162
to meet in the object space. Fig. 3 further shows how the method refined the orientation so that the mean
squared distance between pi? and d? was minimized. Eight iteration loops were needed in order to achieve the
stop criterion (relative decrease in x? less than one per mille). The remaining noise in the right picture of Fig.
3 results partly from the interpolation error in d? and partly from the synthetic noise added to the disparities
pi and q5. The highest peaks are nearby edges where the interpolation error is at its maximum. The weights
W (41,71) in (11) were thus chosen to 0.5 in the edge zones and to one elsewhere in order to compensate the
interpolation error in the outlier sensitive least squares minimization procedure. Preliminary tests with denser
data (N = 128, M = 128) showed decreased interpolation error and more accurate orientation estimation but.
at the expense of increased computation time.
No
DD
NS
100 E NS 1
INE
50 Noos 0-
N > .
© 0 Y N -1
N 10 s
Fig. 3. The difference d(i1,j1) — pi»(5,J1) — 42(4, 71) for (41,1) € Q before iteration (left) and after it-
eration (right) in the case of data 2.
6. CONCLUSIONS
We presented two methods to estimate the relative orientation of two disparity maps obtained by a movable
stereo head. The first method was based on modeled features and the second one on matching the disparity
surfaces in the overlap region. In the preliminary tests with synthetic data, the first method gave more accurate
results than the second one when the modeling was successful. On the other hand, the second method was
capable of handling cases with lack of features. Our future plans include performance tests with real data and
integration of pixel gray level information to the orientation estimation.
7. ACKNOWLEDGMENTS
The Heikki and Hilma Honkanen Foundation is acknowledged for supporting O. Jokinen during this work.
8. REFERENCES
[1] Haggrén, H., Jokinen, O., Niini, I., and Pôntinen, P., 1993. 3-D digitizing of objects using stereo videography.
In: Optical 3-D Measurement Techniques II, Eds. Gruen/Kahmen, Herbert Wichmann Verlag, Karlsruhe, pp.
91-97.
[2] Jokinen, O., 1994. Reconstruction of quadric surfaces from disparity measurements. In: Applications of
Digital Image Processing XVII, Andrew G. Tescher, Editor, Proc. SPIE 2298, pp. 593-604, San Diego.
[3] Kanatani, K., 1994. Analysis of 3-D rotation fitting. IEEE Trans. Pattern Anal. Machine Intell., vol. 16,
no. 5, pp. 943-549.
[4] Niini, I., 1994. Relative Orientation of Multiple Images Using Projective Singular Correlation. Licentiate's
thesis, Helsinki University of Technology, Espoo.
[6] Press, W., Flannery, B., Teukolsky, S., and Vetterling, W., 1986. Numerical Recipes: The Art of Scientific
Computing, Cambridge. f
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995
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