1-1-5 
/} and if is a pair of matched line segments. Strength 
from T K lf to l l . is defined in Figure 2, dragging the 
vertical point q of T k lf to the vertical point p of /J. The 
strength can be decomposed into first rotating T k lf by 
a a to l s , then translating i s by sr to l r . It is 
represented by 
AT k =A R* °A Sh k . (20) 
The volume of the strength from T k lf to is evaluated 
by how much it can be saved in conditional information 
after transformation. It is defined as follows. 
(21) 
Adjustment on T k is calculated by weighed average of 
the strength between matched line segments. 
AT k =AR k 0 ASh k (22) 
AK‘ =- X(V,‘-AR # *). 
©as* 
ASh l =- 
^ (i,j)eh 
direction of V. 
C. Fine adjustment strategy 
Adjustment in each iteration can be estimated by strength 
analysis. Flowever, the distance measure evaluates not 
only the matches between line segments, but also 
between image points. The claimed adjustment by 
strength analysis is invalid if the distance measure can not 
be minified. In that case, to move on to the next iteration, 
all the possible adjustment, increasing or decreasing a 
step value to translation and rotation parameters, are 
tested to find an acceptable adjustment. The iteration will 
be stopped when convergence or the distance measure 
can never be minimized. 
2.2 Matching ground points 
Ground points are extracted as follows. Given a resolution, 
tessellating the laser range image into a two-dimensional 
image along X and Y-axis of the sensor’s coordinate 
system. Pixel value of the image is set by the minimal Z- 
coordinate of the laser range points falling into the 
tessellating cell. Ground points near to the viewpoint are 
interpolated. Matching of ground points is conducted as a 
least square minimization problem. Cost function is 
formed by the residual in Z-coordinate of the ground 
points near to each viewpoint. 
3 MULTIPLE VIEW’S REGISTRATION 
When aligning multiple overlapping laser range images by 
pair-wise registration, estimation error in pair-wise 
registration might be accumulated and propagated. 
Y.Chen and G.Medioni, 1992 solved the problem by 
registering the newly introduced view with the merged 
data of all previous registered views. Shum et al. 1994 
formulated the multiple views’ registration as a problem of 
principal component analysis with missing data, which 
can be generalized as a weighted least square 
minimization problem. Our case is similar to B.Kamgar- 
Parsi et al. 1991, and we agree with them that pair-wise 
registration has optimized local matching, global matching 
should minimize the violation to local matching. We 
formulate the multiple views’ registration as a least square 
minimization problem. The cost function defined involves 
four transformation parameters, a horizontal rotation angle 
and three translation parameters. Generalization of the 
method to more complicated cases is straightforward. The 
cost function is defined as follows (Figure 3). 
E s = co d XK -) 2 + X(«» -“p) 2 
(i,j)eh (i,j)eh\(i,k)eh 
+ £(<?« -^i) 2 +®a 
(i,j)eh (i,j)eh 
(23) 
Where, (^,«^,0..,«..) stand for the values in global 
matching, while (d..,a; y *,0..,a; y ) for those in local 
matching. (co d , co p , co 9 , co a ) serve as weights for different 
contributions of the components. The first two components 
evaluate the violation to the three translation parameters, 
while the last two for the rotation parameter. They are 
independent, and can be treated separately. Minimization