Point-based techniques

Mei’e FangWednesday, November 1, 2006

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

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.

Relative conceptions

NURBS → Meshes → Point-clouds

The topological consistency becomes more and more simply.

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

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. 167–171.

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

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 purely point-based

representations surface splats moving least-squares surfaces

point clouds

purely point-based representations

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:2/32, bottom: 2/1024).

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

surface splats

two tangential axes: the principal curvature directions of the underlying surfacetwo 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;

elliptical splats

Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 2003. Shape modeling with point-sampled geometry. In: Proc. of ACG SIGGRAPH 03.

representing sharp features

moving least-squares surfaces

g is found by minimizing

H 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 Point-Graphics 04.pp. 149–155.

Amenta, N., Kil, Y., 2004. Defining point-set surfaces. In: Proc. of ACM SIGGRAPH 04.

Point-based geometry processing

noise removalPauly, M., Gross, M., 2001. Spectral processing of point-sampled geometry.

In: Proc. of ACM SIGGRAPH 01.

Original Patch Gaussian Wiener noise+blur Layout Filter Filter

summary versatile spectral decomposition of

point-based models

effective filtering

adaptive resampling

efficient processing of large point-sampled models

Pauly, M., Keiser, R., Gross, M., 2003. Multi-scale feature extraction onpoint-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 point-sampled surfaces. In: Proc. of IEEE Visualization 02.

hierarchical clustering method iterative simplification particle simulation

clustering method

iterative simplification

particle simulation

comparison

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

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. onPoint-Based Graphics 04. pp. 57–66.

deformationPauly, 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 Point-Based 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 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 point-based 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

the area formula of B

integration approximation

steps

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

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, area-preserving smoothing, shape recognition, matching…