The Image Irradiance Equation: Its Solution and Application

Item

Title
en_US The Image Irradiance Equation: Its Solution and Application
Creator
en_US Bruss, Anna R.
Date
2004-10-20T20:04:00Z
Date Available
2004-10-20T20:04:00Z
Date Issued
en_US 1981-06-01
Identifier
en_US AITR-623
uri
http://hdl.handle.net/1721.1/6878
Abstract
en_US How much information about the shape of an object can be inferred from its image? In particular, can the shape of an object be reconstructed by measuring the light it reflects from points on its surface? These questions were raised by Horn [HO70] who formulated a set of conditions such that the image formation can be described in terms of a first order partial differential equation, the image irradiance equation. In general, an image irradiance equation has infinitely many solutions. Thus constraints necessary to find a unique solution need to be identified. First we study the continuous image irradiance equation. It is demonstrated when and how the knowledge of the position of edges on a surface can be used to reconstruct the surface. Furthermore we show how much about the shape of a surface can be deduced from so called singular points. At these points the surface orientation is uniquely determined by the measured brightness. Then we investigate images in which certain types of silhouettes, which we call b-silhouettes, can be detected. In particular we answer the following question in the affirmative: Is there a set of constraints which assure that if an image irradiance equation has a solution, it is unique? To this end we postulate three constraints upon the image irradiance equation and prove that they are sufficient to uniquely reconstruct the surface from its image. Furthermore it is shown that any two of these constraints are insufficient to assure a unique solution to an image irradiance equation. Examples are given which illustrate the different issues. Finally, an overview of known numerical methods for computing solutions to an image irradiance equation are presented.
Extent
en_US 109 p.
12230045 bytes
4714728 bytes
Format
application/postscript
application/pdf
Language
en_US
Relation
en_US AITR-623
Item sets
AI Technical Reports (1964 - 2004)