Pointbased techniques

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Point-based techniques

• Meie Fang
• Wednesday, November 1, 2006

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contents

• relative conceptions of point-based surfaces
• point-based representations
• point-based geometry processing
• point-based rendering
• a paper on computing areas of point-based
  surfaces

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main references

• Leif Kobbelt, Mario Botsch. A survey of
  point-based techniques in computer graphics.
  Computers Graphics, 2004 28 801-814.
• Yu-Shen Liu, Jun-Hai Yong, Hui Zhang, Dong-Ming
  Yan, Jia-Guang Sun. A quasi-Monte Carlo method
  for computing areas of point-sampled surfaces.
  CAD, 2006 38 55-68.

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Relative conceptions
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NURBS ? Meshes ? Point-clouds

• The topological consistency becomes more and more
  simply.

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neighborhoods and normals

• two kinds of neighborhoods
• Euclidean neighborhoods
• not suited for irregularly sampled surfaces
  and unreliable in some cases
• k-nearest neighborhoods
• a naturally adaptive neighborhood relation

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• Amenta, N., Bern, M., Kamvysselis, M., 1998. A
  new Voronoi-based surface reconstruction
  algorithm. In Proc. of ACM SIGGRAPH 98.
• Andersson, M., Giesen, J., Pauly, M.,
  Speckmann, B., 2004. Bounds on the k-neighborhood
  for locally uniformly sampled surfaces. In Proc.
  of Symp. on Point-Based Graphics 04. pp. 167171.
• J. Sankaranarayanan, H. Samet, and A. Varshney,
  A Fast k-Neighborhood Algorithm for Large Point
  Clouds. Proceedings of the Symposium on
  Point-Based Graphics July 29 - 30, 2006, Boston,
  MA

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Point-based representations

• purely point-based representations
• surface splats
• moving least-squares surfaces

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purely point-based representations
point clouds
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Grossman, J. P., Dally, W. J., 1998. Point sample
rendering. In Proc. Of Eurographics Workshop on
Rendering 98. pp. 181192.
Similar to image-based approaches, this
representation is also constructed from several
views of an input object, but it differs in that
each pixel is a surface sample containing
geometric position and (view-independent) surface
color.
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Kalaiah, A., Varshney, A., 2003. Statistical
point geometry. In Proc. of Eurographics
Symposium on Geometry Processing 03. pp. 107115.
using a hierarchical PCA analysis to partition
the geometry and its attributes (normals and
colors) into a set of local Gaussian probability
distributions
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Botsch, M., Wiratanaya, A., Kobbelt, L., 2002.
Efficient high quality rendering of point sampled
geometry. In Proc. of Eurographics Workshop on
Rendering 02.
considering the quantization precision to
minimize redundancy and using a hierarchical PBR
to reduce the memory cost
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PBR of a circle with different quantization
levels (left 5 bit, right 10 bit) and different
sampling densities (top2p/32, bottom 2p/1024).
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surface splats

Zwicker, M., Pfister, H., van Baar, J., Gross,
M., 2001. Surface splatting. InProc. of ACM
SIGGRAPH 01. pp. 371378.
circular disks?elliptical splats
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elliptical splats
two tangential axes the principal curvature
directions of the underlying surface two
respective radii inversely proportional to the
corresponding minimum and maximum
curvatures superiorities the same topological
flexibility as pure point clouds the same
approximation order as triangle meshes locally
the best linear approximant to a smooth surface
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representing sharp features
Pauly, M., Keiser, R., Kobbelt, L., Gross, M.,
2003. Shape modeling with point-sampled geometry.
In Proc. of ACG SIGGRAPH 03.
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moving least-squares surfaces
H is found by minimizing
g is found by minimizing
The weight function
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Alexa, M., Behr, J., Cohen-Or, D., Fleishman,
S., Levin, D., Silva, C. T., 2003. Computing and
rendering point set surfaces. IEEE Transactions
on Visualization and Computer Graphics 9 (1),
315.

• Alexa, M., Adamson, A., 2004. On normals and
  projection operators
• for surfaces defined by point sets.In Proc. of
  Symp. on Point-
• Graphics 04.pp. 149155.

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Amenta, N., Kil, Y., 2004. Defining point-set
surfaces. In Proc. of ACM SIGGRAPH 04.
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Point-based geometry processing
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noise removal
Pauly, M., Gross, M., 2001. Spectral processing
of point-sampled geometry. In Proc. of ACM
SIGGRAPH 01.
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Original Patch
Gaussian Wiener noiseblur
Layout Filter
Filter
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summary

• versatile spectral decomposition of point-based
  models
• effective filtering
• adaptive resampling
• efficient processing of large point-sampled models

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Pauly, M., Keiser, R., Gross, M., 2003.
Multi-scale feature extraction onpoint-sampled
surfaces. In Proc. of Eurographics 03.
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Weyrich, T., Pauly, M., Heinzle, S., Keiser, R.,
Scandella, S., Gross, M., 2004.Post-processing of
scanned 3D surface data. In Proc. of Symp. on
Point-Based Graphics 04. pp. 8594.
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decimation
three kinds of decimation methods Pauly, M.,
Gross, M., Kobbelt, L., 2002. Efficient
simplification of point-sampled surfaces. In
Proc. of IEEE Visualization 02.

