334 
Table 1: Estimated rigid motion parameters, where the translation, rotation parameters, and rotational magnitude 
Q(= ||(Rz, Ry, R.)||) are respectively represented as pixels and degrees. 
  
  
Parameters | Calculated Value | Actual Value 
T. 1.006 1.000 
T, 0.990 1.000 
T. 1.000 1.000 
Rz -0.5272 -0.577 
R, -0.583 -0.577 
RE; -0.577 -0.577 
Q 0.999 1.000 
  
  
  
  
  
  
  
Table 2: Estimated motion parameters with intensity and range information. 
  
  
  
  
  
  
  
  
  
Parameters | 1—2|2—3|3—4[4—5[5—6 
T. -0.12 -0.12 0.87 0.84 0.66 
T 4.59 4.02 4.68 1.35 10.02 
T. 1.35 1.05 13.47 20.13 21.33 
Rs 0.18 0.48 6.06 11.22 11.79 
Ry -0.12 -0.21 -0.66 -1.26 | -0.147 
A; -0.18 0.05 0.36 0.57 0.27 
N 4 2 26 27 21 
  
  
  
SIF — F'I? -- w;l|E — E'||? at each iteration does not decrease monotonically. The final solution is obtained as a 
sum of solutions for every iteration. 
5. EXPERIMENTAL RESULTS 
In this section, we present results of motion parameter estimation using the method described previously. One can 
see in Figures 2a to 2f, the first six frames of the motion of a toy and in Figures 3a to 3f, the corresponding intensity 
images. In the experiment, only two successive images for both range and intensity to compute the motion parameters 
were used. Each range and intensity image frame were previously filtered by an intrinsic filter corresponding to a 
scope o = 9.5 pixels. 
5.1 Rigid Body Motion 
One can estimate the 3-D motion parameters of a rigid object from only one range image to validate the rigid motion 
estimation method. The image used is the first frame of the sequence illustrated at Figure 2. The second frame is 
artificially produced by translating and rotating the first frame in order to produce a comparison basis. 
Table 1 shows the estimated rigid motion parameters, where the translation, rotation parameters, and rotational 
magnitude Q(— ||( R5, Ry, R.)||) are respectively represented as pixels and degrees. 
5.2 Estimated Motion Parameters for the Image Sequence 
One can see in Tables 2 and 3, the estimated motion parameters between each frame of the sequence illustrated 
at Figure 2 and Figure 3. Table 2 shows range and intensity information results, whereas Table 3 results indicate 
range information only. The parameters R,, Ry, and R, are the rotational speed in degrees/s and T,, Ty, and T, 
are the translational speed in mm/s. The parameter N is the number of iterations to solve the linear problem. The 
weight factor w; between the intensity and range flow is equal to 0.1. By simple observation, one can see the motion 
parameters between the two sets of results are similar. However, those parameters corresponding to the fusion of 
range and intensity information are more stable since they require less iteration to solve the linear problem. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995 
  
a