The next set of tests of the implementation is done using architectural scenes from the real world. Architectural scenes are chosen next, as they have some nice properties for 3D reconstruction. They mostly consists of large planar or smoothly curved surfaces, that can easily be represented by relatively few vertices.
12.2.1 The Pot
The Pot dataset would probably not be described as a piece of architecture by most people, but it has been included here because it is simple and has many of the same properties as architecture. Image 1, 2 and 3 are chosen as input for the algorithm as they present a challenge because of their difference in light distribution, as will be discussed later. First a simple reconstruction using SSE is performed, as is documented in figure 12.9. As can be seen, the result resembles the pot much better than the initial mesh. The occluded areas has been minimized and the mesh simplified to a balance between the image error and the mesh cost. The general shape of the pot is reconstructed, however the extruding edge in the bottom of the pot has not. When comparing the error buffers, it is difficult to identify the edge as a significant error, which may explain why the model has not adopted to it. In figure 12.10 the convergence is plotted.
12.2 Architectural results 107 Like the Box, it shows a large amount of edge deletes to start with and spatial adjusting towards the end. Interesting is that there also is a notable amount of edge inserts used to adjust the mesh throughout most of the convergence.
Figure 12.9: The first row shows the initial situation. The second row shows the result after convergence. The resulting model can be found in Pot/test1/model1.x3d.
Figure 12.10: The objective function versus the number of proposals used.
Image metric - SSE versus Correlation
The images from this dataset are real world images having visible differences in the color distribution, which would thus make a good foundation to evaluate the differences between the two proposed image metrics, correlation and SSE.
The algorithm is based on a randomized search and it would thus provide an
108 Results inaccurately comparison if evaluating the two image metrics separately. There-fore both have been calculated and stored for each iteration, while only one of them has been the controlling metric, ie. the one used in the proposal selec-tion. To avoid ambiguities, two tests are conducted to let both metrics control a test. Further more the same tests are performed on normalized images from the same dataset, to reveal the possible differences. In theory the random nature of the algorithm could favor one of the image metrics, however because of the vast number of proposals this should not be significant. Figure 12.11 shows the convergence of these 4 tests each with the metric either itself controlling the convergence, or not. To account for the difference in the actual cost, the cost have been normalized.
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SSE in and out of control in Pot
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CORR in and out of control in Pot
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SSE in and out of control when using normalized images
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CORR in and out of control when using normalized images
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Figure 12.11: The convergence using SSE and CORR, both controlled by itself and the other. The upper row shows the result from the original Pot dataset, while the lower shows the result on a normalized version of the same dataset.
As can be seen, the two metrics follow each other in the convergence. In general it seems like the convergence is slightly better when SSE is in control. In the normalized images, the gab between the two metrics are enlarged, which is nat-ural since the advantage using CORR lies in the 1 order statistical differences between the input images. It however is surprising that SSE performs better than CORR in the non-normalized case. In the upper left graph, when SSE
12.2 Architectural results 109 is in control it is expected that the convergence is better than when CORR is controlling, which is the case. In the upper right, however it is unclear if the corresponding is true for CORR. It is expected that CORR would perform no-table better in control than when not, however only a little difference is present.
The test has been performed 3 times, to exclude the possibility of the this result being extra ordinary. All 3 tests showed the same with a significance similar to this. One of the possibly explanation is that SSE uses all 3 color channels in its comparison, while CORR is limited to use a gray scale evaluation. If not, then it comes down to an implementation error, which is highly unlikely the relatively small difference taken into consideration. The last explanation is that the data could favor one of the metrics. Fx the initial model could have areas being wrong, but giving a lower cost to CORR than SSE. Thus it would make SSE seem better, however also this is unlikely to be the case in the amount seen here.
12.2.2 The Masters Lodge
The Masters Lodge shows a real piece of architecture, which is what Vogiatzis proposed as subject for this method to do surface estimation. The surface has a simple overall structure, however it contains a number of small details, that can be difficult to capture. A number of these in increasing level of detail are the actual masters lodge extending from the surface, the roof extending backwards, the windows intruding a little inwards, the embrasures in the walls at the roof etc. For this test, the three images presented in the dataset are used.
The result of a simple test is shown in figure 12.12. The initial mesh only contains 14 vertices, and thus requires many deformations to reach an optimum.
The result shows a much finer grained mesh which encapsulates some of the details mentioned above. The structure of the masters lodge and the tower is captured and the roof extends backwards. The walls in general contains more vertices than seems necessary at first sight. This however is due to the windows in the walls as can be seen in the 3D model. The error buffer shows that there are many details not captured. Fx the structure in the windows are finer than were possible to achieve with the extra vertices. The convergence took approximately 20 minutes.
Annealing Schedules
This datasets is very similar to the second dataset used in Vogiatzis article.
As mentioned in 8.2.2, Vogiatzis uses an annealing schedule, that very rapidly
110 Results
Figure 12.12: The first row shows the initial situation. The second row shows the result after convergence. The resulting model can be found in MastersLodge/test2/model18.x3d.
descents to an almost constant temperature. Two other proposed schedules having a more slow temperature descent where discussed. This together with the choice of having a constant temperature gives 4 different choices. These are tested using the masters lodge dataset, to be able to compare the results to Vogiatzis’s result on the similar dataset.
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Convergence using different annealing schedules Exp Linear Vog None
Figure 12.13:
The result can be seen in figure 12.13, which shows a clear difference between the annealing schedules. The exponential schedule starts in the lead however it is closely followed by the linear method. Both of them converges at close to 1000 iterations since a too small temperature for progress is reached. The schedule proposed by Vogiatzis never gets the chance to use the high temperature which
12.3 Difficult objects 111