of
James Olaleye
A COMPACT VECTOR-SPACE ALOGARITHM FOR AN ANALYTICAL REDUCTION OF A STEREOGRAM
BY
J.B. OLALEYE (DR.) and J.O. SANGODINA
DEPARTMENT OF GEOINFORMATICS & SURVEYING,
FACULTY OF ENGINEERING, UNIVERSITY OF LAGOS,
AKOKA - YABA, LAGOS, NIGERIA.
ABSTRACT
The need for variety and better accuracy of the map products used in the rapidly evolving GIS technology has necessitated the
use of analytical techniques in photogrammetric data processing. The ready availability of small but powerful computers which
are able to support the computational requirements of rigorous solutions, and the flexibility to use analogue or digital input
imageries in the mapping process have combine to make analytical procedures a routine utility. Quite often in all applications,
the basic problem involves the extraction of spatial entities from images, and almost invariably, the most accurate mapping is
achieved through rigorous treatment of stereo images. The. software modules used in the operations are developed based on
appropriate mathematical representations of the relationships between measurements of image features and the corresponding
spatial objects.
From an abstract geometric consideration, each image of a stereogram may be visualized as a 3-D vector space whose elements
are composed action, and the calibrated principal constant of the camera or sensor. The object space, in most practical cases,
may also be represented simply as a 3-D vector space. When suitable coordinate systems are attached to these spaces, they
become Euclidean spaces in which points may be represented simply in position vectors. This space conceptualization enables
the use of vector symbology and linear algebra to develop compact computational algorithms for the reduction process.
Although the theoretical bases of the mathematical formulations used in the treatment of a stereogram are well known and in
fact vector notations have been used to present them. Nevertheless, the computational schemes often adopted are based on long
hand approach in which symbols are used to represent single variables, involving tedious algebraic manipulation. This
inevitably leads to complicate computational procedures, devoid of clear geometric meaning and insightful appeal. This paper
applies the ARDOVS concept, an analytical tool, to the solution of the stereogram problem. It is shown how this methodology
provides a compact and consistent solution scheme which is easy to understand.
. INTRODUCTION
The need for variety and better accuracy of the map products used in the rapidly evolving GIS technology has
necessitated the use of analytical techniques in photogrammetric data processing. The ready availability of small but
powerful computers which are able to support the computational requirements of rigorous solutions, and the flexibility
to use analogue or digital input imageries in the mapping process have combined to make analytical procedures a
routine utility. Quite often in all applications, the basic problem involves the extraction of spatial entities from images,
and almost invariably, the most accurate mapping is achieved through rigorous treatment of stereo images. The
software modules used in the operations are developed based on appropriate mathematical representations of the
relationships between measurements of image features and the corresponding spatial objects.
From an abstract geometric consideration, each image of a stereogram may be visualized as a 3-D vector space (Figure
1) whose elements are composed action, and the calibrated principal constant of the camera or sensor. The object
space, in most practical cases, may also be represented simply as a 3-D vector space. When suitable coordinate
systems are attached to these spaces, they become Euclidean spaces in which points may be represented simply in
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 657
