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126 Reverse Engineering – Recent Advances and Applications 10 Will-be-set-by-IN-TECH refinement step. The complexity to completely generate a mesh representing the unknown surface at refinement level k averages O(k ·|P|). The following time tables confirm the above discussed propositions. Table 1 shows the measured computation times for several data sets (Stanford Scan Repository (2009)) performed on an Intel Pentium 4 system with 1.6 GHz and 256 MB main memory. Table 2 presents more detailed results for the individual reconstruction steps for the Stanford dragon point data set. Object points faces ref. time[sec] time[sec] level reconstr. opt. Rabbit 8171 25234 6 1.058 0.244 Dragon 437645 72955 7 5.345 0.714 Buddha 543652 56292 7 5.170 0.573 Table 1. Computation time table regarding several input models whereas the VM and the mesh-optimization (4 passes) are performed after the last reconstruction step. Ref.- Spatial- HM- HM- Vertex- Opt. Complete Level Partitioning Extraction R Extraction I Mapping [sec] [sec] [sec] [sec] [sec] [sec] 1 0.240 < 0.001 < 0.001 0.019 < 0.001 0.262 2 0.330 < 0.001 < 0.001 0.068 < 0.001 0.401 3 0.388 < 0.001 0.002 0.241 0.002 0.634 4 0.401 < 0.001 0.014 0.676 0.008 1.100 5 0.278 0.002 0.056 0.787 0.050 1.173 6 0.362 0.008 0.170 0.928 0.180 1.648 7 0.662 0.039 0.717 1.683 0.725 3.826 Table 2. Time values for each reconstruction step of the Stanford dragon. 4.2 Robustness and quality As shown by the examples our reconstruction method delivers meshes of good quality, as long as the resolution of the voxel complex does not exceed a point density induced threshold. Topological features, such as holes and cavities were always detected correctly after a proper number of refinements, see figure 8(a). The HM wrapping rules prevent the underlying object from caving by simultaneously covering the real surface completely. Table 3 shows the measured L2-errors obtained by processing point clouds of different models for several refinement levels. ref. level 1 2 3 4 5 6 7 L2-error Bunny 25,86 9.47 3.60 1.13 0.41 0.14 - L2-error Buddha - 51.92 18.80 7.61 3.47 1.58 0.66 Table 3. L2-error values of the Bunny and Buddha reconstruction for each ref. level (measured in lengths of diagonal of the Bounding Box).
Surface Reconstruction from Unorganized 3D Point Clouds Surface Reconstruction from Unorganized 3D Point Clouds 11 (a) (b) Fig. 8. (a) correctly detected holes in the bunny model, (b) fragmentation of the mesh due to lacking density of point cloud. In case the voxel refinement level exceeds a specific bound imposed by sampling density, the resulting mesh may be incomplete in some areas, due to empty voxels, see figure 8(b). If a very fine mesh is desired, one can fix the topology at a coarser level and apply subdivision and vertex mapping in consecutive steps. 5. Experimental reconstruction of environmental point data The exploration of point data sets, like environmental LiDaR data, is a challenging problem of current interest. In contrast to the point clouds obtained from stationary scanning devices, data complexity is increased by e.g., noise, occlusion, alternating sample density and overlapping samples. Despite of the high scanning resolution, additional undersampling may occur at small and fractured artifacts like fences and leaves of trees. These are only some problems immanent to the reconstruction of surfaces from unorganized environmental point clouds. We have applied our method to environmental point clouds in order to analyse the effects of the aforementioned influence factors on our proposed reconstruction approach. In this context we have performed some experiments on environmental input data generated by tripod mounted LiDaR scanners. Figure 10(a) shows a point cloud of a water tower located at the UC Davis, CA, USA. It consists of about 4.3 million points and features complex environmental structures like buildings and trees. Figure 10(b) shows the corresponding reconstruction after 10 steps. The generated mesh exhibiting about 300 thousand faces took 23 seconds on an Intel Core2 Duo system with 4GB RAM to finish. Another example is presented in figure 11. It shows the final surface representation (215 thousand faces) of a slope with parts of a building and some vegetation. The underlying point cloud has 3.8 million points. The reconstruction finished at level 9 after 24 second. The reconstructed mesh features holes and cracks at those areas at which the resolution lacks in density. Environmental point clouds by nature are large (consisting of up to several million points) and feature high complexity. The experiments showed that our reconstruction approach is capable of producing reliable representations even in cases in which the point clouds are not optimally conditioned. However, the reconstruction lacks at some regions in which the point density does not exhibit the required/satisfied resolution. Despite of this fact the introduced method 127
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REVERSE ENGINEERING - RECENT ADVANC
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Contents Preface IX Part 1 Software
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Preface Introduction In the recent
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Preface XI and con’s related to t
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Preface XIII the step-by-step appli
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Part 1 Software Reverse Engineering
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4 Reverse Engineering - Recent Adva
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10 Reverse Engineering - Recent Adv
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58 2. Model driven architecture: An
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62 Fig. 1. Model, metamodels and tr
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A Review on Shape Engineering and D
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Integrating Reverse Engineering and
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Part 3 Reverse Engineering in Medic
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238 5. Summary and discussions Reve
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268 Fig. 6. A closed polygon mesh r
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272 3. Results Reverse Engineering
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