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Citations
... Surface light fields [Wood et al. 2000] are based on a view-dependent level-of-detail rendering for meshes with subdivision connectivity. Using spherical harmonics in this context has been proposed as an effective way to represent a view-dependent function, with broad adoption in rendering and modeling [Cabral et al. 1987;Sillion et al. 1991;Ramamoorthi and Hanrahan 2001a,b;Basri and Jacobs 2003;Sloan et al. 2003Sloan et al. , 2002. Recent works apply view-dependent models to reflectance [Chen et al. 2021a;Sztrajman et al. 2021] via implicit BRDF modeling and use spherical harmonics to describe view-dependent radiance distribution Wizadwongsa et al. 2021]. ...
We propose a differentiable rendering algorithm for efficient novel view synthesis. By departing from volume-based representations in favor of a learned point representation, we improve on existing methods more than an order of magnitude in memory and runtime, both in training and inference. The method begins with a uniformly-sampled random point cloud and learns per-point position and view-dependent appearance, using a differentiable splat-based renderer to evolve the model to match a set of input images. Our method is up to 300x faster than NeRF in both training and inference, with only a marginal sacrifice in quality, while using less than 10~MB of memory for a static scene. For dynamic scenes, our method trains two orders of magnitude faster than STNeRF and renders at near interactive rate, while maintaining high image quality and temporal coherence even without imposing any temporal-coherency regularizers.
... P m l (·) denotes the associated Legendre function. Sets of spherical harmonic terms are frequently employed as an orthonormal basis to describe phenomena as diverse as atomic orbitals, 25, 26 molecular binding sites, 27 computer graphics lighting, 28,29 planetary gravitational and magnetic fields, [30][31][32][33] and the cosmic microwave background: 34 ...
Purpose:
To create models that forecast longitudinal trends in changing tumor morphology and to evaluate and compare their predictive potential throughout the course of radiation therapy.
Methods:
Two morphology feature vectors were used to describe 35 gross tumor volumes (GTVs) throughout the course of intensity-modulated radiation therapy for oropharyngeal tumors. The feature vectors comprised the coordinates of the GTV centroids and a description of GTV shape using either interlandmark distances or a spherical harmonic decomposition of these distances. The change in the morphology feature vector observed at 33 time points throughout the course of treatment was described using static, linear, and mean models. Models were adjusted at 0, 1, 2, 3, or 5 different time points (adjustment points) to improve prediction accuracy. The potential of these models to forecast GTV morphology was evaluated using leave-one-out cross-validation, and the accuracy of the models was compared using Wilcoxon signed-rank tests.
Results:
Adding a single adjustment point to the static model without any adjustment points decreased the median error in forecasting the position of GTV surface landmarks by the largest amount (1.2 mm). Additional adjustment points further decreased the forecast error by about 0.4 mm each. Selection of the linear model decreased the forecast error for both the distance-based and spherical harmonic morphology descriptors (0.2 mm), while the mean model decreased the forecast error for the distance-based descriptor only (0.2 mm). The magnitude and statistical significance of these improvements decreased with each additional adjustment point, and the effect from model selection was not as large as that from adding the initial points.
Conclusions:
The authors present models that anticipate longitudinal changes in tumor morphology using various models and model adjustment schemes. The accuracy of these models depended on their form, and the utility of these models includes the characterization of patient-specific response with implications for treatment management and research study design.
... In the viewing stage, this distribution can be queried with results depending on viewer position. The distribution functions could be stored in a Hemicube as done by Immel et al. [20], as spherical harmonics as done in [5,45], or in hemispherical tables as done in [14,36,42]. The Monte Carlo method could be used by generating outgoing power rays according to the shape of the unemitted power function as shown in Figure 6. ...
... In method 1 the ray tracing is really just to accurately capture specular effects [51] and the radiosity phase my or may not include specular transport [29,46] or directional diffuse transport [36,42,45]. Any problems with the meshing in high gradient areas will be very obvious in method 1, so some form of discontinuity meshing should be used [28]. ...
this document said that absorb and reemit was asymptotically equivalent to the photon tracking model
... For global illumination the space Xn may consist of n boundary elements over which the radiance function is constant . Alternatively, it may consist of fewer boundary elements, but with internal degrees of freedom, such as tensor product polynomi- als [41], spherical harmonics [35], or wavelets [12]. In any case, each element of the function space Xn is a linear combination of a finite number of basis functions, u1, . . . ...
... Immel et al. [17] used subdivided cubes centered at a finite number of surface points to simultaneously discretize directions and positions. Sillion et al. [35] used a truncated series of spherical harmonics to capture directional dependence and a quadrilateral mesh of surface elements for the spatial dependence. As a third contrasting approach, Aupperle et al. [3] used piecewise-constant functions defined over pairs of patches to account for both directional and spatial variations. ...
... For instance, the matrix elements in the Galerkin approach of Zatz [41] required four-fold integrals, which were approximated using Gaussian quadrature. Non-diffuse environments pose a similar difficulty in that the matrix elements entail integration with reflectance functions [35]. Another form of matrix perturbation arises from simplifications made for the sake of efficiency. ...
