OPTIMAL ACQUISITION OF 3D OBJECT COORDINATES
FROM STEREOSCOPIC IMAGE SEQUENCES
Rongxing Li, Mike A. Chapman, and Weihong Zou
Department of Geomatics Engineering, The University of Calgary
2500 University Dr.. N.W., Calgary, AB, Canada
Tel: (403) 220-4112, Fax: (403) 284-1980
E-mail: rli@acs.ucalgary.ca
WWW: http://loihi.ensu.ucalgary.ca/
KEY WORDS: Mobile mapping. Digital photogrammetry, Optimization, Image processing
ABSTRACT:
3D object space coordinates of an object can be uniquely intersected by two geo-referenced digital images that
overlap the object. The selection of the best combination of the two images from an image sequence so that the
coordinates calculation has the optimization properties both in precision and reliability is very important for feature
extraction, image matching, object reconstruction and recognition. Based on Kalman filter theory. great efforts
have been made to research the optimization of 3-D coordinate calculation from the VISAT images. Considerations
are given to a) establishing optimal criteria with precision and reliability, and b) choosing two optimal images from
an image sequence for an intersection. An algorithm has been developed that meets the above requirements.
To verify the algorithm, it was used to extract objects from digital images taken by the VISAT mobile mapping
system. The results show that the optimization algorithm is efficient for calculating 3D coordinates and providing
geometric information for generation of large scale GIS databases.
1. INTRODUCTION
Digital images acquired by the VISAT system, a
mobile mapping system using GPS, INS and CCD
cameras, are georeferenced (Li etal 1996).
Coordinates of any object appearing in a stereo pair
of the images can be calculated by measuring
corresponding image coordinates and by an
intersection in the object space. In order to obtain an
accurate 3D object description, to reduce
computational time, and to enhance the
measurability of the system, an efficient algorithm
for calculating optimal 3D object space coordinates
with precision and reliability is necessary. Without
the optimization using these criteria, some
photogrammetric operations may not be applicable or
practical considering the large amount of data
involved and computational time required. The
optimization algorithm presented in this paper
demonstrates the advance of optimal processing of
the images georeferenced in real-time and acquired
by a mobile mapping system.
2. THE SEQUENTIAL IMAGE MODEL
A statistical model of the evolution of sequential
images containing an object to be measured can be
expressed as
Pi NCOP, Da), (2.1)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
where P, is the 3D object coordinate state of a
normal distribution estimated by k images in which
the object appears; P is it's statistical expectation
E[P,] and D, is the corresponding covariance
matrix.
The updated new collinearity equations using the
(k+1)th image are
Xi Sf U / Quer
Yka 7 fia *Vica/qia (2.2)
where
Wer FM (Xia XO) +m (Yen -Y?ymis(Zia 2°)
Via 7m (Xa -X?ymox(Yya Yo (Zicn -Z°%)
Qe =M3; G4 -X))mso(Yxa Y) mass(Zia -Z°)
and Xi. Yin and Zi, are the coordinates of the
target point from the (k+1)th image; X°, Y° and Z°
are the coordinates of the (k+1)th exposure station;
X41 and y, are image point coordinates in (k+1)th
image: fe is the focal length of the (k+1)th image;
and M3 x 3(m;) is the rotation matrix of the (k+1)th
image.
If only the measurement errors of the image
coordinates are taken into consideration, Equation
(2.2) can be expressed in a linearized form:
