**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31515

##### Visual Hull with Imprecise Input

**Authors:**
Peng He

**Abstract:**

**Keywords:**
Geometric Domain,
Computer Vision,
Computational Geometry,
Visual Hull,
Image-Based reconstruction,
Imprecise Input,
CAD object

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1062650

**References:**

[1] Leda. http://www.mpi-sb.mpg.de/LEDA/leda.html.

[2] M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York, 9th printing edition, 1972.

[3] F. Avnaim, J.-D. Boissonnat, O. Devillers, F. P. Preparata, and M. Yvinec. Evaluation of a new method to compute signs of determinants. In SCG -95: Proceedings of the eleventh annual symposium on Computational geometry, pages 416-417, New York, NY, USA, 1995. ACM.

[4] Andrea Bottino and Aldo Laurentini. The visual hull of smooth curved objects. IEEE Trans. Pattern Anal. Mach. Intell., 26(12):1622-1632, 2004.

[5] Andrea Bottino and Aldo Laurentini. The visual hull of piecewise smooth objects. Comput. Vis. Image Underst., 110(1):7-18, 2008.

[6] Herv'e Br┬¿onnimann, Ioannis Z. Emiris, Victor Y. Pan, and Sylvain Pion. Computing exact geometric predicates using modular arithmetic with single precision. In SCG -97: Proceedings of the thirteenth annual symposium on Computational geometry, pages 174-182, New York, NY, USA, 1997. ACM.

[7] Herv'e Br┬¿onnimann and Mariette Yvinec. Efficient exact evaluation of signs of determinants. In SCG -97: Proceedings of the thirteenth annual symposium on Computational geometry, pages 166-173, New York, NY, USA, 1997. ACM.

[8] N. J. Cutland. Computability: An Introduction to Recursive Function Theory. Cambridge University Press, 1980.

[9] Olivier Devillers, Alexandra Fronville, Bernard Mourrain, and Monique Teillaud. Algebraic methods and arithmetic filtering for exact predicates on circle arcs. In SCG -00: Proceedings of the sixteenth annual symposium on Computational geometry, pages 139-147, New York, NY, USA, 2000. ACM.

[10] C. R. Dyer. Volumetric scene reconstruction from multiple views. In Foundations of Image Understanding, pages 469-489. Kluwer, 2001.

[11] A. Edalat, A. A. Khanban, and A. Lieutier. Delaunay triangulation and Voronoi diagram with imprecise input data. Electronic Notes in Theoretical Computer Science, 66(1), July 2002. Proceedings of the 5th CCA Workshop.

[12] A. Edalat, A. A. Khanban, and A. Lieutier. Computability in computational geometry. New Computational Paradigms, 3526:117-127, 2005.

[13] A. Edalat and A. Lieutier. Foundation of a computable solid modeling. In Proceedings of the fifth symposium on Solid modeling and applications, ACM Symposium on Solid Modeling and Applications, pages 278-284, 1999.

[14] A. Edalat and A. Lieutier. Foundation of a computable solid modelling. Theoretical Computer Science, 284(2):319-345, June 2002.

[15] A. Edalat, A. Lieutier, and E. Kashefi. The convex hull in a new model of computation. In Proceedings of the 13th Canadian Conference on Computational Geometry, pages 93-96, University of Waterloo, August 2001.

[16] Philipp Fechteler and Peter Eisert. Adaptive Colour Classification for Structured Light Systems. IET Journal on Computer Vision, 3(2):49-59, June 2009. Special Issue on 3D Face Processing.

[17] Steven Fortune. Polyhedral modelling with multiprecision integer arithmetic. Computer-Aided Design, 29(2):123-133, 1997.

[18] Steven Fortune and Christopher J. Van Wyk. Efficient exact arithmetic for computational geometry. In SCG -93: Proceedings of the ninth annual symposium on Computational geometry, pages 163-172, New York, NY, USA, 1993. ACM.

[19] Ziv Gigus, John Canny, and Raimund Seidel. Efficiently computing and representing aspect graphs of polyhedral objects. IEEE Trans. on Pat. Matching & Mach. Intelligence, 13(6), June 1991.

[20] Ziv Gigus, John F. Canny, and Raimund Seidel. Efficiently computing and representing aspect graphs of polyhedral objects. Technical Report UCB/CSD-88-432, EECS Department, University of California, Berkeley, Aug 1988.

[21] Chun-Yi Hu, Takashi Maekawa, Evan C. Sherbrooke, and Nicholas M. Patrikalakis. Robust interval algorithm for curve intersections. Computer-Aided Design, 28(6-7):495-506, 1996.

[22] Chun-Yi Hu, Nicholas M. Patrikalakis, and Xiuzi Ye. Robust interval solid modelling part ii: boundary evaluation. Computer-Aided Design, 28(10):819-830, 1996.

[23] A. A. Khanban and A. Edalat. Computing Delaunay triangulation with imprecise input data. In Proceedings of the 15th Canadian Computational Geometry Conference, pages 94-97, 2003.

[24] M. Kreveld, M. Loffler, and J. S. Mitchell. Preprocessing imprecise points and splitting triangulations. In ISAAC -08: Proceedings of the 19th International Symposium on Algorithms and Computation, pages 544-555, Berlin, Heidelberg, 2008. Springer-Verlag.

[25] K. N. Kutulakos and S. M. Seitz. A theory of shape by space carving. Computer Vision, IEEE International Conference on, 1:307-314, 1999.

[26] Kiriakos N. Kutulakos. Approximate N-view stereo. In ECCV -00: Proceedings of the 6th European Conference on Computer Vision-Part I, pages 67-83, London, UK, 2000. Springer-Verlag.

[27] A. Laurentini. The visual hull concept for silhouette-based image understanding. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(2):150-162, February 1994.

[28] Aldo Laurentini. Introducing the reduced aspect graph. Pattern Recogn. Lett., 16(1):43-48, 1995.

[29] Aldo Laurentini. Computing the visual hull of solids of revolution. Pattern Recognition, 32(3):377-388, 1999.

[30] M. Loffler and J. Snoeyink. Delaunay triangulations of imprecise pointsin linear time after preprocessing. In SCG -08: Proceedings of the twenty-fourth annual symposium on Computational geometry, pages 298-304, New York, NY, USA, 2008. ACM.

[31] Franco P. Preparata and Michael I. Shamos. Computational Geometry: An Introduction (Monographs in Computer Science). Springer, August 1985.

[32] D. Salesin, J Stolfi, and L. Guibas. Epsilon geometry: building robust algorithms from imprecise computations. In SCG -89: Proceedings of the fifth annual symposium on Computational geometry, pages 208-217, New York, NY, USA, 1989. ACM.

[33] Daniel Scharstein. High-accuracy stereo depth maps using structured light. pages 195-202, 2003.

[34] Thomas W. Sederberg and Rida T. Farouki. Approximation by interval bezier curves. IEEE Comput. Graph. Appl., 12(5):87-95, 1992.

[35] G. G. Slabaugh, T. Malzbender, W. B. Culbertson, and R. W. Schafer. Improved voxel coloring via volumetric optimization. Technical report, 2003. Center for Signal and Image Processing, Georgia Institute of Technology.

[36] Klaus Weihrauch. Computability. Springer-Verlag New York, Inc., New York, NY, USA, 1987.

[37] Chee Yap and Thomas Dub. The exact computation paradigm. 1994.

[38] Li Zhang, Brian Cudess, and Steven M. Seitz. Rapid shape acquisition using color structured lightand multi-pass dynamic programming. In In The 1st IEEE International Symposium on 3D Data Processing, Visualization, and Transmission, pages 24-36, 2002.