Image synthesis algorithms are commonly compared on the basis of running times and/or perceived quality of the generated images. In the case of Monte Carlo techniques, assessment often entails a qualitative impression of convergence toward a reference standard and severity of visible noise; these amount to subjective assessments of the mean and variance of the estimators, respectively. In this paper we argue that such assessments should be augmented by well-known statistical hypothesis testing methods. In particular, we show how to perform a number of such tests to assess random variables that commonly arise in image synthesis such as those estimating irradiance, radiance, pixel color, etc. We explore five broad categories of tests: 1) determining whether the mean is equal to a reference standard, such as an analytical value, 2) determining that the variance is bounded by a given constant, 3) comparing the means of two different random variables, 4) comparing the variances of two different random variables, and 5) verifying that two random variables stem from the same parent distribution. The level of significance of these tests can be controlled by a parameter. We demonstrate that these tests can be used for objective evaluation of Monte Carlo estimators to support claims of zero or small bias and to provide quantitative assessments of variance reduction techniques. We also show how these tests can be used to detect errors in sampling or in computing the density of an importance function in MC integrations.

We describe an experimental interface that anticipates a user's intentions and accommodates predicted changes in advance. Our canonical example is an interactive version of ``magnetic poetry'' in which rectangular blocks containing single words can be juxtaposed to form arbitrary sentences or ``poetry.'' The user can rearrange the blocks at will, forming and dissociating word sequences. A crucial attribute of the blocks in our system is that they anticipate insertions and gracefully rearrange themselves in time to make space for a new word or phrase. The challenges in creating such an interface are three fold: 1) the user's intentions must be inferred from noisy input, 2) arrangements must be altered smoothly and intuitively in response to anticipated changes, and 3) new and changing goals must be handled gracefully at any time, even in mid animation. We describe a general approach for handling the dynamic creation and deletion of organizational goals. Fluid motion is achieved by continually applying and correcting goal-directed forces to the objects. Future applications of this idea include the manipulation of text and graphical elements within documents and the manipulation of symbolic information such as equations.

A bidirectional reflectance distribution function (BRDF) is often expressed as a function of four real variables: two spherical coordinates in each of the the "incoming" and "outgoing" directions. However, many BRDFs reduce to functions of fewer variables. For example, isotropic reflection can be represented by a function of three variables. Some BRDF models can be reduced further. In this paper, we introduce new sets of coordinates which we use to reduce the dimensionality of several well-known analytic BRDFs as well as empirically measured BRDF data. The proposed coordinate systems are barycentric with respect to a triangular support with a direct physical interpretation. One coordinate set is based on the BRDF model proposed by Lafortune. Another set, based on a model of Ward, is associated with the "halfway" vector common in analytical BRDF formulas. Through these coordinate sets we establish lower bounds on the approximation error inherent in the models on which they are based. We present a third set of coordinates, not based on any analytical model, that performs well in approximating measured data. Finally, our proposed variables suggest novel ways of constructing and visualizing BRDFs.

We describe a system for freehand entry and editing of mathematical expressions using a pen and tablet. The expressions are entered in the same way that they would be written on paper. The system interprets the results and generates output in a form suitable for use in other applications, such as word processors or symbolic manipulators. Interpretation includes character segmentation, character recognition, and formula parsing. Our interface incorporates easy to use tools for correcting interpretation errors at any stage. The user can also edit the handwritten representation and ask the system to reinterpret the results. By recovering the formula's structure directly from its handwritten form, the user is free to use common conventions of mathematical notation without regard to internal representation. We report the results of a small user study, which indicate that the new style of interaction is effective.

We describe a new sketching interface in which shape recognition and morphing are tightly coupled. Raw input strokes are continuously morphed into ideal geometric shapes, even before the pen is lifted. By means of smooth and continual shape transformations the user is apprised of recognition progress and the appearance of the final shape, yet always retains a sense of control over the process. At each time t the system uses the trajectory traced out thus far by the pen coupled with the current appearance of the time-varying shape to classify the sketch as one of several pre-defined basic shapes. The recognition operation is performed using shape-specific fits based on least-squares or relaxation, which are continuously updated as the user draws. We describe the time-dependent transformation of the sketch, beginning with the raw pen trajectory, using a family of first-order ordinary differential equations that depend on time and the current shape of the sketch. Using this formalism, we describe several possible behaviors that result by varying the relative significance of new and old portions of a stroke, changing the “viscosity” of the morph, and enforcing different end conditions. A preliminary user study suggests that the new interface is particularly effective for rapidly constructing diagrams consisting of simple shapes.

In this paper we apply perturbation methods to the problem of computing specular reflections in curved surfaces. The key idea is to generate families of closely related optical paths by expanding a given path into a high-dimensional Taylor series. Our path perturbation method is based on closed-form expressions for linear and higher-order approximations of ray paths, which are derived using Fermat's Variation Principle and the Implicit Function Theorem (IFT). The perturbation formula presented here holds for general multiple-bounce reflection paths and provides a mathematical foundation for exploiting path coherence in ray tracing acceleration techniques and incremental rendering. To illustrate its use, we describe an algorithm for fast approximation of specular reflections on curved surfaces; the resulting images are highly accurate and nearly indistinguishable from ray traced images.

