Point-based techniques
Mei’e Fang
Wednesday, November 1, 2006
contents
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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
main references
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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.
Relative conceptions
NURBS → Meshes → Point-clouds
The topological consistency becomes
more and more simply.
neighborhoods and normals
two kinds of neighborhoods
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Euclidean neighborhoods
not suited for irregularly sampled surfaces
and unreliable in some cases
k-nearest neighborhoods
a naturally adaptive neighborhood relation
Amenta, N., Bern, M., Kamvysselis, M., 1998. A new Voronoi-based surface
reconstruction algorithm. In: Proc. of ACM SIGGRAPH 98.
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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. 167–171.
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J. Sankaranarayanan, H. Samet, and A. Varshney, A Fast k-Neighborhood
Algorithm for Large Point Clouds. Proceedings of the Symposium on PointBased Graphics July 29 - 30, 2006, Boston, MA
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the estimation of normals
the covariance matrix:
The eigenvector corresponding to the
smallest eigenvalue gives an estimate for
the normal direction.
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.,
1992. Surface reconstruction from unorganized points. In: Proc. of
ACM SIGGRAPH92. pp. 71–78.
Point-based representations
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purely point-based representations
surface splats
moving least-squares surfaces
purely point-based representations
point clouds
Grossman, J. P., Dally, W. J., 1998. Point sample rendering.
In: Proc. Of Eurographics Workshop on Rendering 98. pp.
181–192.
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.
Kalaiah, A., Varshney, A., 2003. Statistical point geometry.
In: Proc. of Eurographics Symposium on Geometry
Processing 03. pp. 107–115.
using a hierarchical PCA analysis to partition the geometry and
its attributes (normals and colors) into a set of local Gaussian
probability distributions
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
PBR of a circle with different quantization levels
(left: 5 bit, right 10 bit)
and different sampling densities
(top:2p/32, bottom: 2p/1024).
surface splats
Zwicker, M., Pfister, H., van Baar, J., Gross, M., 2001.
Surface splatting. In:Proc. of ACM SIGGRAPH 01. pp.
371–378.
circular disks→elliptical splats
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;
representing sharp features
Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 2003.
Shape modeling with point-sampled geometry. In:
Proc. of ACG SIGGRAPH 03.
moving least-squares surfaces
H is found by minimizing
g is found by minimizing
The weight function
• 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), 3–15.
• Alexa, M., Adamson, A., 2004. On normals and projection operators
for surfaces defined by point sets.In: Proc. of Symp. on PointGraphics 04.pp. 149–155.
Amenta, N., Kil, Y., 2004. Defining point-set surfaces. In: Proc. of ACM
SIGGRAPH 04.
Point-based geometry
processing
noise removal
Pauly, M., Gross, M., 2001. Spectral processing of point-sampled geometry.
In: Proc. of ACM SIGGRAPH 01.
Original
noise+blur
Patch
Layout
Gaussian
Filter
Wiener
Filter
summary
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versatile spectral decomposition of pointbased models
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effective filtering
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adaptive resampling
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efficient processing of large pointsampled models
Pauly, M., Keiser, R., Gross, M., 2003. Multi-scale feature extraction on
point-sampled surfaces. In: Proc. of Eurographics 03.
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. 85–94.
decimation
three kinds of decimation methods
Pauly, M., Gross, M., Kobbelt, L., 2002. Efficient simplification of pointsampled surfaces. In: Proc. of IEEE Visualization 02.
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hierarchical clustering method
iterative simplification
particle simulation
clustering method
iterative simplification
particle simulation
comparison
a simplification method especially designed
for splat-based surface
Wu, J., Kobbelt, L., 2004. Optimized subsampling of point sets for surface
splatting. In: Proc. of Eurographics 04.
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.
Adams, B., Wicke, M., Dutr´e, 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. 57–66.
deformation
Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 2003. Shape modeling with
point-sampled geometry. In: Proc. of ACG SIGGRAPH 03.
PDE-based segmentation, texture synthesis,
texture inpainting and geometry smoothing
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. 201–211.
• Adams, B., Dutre, P., 2003. Interactive boolean operations on surfel-
bounded solids. In: Proc. of ACM SIGGRAPH 03. pp. 651–656.
• Adams, B., Dutre, P., 2004. Boolean operations on surfel-bounded solids
using programmable graphics hardware. In: Proc. of Symp. on PointBased Graphics 04. pp. 19–24.
Point-based rendering
Botsch, M., Spernat, M., Kobbelt, L., 2004.Phong splatting. In:
Proc. of Symp. on Point-Based Graphics 04.
References
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Grossman, J. P., Dally, W. J., 1998. Point sample rendering. In:
Proc. Of Eurographics Workshop on Rendering 98. pp. 181–192.
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.
Computing the areas of pointbased surfaces
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 2003;35(9):771–82.
the Cauchy–Crofton formula
integration approximation
the area formula of B
steps
the smallest enclosing ball of point sets
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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
generating uniformly distributed lines
http://mathworld.wolfram.com/SpherePointPicking.html
the LPSI algorithm
collecting and clustering inclusion points
classifying clusters
(a) Q contains no intersection point. (b) Q contains only one touching
point.
(c) Q contains only one intersection point. (d) Q contains two intersection
points.
approximation errors
Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel H.P. Multi-level
partition of unity implicits. In: Proceedings of SIGGRAPH’03; 2003.
p. 463-470.
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 SIGGRAPH’99; 1999. p.
317-324.
applications
several point-based processing applications
such as property computation, areapreserving smoothing, shape recognition,
matching…