Algorithms Make the Determination of 3-d Inter-frame Motion a Simple Task. 6.3 Results of 3-d Motion Estimation Ave. Error (%) 0.00 2.45 2.35 1.50

Extensive experiments have been conducted to characterise the performance of the algorithms with both synthetic and real image data. Experimental results have clearly demonstrated the validity of the algorithms and the benefits of making full use of data redundancy. easily be measured. The recovered dimensions from the four views are listed in Table 2. In spite of non-perfect bilateral symmetry of the sponge, the recovered structure in each view is very accurate. The 3-D motion estimation algorithm outlined in Section 5 was tested with the images shown in Figures 6-8. In each case, one of the views was chosen as the reference frame and the absolute orientation technique of Horn [15] was applied to determine the 3-D motion between the reference frame and each of the other frames. The reference frames for the three image sequences are respectively Fig.6(a), Fig.7(a) and Fig.8(a). Since true motion parameters were unknown, the following procedure was adopted to assess, indirectly, the accuracy of the recovered motion. For each sequence the camera coordinates of all points in all frames (except the reference frame of course) were predicted based on the recovered motion and the recovered camera coordinates of the same points in the reference frame. Image positions of all points in all frames were reconstructed from the predicted coordinates. The reconstructed positions were then compared with the original image positions. The results are shown in Table 3. In all cases, the average absolute error (distance) between the original and the reconstructed image positions is around 1 pixel, indicating a good level of accuracy of the recovered motion parameters. 7 Conclusions Several novel algorithms have been described for recovering the range parameters of bilateral symmetric objects using single perspective views. Unlike many existing algorithms, the new algorithms do not rely on the error-prone process of vanishing point detection. Particular attention has been given to the maximum exploitation of data redundancy for the sake of noise robustness. It has been shown that the range recovery Table 2 : Recovered dimensions (in mm) of the sponge sequence (Fig.8) Table 3 : Errors (in pixels) between original and motion-reconstructed image points Motion Fig6(a) to Fig.6(b) Fig.6(a) to Fig.6(c) Fig.7(a) to Fig.7(b) Fig.7(a) to Fig.7(c) Fig.8(a) to Fig.8(b) Fig.8(a) to Fig.8(c) Fig.8(a) to Fig.8(d) Table 1. The true dimensions were measured by hand and therefore subject to some measurement errors. Again the recovered structure tallies well with the measured ones, …