We describe an approach for interactively approximating specular reflections in arbitrary curved surfaces. The technique is applicable to any smooth implicitly defined reflecting surface that is equipped with a ray intersection procedure; it is also extremely efficient as it employs local perturbations to interpolate point samples analytically. After ray tracing a sparse set of reflection paths with respect to a given vantage point and static reflecting surfaces, the algorithm rapidly approximates reflections of arbitrary points in 3-space by expressing them as perturbations of nearby points with known reflections. The reflection of each new point is approximated to second-order accuracy by applying a closed-form perturbation formula to one or more nearby reflection paths. This formula is derived from the Taylor expansion of a reflection path and is based on first and second-order path derivatives. After preprocessing, the approach is fast enough to compute reflections of tessellated diffuse objects in arbitrary curved surfaces at interactive rates using standard graphics hardware. The resulting images are nearly indistinguishable from ray traced images that take several orders of magnitude longer to generate.

We describe a new approach for creating concise high-level generative models from range images or other approximate representations of real objects.Using data from a variety of acquisition techniques and a user-defined class of models, our method produces a compact object representation that is intuitive and easy to edit.The algorithm has two inter-related phases: recognition, which chooses an appropriate model within a user-specified hierarchy, and parameter estimation, which adjusts the model to best fit the data.Since the approach is model-based, it is relatively insensitive to noise and missing data.We describe practical heuristics for automatically making tradeoffs between simplicity and accuracy to select the best model in a given hierarchy.We also describe a general and efficient technique for optimizing a model by refining its constituent curves.We demonstrate our approach for model recovery using both real and synthetic data and several generative model hierarchies.

Our goal is to develop physically based lighting models and perceptually based rendering procedures for computer graphics that will produce synthetic images that are visually and measurably indistinguishable from real-world images. Fidelity of the physical simulation is of primary concern. Our research framework is subdivided into three sub-sections: the local light reflection model, the energy transport simulation, and the visual display algorithms. The first two subsections are physically based, and the last is perceptually based. We emphasize the comparisons between simulations and actual measurements, the difficulties encountered, and the need to utilize the vast amount of psychophysical research already conducted. Future research directions are enumerated. We hope that results of this research will help establish a more fundamental, scientific approach for future rendering algorithms. This presentation describes a chronology of past research in global illumination and how parts of our new system are currently being developed.

We present new techniques for computing illumination from non-di#use luminaires and scattering from non-di#use surfaces. The methods are based on new closed-form expressions derived using a generalization of irradiance known as irradiance tensors. The elements of these tensors are angular moments, weighted integrals of the radiation field that are useful in simulating a variety of non-di#use phenomena. Applications include the computation of irradiance due to directionally-varying area light sources, reflections from glossy surfaces, and transmission through glossy surfaces. The principles apply to any emission, reflection, or transmission distribution expressed as a polynomial over the unit sphere. We derive expressions for a simple but versatile subclass of these functions, called axial moments, and present complete algorithms their exact evaluation in polyhedral environments. The algorithms are demonstrated by simulating Phong-like emission and scattering e#ects. CR Categories an...

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The irradiance at a point on a surface due to a polyhedral source of uniform brightness is given by a well-known analytic formula. In this paper we derive the corresponding analytic expression for the irradiance Jacobian, the derivative of the vector representation of irradiance. Although the result is elementary for unoccluded sources, within penumbrae the irradiance Jacobian must incorporate more information about blockers than either the irradiance or vector irradiance. The expression presented here holds for any number of polyhedral blockers and requires only a minor extension of standard polygon clipping to evaluate. To illustrate its use, three related applications are briefing described: direct computation of isolux contours, finding local irradiance extrema, and iso-meshing. Isolux contours are curves of constant irradiance across a surface that can be followed using a predictor-corrector method based on the irradiance Jacobian. Similarly, local extrema can be found using a descent method. Finally, iso-meshing is a new approach to surface mesh generation that incorporates families of isolux contours.

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 consists 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 boundary elements 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.

We present an approach for accelerating hierarchical radiosity by clustering objects. Previous approaches constructed effective hierarchies by subdividing surfaces, but could not exploit a hierarchical grouping on existing surfaces. This limitation resulted in an excessive number of initial links in complex environments. Initial linking is potentially the most expensive portion of hierarchical radiosity algorithms, and constrains the complexity of the environments that can be simulated. The clustering algorithm presented here operates by estimating energy transfer between collections of objects while maintaining reliable error bounds on each transfer. Two methods of bounding the transfers are employed with different tradeoffs between accuracy and time. In contrast with the O(s2) time and space complexity of the initial linking in previous hierarchical radiosity algorithms, the new methods have complexities of O(slogs) and O(s) for both time and space. Using these methods we have obtained speedups of two orders of magnitude for environments of moderate complexity while maintaining comparable accuracy.

