Surface Reflectance Estimation and Natural Illumination Statistics

Humans recognize optical reflectance properties of surfaces such as metal, plastic, or paper from a single image without knowledge of illumination. We develop a machine vision system to perform similar recognition tasks automatically. Reflectance estimation under unknown, arbitrary illumination proves highly underconstrained due to the variety of potential illumination distributions and surface reflectance properties. We have found that the spatial structure of real-world illumination possesses some of the statistical regularities observed in the natural image statistics literature. A human or computer vision system may be able to exploit this prior information to determine the most likely surface reflectance given an observed image. We develop an algorithm for reflectance classification under unknown real-world illumination, which learns relationships between surface reflectance and certain features (statistics) computed from a single observed image. We also develop an automatic feature selection method.

Symbolic Mathematical Laboratory

A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

The Structure of Mathematical Knowledge

This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.