Surface Reflectance Recognition and Real-World Illumination Statistics

Humans distinguish materials such as metal, plastic, and paper effortlessly at a glance. Traditional computer vision systems cannot solve this problem at all. Recognizing surface reflectance properties from a single photograph is difficult because the observed image depends heavily on the amount of light incident from every direction. A mirrored sphere, for example, produces a different image in every environment. To make matters worse, two surfaces with different reflectance properties could produce identical images. The mirrored sphere simply reflects its surroundings, so in the right artificial setting, it could mimic the appearance of a matte ping-pong ball. Yet, humans possess an intuitive sense of what materials typically "look like" in the real world. This thesis develops computational algorithms with a similar ability to recognize reflectance properties from photographs under unknown, real-world illumination conditions. Real-world illumination is complex, with light typically incident on a surface from every direction. We find, however, that real-world illumination patterns are not arbitrary. They exhibit highly predictable spatial structure, which we describe largely in the wavelet domain. Although they differ in several respects from the typical photographs, illumination patterns share much of the regularity described in the natural image statistics literature. These properties of real-world illumination lead to predictable image statistics for a surface with given reflectance properties. We construct a system that classifies a surface according to its reflectance from a single photograph under unknown illuminination. Our algorithm learns relationships between surface reflectance and certain statistics computed from the observed image. Like the human visual system, we solve the otherwise underconstrained inverse problem of reflectance estimation by taking advantage of the statistical regularity of illumination. For surfaces with homogeneous reflectance properties and known geometry, our system rivals human performance.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.

The Logical Problem of Language Change

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars ${cal G}$, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one otherwise could not ask, such as the effect of varying initial conditions on the resulting diachronic trajectories. From a more programmatic perspective, we give an example of how the dynamical system model for language change can serve as a way to distinguish among alternative grammatical theories, introducing a formal diachronic adequacy criterion for linguistic theories.

Multivariate Density Estimation: An SVM Approach

We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters.

Electrical Design: A Problem for Artificial Intelligence Research

This report outlines the problem of intelligent failure recovery in a problem-solver for electrical design. We want our problem solver to learn as much as it can from its mistakes. Thus we cast the engineering design process on terms of Problem Solving by Debugging Almost-Right Plans, a paradigm for automatic problem solving based on the belief that creation and removal of "bugs" is an unavoidable part of the process of solving a complex problem. The process of localization and removal of bugs called for by the PSBDARP theory requires an approach to engineering analysis in which every result has a justification which describes the exact set of assumptions it depends upon. We have developed a program based on Analysis by Propagation of Constraints which can explain the basis of its deductions. In addition to being useful to a PSBDARP designer, these justifications are used in Dependency-Directed Backtracking to limit the combinatorial search in the analysis routines. Although the research we will describe is explicitly about electrical circuits, we believe that similar principles and methods are employed by other kinds of engineers, including computer programmers.

Inverse Metabolic Engineering of Synechocystis PCC 6803 for Improved Growth Rate and Poly-3-hydroxybutyrate Production

Synechocystis PCC 6803 is a photosynthetic bacterium that has the potential to make bioproducts from carbon dioxide and light. Biochemical production from photosynthetic organisms is attractive because it replaces the typical bioprocessing steps of crop growth, milling, and fermentation, with a one-step photosynthetic process. However, low yields and slow growth rates limit the economic potential of such endeavors. Rational metabolic engineering methods are hindered by limited cellular knowledge and inadequate models of Synechocystis. Instead, inverse metabolic engineering, a scheme based on combinatorial gene searches which does not require detailed cellular models, but can exploit sequence data and existing molecular biological techniques, was used to find genes that (1) improve the production of the biopolymer poly-3-hydroxybutyrate (PHB) and (2) increase the growth rate. A fluorescence activated cell sorting assay was developed to screen for high PHB producing clones. Separately, serial sub-culturing was used to select clones that improve growth rate. Novel gene knock-outs were identified that increase PHB production and others that increase the specific growth rate. These improvements make this system more attractive for industrial use and demonstrate the power of inverse metabolic engineering to identify novel phenotype-associated genes in poorly understood systems.