In this paper we identify sources of error in global illumination algorithms and derive bounds for each distinct category. Errors arise from three sources: inaccuracies in the boundary data, discretization, and computation. Boundary data consist of surface geometry, reflectance functions, and emission functions, all of which may be perturbed by errors in measurement or simulation, or by simplifications made for computational efficiency. Discretization error is introduced by replacing the continuous radiative transfer equation with a finite-dimensional linear system, usually by means of boundaryelements and a corresponding projection method. Finally, computational errors perturb the finite-dimensional linear system through imprecise form factors, inner products, visibility, etc., as well as by halting iterative solvers after a finite number of steps. Using the error taxonomy introduced in the paper we examine existing global illumination algorithms and suggest new avenues of research. ...
... The result of illumination computations, the radiance L(x;!), is a function which is defined over all surfaces and all directions. For example, Sillion et al. [26] used spherical harmonics to model the directional distribution of radiance. As in the case of BRDF representations, the disadvantages of using spherical harmonics to represent radiance are due to the global support and high cost of evaluation. ...
Wavelets have proven to be powerful bases for use in numerical analysis and signal processing. Their power lies in the fact that they only require a small number of coefficients to represent general functions and large data sets accurately. This allows compression and efficient computations. Classical constructions have been limited to simple domains such as intervals and rectangles. In this paper we present a wavelet construction for scalar functions defined on the sphere. We show how biorthogonal wavelets with custom properties can be constructed with the lifting scheme. The bases are extremely easy to implement and allow fully adaptive subdivisions. We give examples of functions defined on the sphere, such as topographic data, bidirectional reflection distribution functions, and illumination, and show how they can be efficiently represented with spherical wavelets.
... In the viewing stage, this distribution can be queried with results depending on viewer position. The distribution functions could be stored in a Hemicube as done by Immel et al. [22], as spherical harmonics as done in [6,51], or in hemispherical tables as done in [16,42,48]. These latter methods use Monte Carlo by generating outgoing power rays according to the shape of the unemitted power function as shown in Figure 6. ...
... In method 1 the ray tracing is really just to accurately capture specular effects [59] and the radiosity phase my or may not include specular transport [33,52] or directional diffuse transport [42,48,51]. Any problems with the meshing in high gradient areas will be very obvious in method 1, so some form of discontinuity meshing should be used [32]. ...
Images of the real world are formed by visible light being scattered by surfaces and volumes. The goal of global illumination methods is to simulate the path of light in an environment through the image plane in order to compute realistic images. Not all applications require the accuracy attainable with global illumination methods, and not all global illumination methods are good for all possible lighting effects. In this course the audience will be given a vocabulary and taxonomy for understanding global illumination. Insight into the basic methods will be provided using comparison to physical experiments. The target audience includes: people who are new to graphics who want to be generally informed, people who teach graphics courses but specialize in some other area of graphics, and/or people who think they may need global illumination for their application and want to understand how these methods differ from other rendering techniques. 1-2 ABOUT THE SPEAKERS David C. Banks Assist...
... Because ( 0 ; ? 0 ) is a coordinate system on the hemisphere, spherical harmonics have been employed [4,38,42]. Zernike polynomials, defined on the hemisphere rather than the sphere, have also been used [7]. The danger of using these orthogonal bases is ringing, which can cause visual artifacts. ...
We discuss the theory and practical issues behind creating reflection models to show the difficulty of the problem. We survey the current approaches towards reflection models for computer graphics to show that even for simple surfaces, the important issues are far from settled. We briefly discuss future directions for research. Finally, we present a case study of a particular type of light reflection that captures some important aspects of appearance for a limited class of materials with subsurface reflection.
... Several researchers have proposed methods for generating and displaying view-independent non-diffuse global illumination solutions (e.g. [6,11]). Practical application of such methods has so far been hampered by their high computational cost, large storage requirements, and slow display speeds. ...
This paper describes a technique for using a simple shadingmethod, such as the Phong lighting model, to approximatethe appearance calculated by a more accurate method.The results are then suitable for rapid display using existinggraphics hardware and portable via standard graphicsAPI's. Interactive walkthroughs of view-independent nondi#use global illumination solutions are explored as the motivatingapplication.CR Categories: I.3.7 [Computer Graphics]: Three DimensionalGraphics and...
... Several researchers have proposed methods for generating and displaying view-independent non-diffuse global illumination solutions (e.g. [6,11]). Practical application of such methods has so far been hampered by their high computational cost, large storage requirements, and slow display speeds. ...
This paper describes a technique for using a simple shading method, such as the Phong lighting model, to approximate the appearance calculated by a more accurate method. The results are then suitable for rapid display using existing graphics hardware and portable via standard graphics API's. Interactive walkthroughs of view-independent nondi #use global illumination solutions are explored as the motivating application. CR Categories: I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism---Shading Keywords: interactive walkthroughs, non-di#use appearance, global illumination, Phong shading 1 INTRODUCTION This paper describes a method to take a view-independent non-di#use global illumination solution and approximate it in a form that is suitable for rapid display and interactive walkthroughs. The method fits "virtual lights" to each object that, when displayed using a simple Phong lighting model, will closely reproduce its correct appearance. One goal of realistic comput...
... This strategy is memory intensive and how the interpolation should be done in the table is not clear. Because 0 ; , 0 is a coordinate system on the hemisphere, spherical harmonics have been employed [5,62,75]. Zernike polynomials, defined on the hemisphere rather than the sphere, have also been used [?]. The danger of using these orthogonal bases is ringing, which can cause visual artifacts. ...
