Abstract
We describe a new and simple variational formulation to reconstruct the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. Point clouds are nowadays obtained using a variety of techniques, including structured lighting systems, pasive multi-view stereo algorithms, and 3D laser scanning. In our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. The formulation allows for a number of different efficient discretizations, reduces to a finite dimensional least squares problem for all linearly parameterized families of functions, does not require the specification of boundary conditions, and it is particularly good at extrapolating missing and/or irregularly sampled data. The resulting algorithms are significantly simpler and easier to implement than alternative methods. In particular, our implementation based on a primal-graph octree-based hybrid finite element-finite difference discretization, and the Dual Marching Cubes isosurface extraction algorithm is very efficient, and produces high quality crack-free adaptive manifold polygon meshes. After the geometry and topology are reconstructed, the color information from the points is smoothly extrapolated to the surface by solving a second variational problem which also reduces to a finite dimensional least squares problem. The resulting method produces high quality polygon meshes with smooth color maps, which accurately approximate the source colored oriented points. An open source implementation of this method is available for download. We describe applications to digital archaeology, 3D forensics, and 3D broadcasting.
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Sibley, P.G., Taubin, G.: Vectorfield Isosurface-Based Reconstruction from Oriented Points. In: ACM Siggraph 2005 Sketches, p. 29. ACM (2005)
Snavely, N., Seitz, S., Szeliski, R.: Photo Tourism: Exploring Photo Collections in 3D. ACM Transactions on Graphics 25, 835–846 (2006)
Crispell, D., Lanman, D., Sibley, P.G., Zhao, Y., Taubin, G.: Beyond silhouettes: Surface reconstruction using multi-flash photography. In: Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT 2006), pp. 405–412. IEEE (2006)
Lanman, D., Sibley, P., Crispell, D., Zhao, Y., Taubin, G.: Multi-Flash 3D Photography: Capturing Shape and Appearance. In: Siggraph 2006 Posters (August 2006)
Furukawa, Y., Ponce, J.: Accurate, Dense, and Robust Multi-View Stereopsis. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(8), 1362–1376 (2010)
Furukawa, Y., Ponce, J.: Patch-Based Multi-View Stereo Software (PMVS - Version 2) (2010), http://grail.cs.washington.edu/software/pmvs/
Calakli, F., Taubin, G.: Smooth Signed Distance Surface Reconstruction. Computer Graphics Forum 30(7) (2011)
Calakli, F., Taubin, G.: Smooth Signed Distance Surface Reconstruction. Open source Software Released (2011), http://mesh.brown.edu/ssd
Andalo, F.A., Calakli, F., Taubin, G., Goldenstein, S.: Accurate 3D Footwear Impression Recovery From Photographs. In: Proceedings of the 4th International Conference on Imaging for Crime Detection and Prevention (ICDP 2011), Kington Upon Thames, London (November 2011)
Calakli, F., Taubin, G.: SSD-C: Smooth Signed Distance Colored Surface Reconstruction. In: Expanding The Frontiers of Visual Analytics and Visualization, Part 4, ch. 18, pp. 323–338. Springer (2012)
Cooper, D.B., et al.: Reconstruction and Exploratory Visualization: Engineering meets ArchaeoLogy (REVEAL), A System for Streamlined Powerful Sensing, Archiving, Extracting Information from, Visualizing and Communicating, Archaeological Site-excavation Data (2008–2008), http://vision.lems.brown.edu/project_desc/Reveal
Gay, E., et al.: REVEAL Analyze. Open Source Archaeological Database Browser and Analysis Software releases (2012), http://sourceforge.net/projects/revealanalyze/
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Taubin, G. (2012). Smooth Signed Distance Surface Reconstruction and Applications. In: Alvarez, L., Mejail, M., Gomez, L., Jacobo, J. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2012. Lecture Notes in Computer Science, vol 7441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33275-3_4
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DOI: https://doi.org/10.1007/978-3-642-33275-3_4
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