4.3.2 Least Squares Matching with Geometric 
Constraints: The area based process employed for the 
refined matching of the point position relies on the correlation 
of grey-scale patches in target and conjugate search images. 
The initial estimate of corresponding pixels in conjugate 
images, as provided by the epipolar matching, is required to 
within one or two pixels (the "pull-in range") in order to 
achieve a solution. In order to obtain an optimum accuracy 
for the final point position, the area-based least squares 
algorithm is supported by affine patch shaping and geometric 
constraints in the form of the collinearity equations (Gruen, 
1988). 
4.4 Space Intersection 
In addition to providing geometric constraints to the least 
squares matching, the collinearity equations also serve to 
produce the three dimensional (XYZ) object space co- 
ordinates of the points of interest, which are being matched 
after selection of the best candidate. The image matching 
routine produces both digital elevation model (DEM) data in 
the form of XYZ co-ordinates and error estimates for the 
object space co-ordinates as a consequence of the least 
squares estimation model. 
During the tests carried out for the project the desired sub- 
millimetre accuracy was achieved for all points in depth, 
while X and Y ordinates proved typically better by 
approximately a factor of ten. 
4.5 Deformation Analysis 
The output of the digital photogrammetric process is a dense 
point cloud of three dimensional (XYZ) co-ordinates which 
represent the rock face. This data is processed further in finite 
element models for rock mechanics studies of the blasting 
process during pre-conditioning. Results of this aspect of the 
project will be reported elsewhere. 
S. CONCLUDING REMARKS 
The final analysis of the data made it apparent that digital 
photogrammetry is highly suitable for the determination of 
rock surface digital elevation models for subsequent 
deformations analysis. The relative speed of the process and 
the convenient size of the equipment made the technology 
especially suited to the demanding underground mining 
environment. Difficulties which arose from the size, shape 
and environment of the object in the highly restrictive 
environment, were overcome by careful planning and pre- 
analysis which led to the incorporation of additional tie points 
placed on target poles in front of the object. The feasibility of 
this approach was confirmed by the high accuracy of the final 
surface point co-ordinates. 
For future application of the technique, a second reference 
frame at the opposite extreme of the wall is proposed. The 
digital form of the images also makes it possible to employ 
image processing techniques for fracture pattern analysis and 
particle analysis. 
733 
6. ACKNOWLEDGEMENTS 
Without the assistance of Mining Technology, the rock 
engineering division of the Council for Scientific and 
Industrial Research (CSIR), Johannesburg, South Africa this 
research would not have been possible. Thanks are extended 
to them for their contribution. 
For his valuable assistance in the early stages of the project 
and for the use of his bundle adjustment software, the 
contribution of Graeme van der Vlugt is acknowledged. 
The author's are also grateful to the Foundation for Research 
Development (FRD) and the University of Cape Town for 
their financial support. 
REFERENCES 
Canny, J., 1986. A Computational Approach to Edge 
Detection. IEEE Transactions on Pattern Analysis and 
Machine Intelligence, Vol. PAMI-8, No. 6, pp 670-698. 
Gruen, A.W. and Baltsavias, E.P., 1988. Geometrically 
Constrained Multiphoto Matching. Photogrammetric 
Engineering and Remote Sensing, Vol. 54, No. 5, pp 633- 
641. 
Haralick, R.M. and Shapiro, L.G., 1992. Computer and 
Robot Vision. Vol. 1, Addison-Wesley Publishing Company, 
pp 337-346. 
Lim, J.S., 1984. Image Enhancement in Digital Image 
Processing Techniques. Edited by Estrom, M.P., Vol. 2 in 
COMPUTATIONAL TECHNIQUES edited by Alder, B.J. 
and Fernbach, S., Academic Press, pp 1-51. 
van der Vlugt, G. and Rüther, H., 1994. The Development of 
an Automated Surface Measurement System. Paper 
presented at the ISPRS Commission V, Working Group 3, 
Melbourne, Australia. 
Wong, K.M. and Ho, W., 1986. Close-Range Mapping with 
a Solid State Camera. Photogrammetric Engineering and 
Remote Sensing, Vol. 52, No. 1, pp 67-74. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996