Article Painting with light Share on Authors: Chris Schoeneman View Profile , Julie Dorsey View Profile , Brian Smits View Profile , James Arvo View Profile , Donald Greenberg View Profile Authors Info & Claims SIGGRAPH '93: Proceedings of the 20th annual conference on Computer graphics and interactive techniquesSeptember 1993 Pages 143–146https://doi.org/10.1145/166117.166135Online:01 September 1993Publication History 98citation1,320DownloadsMetricsTotal Citations98Total Downloads1,320Last 12 Months47Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We present a new radiosi[y algorithm for efficiently computing global solutions with respect to a constrained set of views.Radiosities of directly visible surfaces are computed to high accuracy, while those ot' surfaces having only an indirect effect are computed to an accuracy commensurate with their contribution.The algorithm uses an adaptive subdivision scheme that is guided by the interplay between two closely related transport processes: one propagating power from the light sources, and the other propagating imporrarwc from the visible surfaces.By simultaneously refining approximate solutions to the dud transport equations, computation is significantly reduced in areas that contribute little to the region of interest.This approach is very effective for complex environments in which only a small fraction is visible at any time.Our statistics show dramatic speedups over the fastest previous radiosity algorithms for diffuse environments with details at a wide range of scales.

We describe a physically-based Monte Carlo technique for approximating bidirectional reflectance distribution functions (BRDFs) for a large class of geometries by directly simulating optical scattering.The technique is more general than previous analytical models: it removes most restrictions on surface microgeometry.Three main points are described: a new representation of the BRDF, a Monte Carlo technique to estimate the coefficients of the representation, and the means of creating a milliscale BRDF from microscale scattering events.These allow the prediction of scattering from essentially arbitrary roughness geometries.The BRDF is concisely represented by a matrix of spherical harmonic coefficients; the matrix is directly estimated from a geometric optics simulation, enforcing exact reciprocity.The method applies to roughness scales that are large with respect to the wavelength of light and small with respect to the spatial density at which the BRDF is sampled across the surface; examples include brushed metal and textiles.The method is validated by comparing with an existing scattering model and sample images are generated with a physically-based global illumination algorithm.

We examine a class of adaptive sampling techniques employed in image synthesis and show that those commonly used for efficient anti-aliasing are statistically biased. This bias is dependent upon the image function being sampled as well as the strategy for determining the number of samples to use. It is most prominent in areas of high contrast and is attributable to early stages of sampling systematically favoring one extreme or the other. If the expected outcome of the entire adaptive sampling algorithm is considered, we find that the bias of the early decisions is still present in the final estimator. We propose an alternative strategy for performing adaptive sampling that is unbiased but potentially more costly. We conclude that it may not always be practical to mitigate this source of bias, but as a source of error it should be considered when high accuracy and image fidelity are a central concern.

A general light transfer simulation algorithm for environments composed of materials with arbitrary reflectance functions is presented. This algorithm removes the previous practical restriction to ideal specular and/or ideal diffuse environments, and supports complex physically based reflectance distributions, This is accomplished by extending previous two-pass ray-casting radiosity approaches to handle non-uniform intensity distributions, and resolving all possible energy transfers between sample points. An implementation is described based on a spherical harmonic decomposition for encoding both bidirectional reflectance distribution functions for materials, and directional intensity distributions for illuminated surfaces. The method compares favorably with experimental measurements.

The rendering equation is similar to the linear Boltzmann equation which has been widely studied in physics and nuclear engineering. Consequently, many of the powerful techniques which have been developed in these fields can be applied to problems in image synthesis. In this paper we adapt several statistical techniques commonly used in neutron transport to stochastic ray tracing and, more generally, to Monte Carlo solution of the rendering equation. First, we describe a technique known as Russian roulette which can be used to terminate the recursive tracing of rays without introducing statistical bias. We also examine the practice of creating ray trees in classical ray tracing in the light of a well-known technique in particle transport known as splitting. We show that neither ray trees nor paths as described in [10] constitute an optimal sampling plan in themselves and that a hybrid may be more efficient.

We describe a new approach to ray tracing which drastically reduces the number of ray-object and ray-bounds intersection calculations by means of 5-dimensional space subdivision. Collections of rays originating from a common 3D rectangular volume and directed through a 2D solid angle are represented as hypercubes in 5-space. A 5D volume bounding the space of rays is dynamically subdivided into hypercubes, each linked to a set of objects which are candidates for intersection. Rays are classified into unique hypercubes and checked for intersection with the associated candidate object set. We compare several techniques for object extent testing, including boxes, spheres, plane-sets, and convex polyhedra. In addition, we examine optimizations made possible by the directional nature of the algorithm, such as sorting, caching and backface culling. Results indicate that this algorithm significantly outperforms previous ray tracing techniques, especially for comples environments.