International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
In Fig. 3, the gid of bold line denotes that the value of a 
hexagonal grid is directly assigned as the value of the grid value 
of regular space where its centre resides, and this is adopted by 
the current algorithm; Grid of dotted line denotes that the value 
of a hexagonal grid is assigned by several values of the nearest 
grids of regular space. 
columns of hexagonal space are derived from even-number row 
of regular space, and grid values of even-number columns of 
hexagonal space are derived from odd-number row of regular 
space. 
Of the same scale of x and y directions, there is no one-to-one 
and pixel-to-pixel mapping between these two raster spaces 
exists. The proposed mapping algorithm is not designed to 
preserve all information kept in the original regular raster space. 
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5 
mh 
© C RN : 7 
(c) 
(a) 
Figure 4: The use of hexagonal space in pattern matching (a) 
Numerating of neighbours of a grid in question in a 
hexagonal raster space. (b) The six lines of profile 
provided by the nature of hexagons. (c) An example 
profile used in pattern matching, where the left-most 
hexagon is the grid in question. 
4. RESULTS AND DISCUSSION 
As the author described above, to make sure each calculation is 
explicitly defined by primitive mathematical equations from the 
bases, a concise fundamental spatial library is developed, and it 
plays a role of primitives in implementing the algorithms shown 
in Fig. | and Fig. 2. This photogrammetric package is already 
used to derive the displacement data of the surface rupture of a 
test area in northern segment of Chelungpu Fault, and the results 
are prepared for further publication. 
The architecture of using a spatial library was designed in the 
beginning of developing the photogrammetric algorithms. As the 
algorithms are developed, this library seems to be unnecessary 
although it is in essence a concise one. The geometry is in such 
a simple form that the author has implemented part of the 
algorithms as an ASIC (Application Specific Integrated Circuits) 
in Verilog It should be an easy task for a single experienced 
programmer to implement these algorithms, too. 
Since the photogrammetric algorithms are developed totally 
based on geometry, there would be some influences on the 
Noted that grid values of odd-number 
   
process of calibration. Intuitively, an imperfect lens with 
distortion can be calibrated through a matrix of distortion values. 
and this characteristic would be a major advantage for a non- 
metric camera to be used in photogrammetry. 
The author has also shown how to fast georeference images 
through the use of grid arithmetic and hexagonal spaces. The 
known abilities of grid arithmetic are used to implement pattern 
recognition functionality, and the nature of hexagonal spaces 
ensures the behaviours of each grid have equal relationships with 
the grid's six adjacent neighbours. 
5. CONCLUSION 
The author presents in this paper newly designed generalized 
algorithms for photogrammetry, totally based on the 
characteristics of perspective geometry and an approach toward 
pattern recognition by the use of grid arithmetic and hexagonal 
spaces. These two branches of techniques are both intended to 
improve the efficiencies of generalized photogrammetric tasks 
by designing new algorithms to reduce the overheads needed to 
complete the calculations. 
The latest information of related source codes of the algorithms 
presented in this paper can be download from the author's 
working page: http://savannah.gnu.org/users/chstoneliu/. 
ACKNOWLEDGEMENTS 
The author would like to thank Syue-Ping Ma for her useful idea 
in simplifying the geometry of space resection. The general 
support on grid arithmetic of Dr Jinn-Guey Lay is also 
gratefully acknowledged. 
REFERENCES 
Celikoyan, T. M. and Altan M. O., 1999, Automatic matching 
of non-geometric items in digital photogrammetry. Third 
Turkish-German Joint Geodetic Days, 1-4 June 1999, Istanbul, 
Turkey, pp. 423-430. 
El-Hakim, S. F., Brenner, C., and Roth G., 1998. A multi- 
sensor approach to creating accurate virtual environments. 
ISPRS Journal of Photogrammetry & Remote Sensing 53 (1998), 
pp- 379-391. 
Ho, W. S., 1995. Aerial photogrammetry (in Chinese). 
China Books Ltd., Taiwan. 
Great 
Lay, 1-G. Tiu, C-H- Lee J.-F. “and Wang, W-L., 2004. 
Morphometric Analysis of Landslides (in Chinese). Submitted 
to Bulletin of Geography for further publication, Taiwan. 
Liu, C.-H., Lee, J.-F., and Huang, C.-C., 2000. Three- 
dimensional displacement in northern segment of Chi-Chi 
Earthquake surface rupture. International Workshop on Annual