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Page 1: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds

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Efficient Collision Detection for Large-Scale Point-Clouds

Takeru NIWA and Hiroshi MASUDA

Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds are useful for collision detection of objects that move in engineering plants. We propose a real-time collision detection method for large-scale point-clouds. In our method, statuses are classified into collision, no collision, and unknown. The unknown status indicates that points are missing at the object position because of occlusion. Collisions are evaluated on depth-maps, which are generated from point-clouds. Two-resolution of depth-maps are used for improving performance. High-resolution depth maps are used only when objects collide on rough resolution depth maps. Our experimental results show that our method could quickly detect collisions between a large-scale point-cloud and mesh models.

Key words: point- cloud, laser scanner, collision detection

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Page 2: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds

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Fig.4 Generation of depth maps

(a) Point-cloud

(b) Projection on 2D plane

(c) Multi-resolution depth map

(d) Depth values of front and back

(e) Projection of virtual models

(f) Comparison with depths

(g) Relationship of depth values

(h) Collision detection

Fig.3 Overview of collision detection process

Fig.2 Process of collision detection

Page 3: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds

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Fig.7 Relationships among depth values

Fig.9 Detection of outliers using neighbor points

Fig.8 Object placed in an occluded region

Fig.5 Projection of mesh onto depth map

(a) Perspective image (b) =- image

Fig.6 Distortion of straight lines on =- plane

Fig.10 Generation of multi-resolution depth maps

Page 4: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds

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Fig.12 Results of collision detection

Fig.13 Example of point-clouds

Fig.11 Relationships of depth values on multiple depth map

Page 5: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds

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Table.1 Three cases of depth maps Low Middle High

1 Layer - - 5760 11520

2 Layers 360 720 - 5760 11520

3 Layers 360 720 1440 2880 5760 11520

Table.2 Performance evaluation (frame per second) No Collision Collision Unknown Average

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2 Layers 578 548 544 562

3 Layers 289 284 287 287

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Table.3 Performance evaluation (frame per second) Triangles No Collision Collision Unknown Average

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Table.4 Worst cases of processing time (frame per second) Triangles No Collision Collision Unknown

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Table.5 Performance evaluation (frame per second) Cube size No Collision Collision Unknown Average

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100cm 213 229 216 222

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Page 6: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds

1) M. Figueiredo, J. Oliveira, B. Araújo, J. Pereira: An efficient collision detection algorithm for point cloud models, 20th International conference on Computer Graphics and Vision, 43 (2010) 44

2) J. Pan, I. A. Sucan, S. Chitta, D. Manocha: Real-time collision detection and distance computation on point cloud sensor data, In Robotics and Automation (ICRA), 2013 IEEE International Conference on, (2013) 3593-3599

3) J. Klein, G. Zachmann: Point cloud collision detection, Computer Graphics Forum, 23 (2004) 567-576

4) M. Radwan, S. Ohrhallinger, M. Wimmer: Efficient collision detection while rendering dynamic point clouds, In Proceeding of 2014 Graphics Interface Conference, Canadian Information Processing Society, (2014) 25-33

5) : a (2013) M67

6) H. Masuda, I. Tanaka, M. Enomoto: Reliable surface extraction from point-clouds using scanner-dependent parameters, Computer-Aided Design and Applications, 10(2) (2013) 265-277

Page 7: -O>BK0 *.6@ - Masuda Laboratory (増田研究室) · Takeru NIWA and Hiroshi MASUDA Terrestrial laser scanners can capture dense point-clouds from engineering plants. Dense point-clouds