• hierarchical clustering method
• iterative simplification
• particle simulation

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clustering method
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iterative simplification
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particle simulation
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comparison
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Wu, J., Kobbelt, L., 2004. Optimized subsampling
of point sets for surfacesplatting. In Proc. of
Eurographics 04.
a simplification method especially designed
for splat-based surface
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editing
Zwicker, M., Pauly, M., Knoll, O., Gross, M.,
2002. PointShop 3D An interactive system for
point-based surface editing. In Proc. of ACM
SIGGRAPH02.
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Adams, B., Wicke, M., Dutre, P., Gross, M.,
Pauly, M., Teschner, M., 2004. Interactive 3D
painting on point-sampled objects. In Proc. of
Symp. on Point-Based Graphics 04. pp. 5766.
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deformation
Pauly, M., Keiser, R., Kobbelt, L., Gross, M.,
2003. Shape modeling with point-sampled geometry.
In Proc. of ACG SIGGRAPH 03.
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PDE-based segmentation, texture synthesis,
texture inpainting and geometry smoothing
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Constructive Solid Geometry technique

• references
• Clarenz, U., Rumpf, M., Telea, A., 2004. Finite
  elements on point based surfaces.In Proc. of
  Symp. on Point-Based Graphics 04. pp. 201211.
• Adams, B., Dutre, P., 2003. Interactive boolean
  operations on surfel-bounded solids. In Proc. of
  ACM SIGGRAPH 03. pp. 651656.
• Adams, B., Dutre, P., 2004. Boolean operations
  on surfel-bounded solids using programmable
  graphics hardware. In Proc. of Symp. on
  Point-Based Graphics 04. pp. 1924.

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Point-based rendering
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Botsch, M., Spernat, M., Kobbelt, L., 2004.Phong
splatting. In Proc. of Symp. on Point-Based
Graphics 04.
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References

• Grossman, J. P., Dally, W. J., 1998. Point sample
  rendering. In Proc. Of Eurographics Workshop on
  Rendering 98. pp. 181192.
• Dachsbacher, C., Vogelgsang, C., Stamminger, M.,
  2003. Sequential point trees. In Proc. of ACM
  SIGGRAPH 03.
• Botsch, M., Kobbelt, L., 2003. High-quality
  point-based rendering on modern GPUs. In Proc.
  of Pacific Graphics 03.
• Guennebaud, G., Paulin, M., 2003. Efficient
  screen space approach for hardware accelerated
  surfel rendering. In Proc. of Vision, Modeling,
  and Visualization 03.
• Botsch, M., Spernat, M., Kobbelt, L., 2004. Phong
  splatting. In Proc. Of Symp. on Point-Based
  Graphics 04.
• Zwicker, M., Räsänen, J., Botsch, M.,
  Dachsbacher, C., Pauly, M., 2004. Perspective
  accurate splatting. In Proc. of Graphics
  Interface 04.

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Computing the areas of point-based surfaces
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Quasi-Monte Carlo method
Yu-Shen Liu, Jun-Hai Yong, Hui Zhang,
Dong-Ming Yan, and Jia-Guang Sun. A quasi-Monte
Carlo method for computing areas of point-sampled
surfaces. Computer-Aided Design 2006 38(1)
55-68.
Li X, Wang W, Martin RR, Bowyer A. Using
low-discrepancy sequences and the Crofton formula
to compute surface areas of geometric models.
Comput Aided Design 200335(9)77182.
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the CauchyCrofton formula
integration approximation
the area formula of B
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steps
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the smallest enclosing ball of point sets

• Gärtner B. Fast and robust smallest enclosing
  balls. In Proc. 7th Annual European Symposium on
  Algorithms (ESA). Volume 1643 of Lecture Notes in
  Computer Science, Springer-Verlag (1999), p.
  325-338, 1999.
• http//www.inf.ethz.ch/personal/gaertner/miniball.
  html

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generating uniformly distributed lines
http//mathworld.wolfram.com/SpherePointPicking.ht
ml
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the LPSI algorithm
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collecting and clustering inclusion points
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classifying clusters
(a) Q contains no intersection point. (b) Q
contains only one touching point.
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(c) Q contains only one intersection point. (d) Q
contains two intersection points.
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approximation errors
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Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel
H.P. Multi-level partition of unity implicits.
In Proceedings of SIGGRAPH03 2003. p. 463-470.
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http//graphics.stanford.edu/data/3Dscanrep/
Desbrun M., Meyer M., SchrÖder P., Barr A.H.
Implicit fairing of irregular meshes using
diffusion and curvature flow. In Proceedings of
SIGGRAPH99 1999. p. 317-324.
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applications

• several point-based processing applications
  such as property computation, area-preserving
  smoothing, shape recognition, matching