Visualization of Point-Based Surfaces with Locally Reconstructed Subdivision Surfaces

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Visualization of Point-Based Surfaces with
Locally Reconstructed Subdivision Surfaces

• Tamy Boubekeur
• Patrick Reuter
• Christophe Schlick
• LaBRI, LIPSI - University of Bordeaux - France

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Point-Based Graphics

• Core unstructured point cloud
• Points with attributes
• Color
• Normal
• Etc.
• Advantages
• Acquisition
• Multiresolution
• Storage
• Drawback visualization

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Previous work Surface Splatting

• For each point in the object space, draw a small
  circle or ellipse in the image space to obtain a
  hole-free surface.
• Surface Splatting
• Zwicker et al. 2001
• Phong Splatting
• Botsch et al. 2004
• High Quality Surface Splatting on Todays GPUs
• Botsch et al. 2005
• Drawback complete rewriting of rendering
  algorithms

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Alternative Surface Reconstruction

• Conversion from a point cloud to an other model
  (mesh, NURBS, implicit, etc.)
• Implicit approaches MPU, RBF
• Othake et al. 2003Tobor et al. 2004
• Explicit approaches Voronoï/Delaunay
• Amenta et al. 99Dey et al. 2001
• Other approaches deformable models, direct
  parametrization, etc.
• Drawback generation time

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Problem ?

• Handle large point clouds
• Object-space reconstruction
• Rapid visualization
• Hardware acceleration

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Solution

• Handle large point clouds
• Object-space reconstruction
• Rapid Visualization
• Hardware acceleration

Local approach Polygonal reconstruction Trade-off
between quality and performance Standard hardware
rendering pipeline
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Our approach

• Spatial partitioning with octree
• Local polygonal reconstruction in each partition
  overlappings between partitions
• Aggregation of the pieces of surfaces with
  subdivision

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Our approach
Overview

• Usual bottleneck mesh generation /
  reconstruction
• Efficient local reconstruction ? constrained
  partitioning

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Local Reconstruction

• Height-map property locally, a surface can be
  defined by z f(x,y)
• Local 2D incremental Delaunay Triangulation
• Computational complexity in O(n.log(n)) for n
  points
• More economic and faster than 3D triangulations

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Local Reconstruction
Partition point cloud
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Local Reconstruction
Projection onto the average plane
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Local Reconstruction
2D Triangulation
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Local Reconstruction
3D projection
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Local Reconstruction
The piece of surface obtained
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Local Reconstruction
Sudivision
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Overlappings

• Problem holes inbetween the pieces of surfaces
• Solution
• enlarging temporarily the reconstruction support,
  by creating overlappings between neighboring
  surfaces
• Taking benefit of the partitioning structure

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Partitioning
Level 5
Level 6

• Octree simple, adaptive, convergence toward the
  surface
• Drive the reconstruction step by providing a good
  approximation of the global topology

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Partitioning

• Local Height Map criteria
• Normal Deviation criteria
• Geometric Deviation criteria

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Partitioning

• Partition size criteria
• Balance complexity
• Helps to resolve a wide range of topological
  inconsistencies

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Subdivision Surfaces

• Application to local piece of mesh piecewise C2
  continuity (C1 for extraordinary vertices)
  Loop 1987
• Eliminates artefacts in overlappings zones
  (interpolatory boundary rules)
• Modification projective Loop Scheme

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Hardware Rendering

• No GPU programming
• Visibility tests (octree)
• Standard (OpenGL)
• Example Environnement Cube Mapping

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High Quality Rendering

• Point cloud raytracing
• Just a ray-triangle intersection test
• lazy generation
• Huge scene rendering

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Results
Torso 2941 pts 0.33 sec.

• Smoothing by subdivision without visual
  artefacts.

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Results

• Visual continuity

Quasi-Delaunay mesh
AdamKraft 7073 pts 4.12 sec.
Dragon 100251 pts 4.83 sec.
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Results
Bottle 42736 pts 2.13 sec.
Knot 28659 pts 1.40 sec.
Robust against non uniform point clouds and
complex topologies.
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Results
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Results
Near-linear complexity in time
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Conclusion

• Advantages
• Local and fast approach
• Quasi-Delaunay polygonal output
• A visual continuity
• Can replace true surface reconstruction in
  various cases
• Limitations
• Very non uniform point clouds

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Conclusion
Comparison with other approaches
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Current/Future Work

• Surface reconstruction
• Huge data (out-of-core processing/clusters)
• Point-cloud resampling
• Improved projection rule
• Manifold extraction

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Current/Future Works

• Visualization
• A complete polygonal approach for high-quality
  rendering of point clouds
• PointShop 3D integration

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Thank you for your attention !

• www.labri.fr/boubek