Advisor Feed
https://feeds.library.caltech.edu/people/Arvo-J-R/advisor.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:51:37 +0000Creating Generative Models from Range Images
https://resolver.caltech.edu/CaltechTHESIS:10162018-111851476
Authors: {'items': [{'email': 'ravir@cs.ucsd.edu', 'id': 'Ramamoorthi-Ravi', 'name': {'family': 'Ramamoorthi', 'given': 'Ravi'}, 'show_email': 'NO'}]}
Year: 1998
DOI: 10.7907/VZXG-Q639
<p>We describe a new approach for creating concise high-level generative models from one or more approximate range images. Using simple acquisition techniques and a user-defined class of models, our method produces a simple and intuitive object description that is relatively insensitive to noise and is easy to manipulate and edit. The algorithm has two inter-related phases—recognition, which chooses an appropriate model within a given hierarchy, and parameter estimation, which adjusts the model to fit the data. We give a simple method for automatically making tradeoffs between simplicity and accuracy to determine the best model. We also describe general techniques to optimize a specific generative model. In particular, we address the problem of creating a suitable objective function that is sufficiently continuous for use with finite-difference based optimization techniques. Our technique for model recovery and subsequent manipulation and editing is demonstrated on real objects—a spoon, bowl, ladle, and cup—using a simple tree of possible generative models.</p>
<p>We believe that higher-level model representations are extremely important, and their recovery for actual objects is a fertile area of research towards which this thesis is a step. However, our work is preliminary and there are currently several limitations. The user is required to create a model hierarchy (and supply methods to provide an initial guess for model parameters within this hierarchy); the use of a large pre-defined class of models can help alleviate this problem. Further, we have demonstrated our technique on only a simple tree of generative models. While our approach is fairly general, a real system would require a tree that is significantly larger. Our methods work only where the entire object can be accurately represented as a single generative model; future work could use constructive solid geometry operations on simple generative models to represent more complicated shapes. We believe that many of the above limitations can be addressed in future work, allowing us to easily acquire and process three-dimensional shape in a simple, intuitive and efficient manner.</p>https://thesis.library.caltech.edu/id/eprint/11234Analysis of scalable algorithms for dynamic load balancing and mapping with application to photo-realistic rendering
https://resolver.caltech.edu/CaltechETD:etd-01232008-111520
Authors: {'items': [{'email': 'heirich@alumni.caltech.edu', 'id': 'Heirich-A-B', 'name': {'family': 'Heirich', 'given': 'Alan Bryant'}, 'show_email': 'NO'}]}
Year: 1998
DOI: 10.7907/ZVYW-H876
This thesis presents and analyzes scalable algorithms for dynamic load balancing and mapping in distributed computer systems. The algorithms are distributed and concurrent, have no central thread of control, and require no centralized communication. They are derived using spectral properties of graphs: graphs of physical network links among computers in the load balancing problem, and graphs of logical communication channels among processes in the mapping problem. A distinguishing characteristic of these algorithms is that they are scalable: the expected cost of execution does not increase with problem scale. This is proven in a scalability theorem which shows that, for several simple disturbance models, the rate of convergence to a solution is independent of scale. This property is extended through simulated examples and informal argument to general and random disturbances. A worst case disturbance is presented and shown to occur with vanishing probability as the problem scale increases. To verify these conclusions the load balancing algorithm is deployed in support of a photo-realistic rendering application on a parallel computer system based on Monte Carlo path tracing. The performance and scaling of this application, and of the dynamic load balancing algorithm, are measured on different numbers of computers. The results are consistent with the predictions of scalability, and the cost of load balancing is seen to be non-increasing for increasing numbers of computers. The quality of load balancing is evaluated and compared with the quality of solutions produced by competing approaches for up to 1,024 computers. This comparison shows that the algorithm presented here is as good as or better than the most popular competing approaches for this application. The thesis then presents the dynamic mapping algorithm, with simulations of a model problem, and suggests that the pair of algorithms presented here may be an ideal complement to more expensive algorithms such as the well-known recursive spectral bisection.
