9. ANÁLISIS E INTERTPRETACIÓN DE LOS RESULTADOS
9.5 Estrategias didácticas
9.5.1 Estrategias didácticas para enseñar y aprender
5.4.2.1 Methods
The surface model from section 4.4.2 was used with a series of video images that repre- sented a rotation of up to 90 degrees. The rst image was that shown in gure 5.1(a) and is labelled as image 0 as it is the reference image. Further video images were taken where the skull was rotated by 5, 10, 30, 50, 70 and 90 degrees. Each image was labelled accord- ing to its angle of rotation from the reference image. The gold standard registration for each view was calculated by localising the ducials and using Tsai's algorithm [Tsai, 1987] as described in section 4.3.10. Registrations were performed using pairs of video image simultaneously. Pairs of images tested were images (0
;
5);
(0;
10);
(0;
30);
(0;
50);
(0;
70) and (0;
90). Registration to each pair of images and for the two multiple view meth-5.4 Experiments
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ods combining and adding were tested using a misregistration size of
t
=8 mm anddegrees. After each successful registration, the projection and 3D error was calculated. The mean and standard deviation projection and 3D errors were calculated for each pair of images.
5.4.2.2 Results
The mean (standard deviation) projection and 3D errors for each pair of images can be found in table 5.2. Table 5.2(a) shows the results for cases in which the information from each rendered and video image pair is added and table 5.2(b) shows the errors for cases in which the information from each rendered and video image pair is combined.
It can be seen that the combining method has a higher success rate for the pairs of images (0,5) and (0,10). Both methods completely fail for the image pair (0,90). From this experiment, the (0,30) pair of images and the combining method has the lowest mean projection and 3D errors i.e. 1.39 (0.15) and 1.73 (0.28) mm respectively with a 100 % success rate. Table 4.3(a) showed the mean (standard deviation) of the projection and 3D errors for the mono case was 1.25 (0.55) and 6.20 (1.22) mm respectively. Table 4.3(b) showed the mean (standard deviation) of the projection and 3D errors for the second mono case was 3.86 (1.87) and 8.17 (1.55) mm respectively. The (0,30) pair of video images and the combining method therefore has a lower 3D error than the mono cases, and a comparable projection error.
Figure 5.2 illustrates mono and multiple view registration results. The top row is a mono view registration result. The outline of the rendered surface model is displayed as a white line, overlayed onto the video image. The image in gure 4.7(a) shows a registration result for the mono view algorithm of the previous chapter. The recovered extrinsic parameters of this registration are shown in table 5.3 in the row labelled `Mono'. The main registration error is along the optical axis of the camera. In image (a), which was the image used for the registration the rendered overlay appears well aligned. The image in gure 5.2(b) is another `overlay image' from a camera that is rotated by 30 degrees, from image (a) but showing the registration result produced when registering to image (a). The errors in the mono view registration are apparent as the rendering appears shifted to the right relative to the skull in the video image.
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(a) (b)
(c) (d)
(e) (f)
Figure 5.2: Registration results using (a) and (b), mono video image, (c) and (d) two images separated by 30 degrees, (e) and (f) two images separated by 70 degrees (see text section 5.4.2.2).
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Solution Post-Registration Extrinsic Parameters
t x t y t z r x r y r z Gold Standard 0 0 0 0 0 0 Mono -0.09 -0.13 8.20 0.57 -0.31 -0.02 Stereo, 30 Degrees 0.53 0.89 -0.34 0.46 0.15 -0.13 Stereo, 70 Degrees 2.99 -1.19 3.35 2.34 0.01 -2.03
Table 5.3: Examples of post-registration extrinsic parameters for mono and stereo results. See section 5.4.2.2.
Images (c) and (d) are results from a stereo view registration. The angle of disparity between the views is 30 degrees. Both views are accurately aligned giving lower projection and 3D errors than the mono view algorithm. Images (e) and (f) are also results from a stereo view registration. The angle of disparity between the view is 70 degrees. Neither view is accurately aligned. The actual registration results are shown in table 5.3. The gold standard position is represented by 0 for all
t
x:::r
z. This table shows that themono view algorithm fails to recover
t
z. The stereo algorithm with 30 degrees disparityrecovers all parameters close to their gold standard values, and the stereo algorithm with 70 degrees recovers all parameters, but not very accurately.
5.4.2.3 Conclusions
The experiments testing what angle to use between two video views (section 5.4.2) showed that an angle dierence of 30 degrees gave the best performance. With the angle less that 30, the errors increased and became similar to the mono view performance. With an angle larger than 30 degrees, the errors also increased as registration performance worsened. At a separation of 90 degrees the algorithm failed completely. This could be due to the search space becoming nearly at, and the search strategy failing. As each new pose was tested, a change in the parameters will produce an improvement in the similarity measure with respect to a single view, and possibly a similar decrease in similarity with respect to another view. If these changes are equal and opposite when the angle of separation approaches 90 degrees then the search space becomes atter, and the search strategy is more likely to fail.
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Set of Projection Error (mm) 3D Error (mm) Percentage
Images Mean (StdDev) Mean (StdDev) Success
(0,10) 3.98 (1.23) 4.81 (1.72) 100
(0,10,30) 1.44 (0.22) 1.93 (0.32) 100
(0,10,30,50) 2.16 (0.36) 3.08 (0.36) 100
(0,10,30,50,70) 3.68 (0.43) 5.52 (0.58) 94
(0,10,30,50,70,90) - - 0
Table 5.4: Mean (standard deviation) projection and 3D error for each number of images.