al. and Schwarzhaupt et al. proposed a more accurate visibility-aware Hessian-based model to greatly improve the placement of records in the scene for use in an irradiance caching context, significantly increasing the quality and performance of the baseline approach. In this thesis, we extended similar approaches introduced in these aforementioned work to the problem of radiance caching to improve the placement of records. We also discovered a crucial problem overlooked in the previous work due to the choice of test scenes. We did a preliminary study of this problem, and found several potential solutions worth further investigation