https://thesis.library.caltech.edu/id/eprint/304Mathematical Methods for Image Synthesis
https://resolver.caltech.edu/CaltechTHESIS:08272010-091235772
Authors: {'items': [{'id': 'Chen-Min-Computer-Science', 'name': {'family': 'Chen', 'given': 'Min'}, 'show_email': 'NO'}]}
Year: 2002
DOI: 10.7907/WDPH-N912
<p>This thesis presents the application of some advanced mathematical methods to image synthesis. The mainstream of our work is to formulate and analyze some rendering problems in terms of mathematical concepts, and develop some new mathematical machineries to pursue analytical solutions or nearly analytical approximations to them. An enhanced Taylor expansion formula is derived for the perturbation of a general ray-traced path and new theoretical results are presented for spatially-varying luminaires. On top of them, new deterministic algorithms are presented for simulating direct lighting and other scattering effects involving a wide range of non-diffuse surfaces and spatially-varying luminaires. Our work greatly extends the repertoire of non-Lambertian effects that can be handled in a deterministic fashion.</p>
<p>First, my previous work on "Perturbation Methods for Image Synthesis” is extended here in several ways: 1) I propose a coherent framework using closed-form path Jacobians and path Hessians to perturb a general ray-traced path involving both specular reflections and refractionsi and an algorithm similar to that used for interactive specular reflections is employed to simulate lens effects. 2) The original path Jacobian formula is simplified by means of matrix manipulations. 3) Path Jacobians and Hessians are extended to parametric surfaces which may not have an implicit definition. 4) Theoretical comparisons and connections are made with related work including pencil tracing and ray differentials. 5) Identify potential applications of perturbation methods of this nature in rendering and computer vision.</p>
<p>Next, a closed-form solution is derived for the irradiance at a point on a surface due to an arbitrary polygonal Lambertian luminaire with linearly-varying radiant exitance. The solution consists of elementary functions and a single well-behaved special function known as the Clausen integral. The expression is derived from the Taylor expansion and a recurrence formula derived for an extension of double-axis moments, and then verified by Stokes' theorem and Monte Carlo simulation. The study of linearly-varying luminaires introduces much of the machinery needed to derive closed-form solutions for the general case of luminaires with radiance distributions that vary polynomially in both position and direction.</p>
<p>Finally, the concept of irradiance tensors is generalized to account for inhomogeneous radiant exitance distributions from luminaires. These tensors are comprised of scalar elements that consist of constrained rational polynomials integrated over regions of the sphere, which arise frequently in simulating some rendering effects due to polynomially-varying luminaires. Several recurrence relations are derived for generalized irradiance tensors and their scalar elements, which reduce the surface integrals associated with spatially-varying luminaires to one-dimensional boundary integrals, leading to closed-form solutions in polyhedral environments. These formulas extend the range of illumination and non-Lambertian effects that can be computed deterministically, which includes illumination from polynomially-varying luminaires, reflections from and transmissions through glossy surfaces due to these emitters. Particularly, we have derived a general tensor formula for the irradiance due to a luminaire whose radiant exitance varies according to a monomial of any order, which subsumes Lambert's formula and expresses the solution for higher order monomials in terms of those for lower-order cases.</p>https://thesis.library.caltech.edu/id/eprint/6013Discrete Exterior Calculus
https://resolver.caltech.edu/CaltechETD:etd-05202003-095403
Authors: {'items': [{'email': 'hirani@illinois.edu', 'id': 'Hirani-Anil-Nirmal', 'name': {'family': 'Hirani', 'given': 'Anil Nirmal'}, 'orcid': '0000-0003-3506-1703', 'show_email': 'YES'}]}
Year: 2003
DOI: 10.7907/ZHY8-V329
<p>This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complex and its geometric dual. The derivation of these may require that the objects on the discrete mesh, but not the mesh itself, are interpolated.</p>
<p>Our theory includes not only discrete equivalents of differential forms, but also discrete vector fields and the operators acting on these objects. Definitions are given for discrete versions of all the usual operators of exterior calculus. The presence of forms and vector fields allows us to address their various interactions, which are important in applications. In many examples we find that the formulas derived from DEC are identitical to the existing formulas in the literature. We also show that the circumcentric dual of a simplicial complex plays a useful role in the metric dependent part of this theory. The appearance of dual complexes leads to a proliferation of the operators in the discrete theory.</p>
<p>One potential application of DEC is to variational problems which come equipped with a rich exterior calculus structure. On the discrete level, such structures will be enhanced by the availability of DEC. One of the objectives of this thesis is to fill this gap. There are many constraints in numerical algorithms that naturally involve differential forms. Preserving such features directly on the discrete level is another goal, overlapping with our goals for variational problems.</p>
<p>In this thesis we have tried to push a purely discrete point of view as far as possible. We argue that this can only be pushed so far, and that interpolation is a useful device. For example, we found that interpolation of functions and vector fields is a very convenient. In future work we intend to continue this interpolation point of view, extending it to higher degree forms, especially in the context of the sharp, Lie derivative and interior product operators. Some preliminary ideas on this point of view are presented in the thesis. We also present some preliminary calculations of formulas on regular nonsimplicial complexes</p>https://thesis.library.caltech.edu/id/eprint/1885