Point-based techniques Mei ’ e Fang Wednesday, November 1, 2006

contents relative c onceptions 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, : 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, :

Relative c onceptions

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., A new Voronoi-based surface reconstruction algorithm. In: Proc. of ACM SIGGRAPH 98. Andersson, M., Giesen, J., Pauly, M., Speckmann, B., 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 , 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., 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., 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., 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., 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., 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 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; elliptical splats

Pauly, M., Keiser, R., Kobbelt, L., Gross, M., 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., Computing and rendering point set surfaces. IEEE Transactions on Visualization and Computer Graphics 9 (1), 3–15. Alexa, M., Adamson, A., 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., Defining point-set surfaces. In: Proc. of ACM SIGGRAPH 04.

Point-based geometry processing

noise removal Pauly, M., Gross, M., 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., 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., 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., Optimized subsampling of point sets for surface splatting. In: Proc. of Eurographics 04. a simplification method especially designed for splat-based surface

editing Zwicker, M., Pauly, M., Knoll, O., Gross, M., 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., 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., 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., Finite elements on point based surfaces.In: Proc. of Symp. on Point-Based Graphics 04. pp. 201–211. Adams, B., Dutre, P., Interactive boolean operations on surfel- bounded solids. In: Proc. of ACM SIGGRAPH 03. pp. 651–656. Adams, B., Dutre, P., 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., Point sample rendering. In: Proc. Of Eurographics Workshop on Rendering 98. pp. 181–192. Dachsbacher, C., Vogelgsang, C., Stamminger, M., Sequential point trees. In: Proc. of ACM SIGGRAPH 03. Botsch, M., Kobbelt, L., High-quality point-based rendering on modern GPUs. In: Proc. of Pacific Graphics 03. Guennebaud, G., Paulin, M., Efficient screen space approach for hardware accelerated surfel rendering. In: Proc. of Vision, Modeling, and Visualization 03. Botsch, M., Spernat, M., Kobbelt, L., Phong splatting. In: Proc. Of Symp. on Point-Based Graphics 04. Zwicker, M., Räsänen, J., Botsch, M., Dachsbacher, C., Pauly, M., 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): 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. 7 th Annual European Symposium on Algorithms (ESA). Volume 1643 of Lecture Notes in Computer Science, Springer-Verlag (1999), p ,

generating uniformly distributed lines

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; p

Desbrun M., Meyer M., Schr Ö der P., Barr A.H. Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of SIGGRAPH’99; p

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