Huijing Zhao 
  
distance between and , which is equal to . On the other hand, due to the difference between and , the location 
of range frame is projected to (Figure 3(b)). Violation in rotation matrix is evaluated by averaging its effect on 
all nearby range frames as follows. 
1 ‘ ; 
Vio}; = —( NS wir Vio} + > wikV 105a.) (4) 
(ük)eS (i,k)€S 
where, Vio}; = IR; Sh; — RüShij|; S is the set of all neighboring range images; n is the number of all 
range image pairs of V; and Vj; wj is a confidence value to the relative transformation obtained in pair-wise 
registration. 
Multiple registration is to minimize the following cost function. 
F; = S^ wi; Vio]; (5) 
(4,k)eS 
Through the experiment in Zhao and Shibasaki 1999, we found that a failure or an unreliable pair-wise reg- 
istration is always caused by extremely less overlay between range image pairs. An enough overlay between 
range image pairs is a premise for a reliable registration, whereas it might not be always satisfied in urban 
outdoor environment due to occlusions. To evaluate the reliability of pair-wise registration, in this research, the 
confidence value wj; is assigned as the number of the matched range points between V; and V;. After aligning V, 
and V; to a common coordinate system by the pair-wise registration result, matched range points are counted 
as the point pairs, which have distances smaller than a given threshold. 
2.4 Multiple registration when location of several viewpoints in world coordinate system is known 
When the world coordinates (e.g. GPS coordinate system) of several viewpoints are known, all range images 
can be directed aligned into the world coordinate system. Suppose (V;]l s nm] is the set of range images 
of which locations (p,|]l s n} in a world coordinate system is known. The addition work other than those 
addressed above is we have to find the transformation matrixes from {V;|1 s m] to the world coordinate 
system. It is conducted as follows. Arbitrarily select one range image Vi, 1 1k n, sequentially align all 
range images to the coordinate system of Vj. Let (p,]l s nm] bethe viewpoints of (V;,|]l s mj with 
f Sh. transforming (p,|]| s m] 
Rs; “Sh, 
0 1 
respect to the coordinate system of V,. A transformation matrix ( 
to {ps|l s n} can be obtained using least square method. Transformation matrix 
) from the 
coordinate system of V;, 1 s nto the global coordinate system is obtained as follows. 
iffszckh then RB, =R;. Sh, =p, ~ p. 
ifszk then R, = Ra. Ras, 9h, = Di p. (6) 
3 EXPERIMENT RESULTS AND DISCUSSIONS 
42 overlapping range images were measured around a building in the campus of the Univ. of Tokyo. A map 
of the locations is given in Figure 4. Range images used in the experiment are measured by [—180°, +180°] 
in horizontal rotation angle and |—20?, --40?] in vertical rotation angle, with the resolution of 2 sample per 
horizontal degree and 1 sample per vertical degree. Laser range measurement has an accuracy of ^ 5cm. In 
the followings, we present two sets of experimental results. The first experiment examines the accuracy of 
multiple registration when location and direction of range frame are totally unknown. We specify the global 
coordinate system as that of range image #1. All range images are registered, and a model of the buildings 
with respect to the coordinate system of range image #1 is obtained. The second experiment examines the 
registration accuracy when absolute location of several range frames are known. We compare the registration 
accuracy when given different number of absolute locations. Two sets of ground truth are used to examine the 
registration accuracy. They are 1) a 1:500 scale digital map and, 2) location of viewpoints measured by GPS 
with an accuracy of 20cm. 
3.1 Multiple registration when location and direction of range images are unknown 
Range images are first sequentially aligned to the coordinate system of range image #1. A conceptual structure 
of the alignment is shown in Figure 5. Since after sequential alignment, violation exists only in the neighboring 
  
1036 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.