Object Completion using k-Sparse Optimization
We present a new method for the completion of partial globally‐symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficie...
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| Vydané v: | Computer graphics forum Ročník 34; číslo 7; s. 13 - 21 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Oxford
Blackwell Publishing Ltd
01.10.2015
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | We present a new method for the completion of partial globally‐symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficiently using a robust RANSAC‐based optimizer. The detected partial symmetries are then reused iteratively, in order to complete the missing parts of the object. A global error relaxation method minimizes the accumulated alignment errors and a non‐rigid registration approach applies local deformations in order to properly handle approximate symmetry. Unlike previous approaches, our method does not rely on the computation of features, it uniformly handles translational, rotational and reflectional symmetries and can provide plausible object completion results, even on challenging cases, where more than half of the target object is missing. We demonstrate our algorithm in the completion of 3D scans with varying levels of partiality and we show the applicability of our approach in the repair and completion of heavily eroded or incomplete cultural heritage objects. |
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| AbstractList | We present a new method for the completion of partial globally-symmetric 3D objects, based on the detection of partial and approximate symmetries in the incomplete input dataset. In our approach, symmetry detection is formulated as a constrained sparsity maximization problem, which is solved efficiently using a robust RANSAC-based optimizer. The detected partial symmetries are then reused iteratively, in order to complete the missing parts of the object. A global error relaxation method minimizes the accumulated alignment errors and a non-rigid registration approach applies local deformations in order to properly handle approximate symmetry. Unlike previous approaches, our method does not rely on the computation of features, it uniformly handles translational, rotational and reflectional symmetries and can provide plausible object completion results, even on challenging cases, where more than half of the target object is missing. We demonstrate our algorithm in the completion of 3D scans with varying levels of partiality and we show the applicability of our approach in the repair and completion of heavily eroded or incomplete cultural heritage objects. |
| Author | Sipiran, I. Andreadis, A. Papaioannou, G. Mavridis, P. |
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| Cites_doi | 10.1145/1778765.1778831 10.1111/cgf.12010 10.1145/1141911.1141925 10.1145/1618452.1618521 10.1111/cgf.12446 10.1145/1778765.1778840 10.1145/1618452.1618484 10.1145/1057432.1057448 10.1016/j.gmod.2013.03.001 10.1145/2366145.2366200 10.1109/34.476508 10.1111/cgf.12481 10.1109/34.88573 10.1007/s11263-010-0356-4 10.1111/j.1467-8659.2009.01515.x 10.1145/2601097.2601220 10.1007/s001380050048 10.1007/s11042-014-2267-9 10.1145/2070781.2024159 10.1145/1141911.1141924 10.1016/0262-8856(92)90066-C 10.1111/cgf.12306 10.1111/cgf.12430 10.1111/cgf.12454 10.1145/2532548 |
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| Copyright | 2015 The Author(s) Computer Graphics Forum © 2015 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2015 The Eurographics Association and John Wiley & Sons Ltd. |
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| References_xml | – reference: Sun J., Ovsjanikov M., Guibas L.J.: A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion. Comput. Graph. Forum 28, 5 (2009). 2 – reference: Tevs A., Huang Q., Wand M., Seidel H.-P., Guibas L.: Relating shapes via Geometric Symmetries and Regularities. ACM Trans. Graph. 33, 4 (2014). 2 – reference: Lipman Y., Chen X., Daubechies I., Funkhouser T.: Symmetry Factored Embedding and Distance. ACM Trans. Graph. 29, 4 (July 2010), 103:1-103:12. 2 – reference: Mitra N.J., Guibas L.J., Pauly M.: Partial and Approximate Symmetry Detection for 3D Geometry. ACM Trans. Graph. 25, 3 (July 2006), 560-568. 2 – reference: Bermanis A., Averbuch A., Keller Y.: 3-D Symmetry Detection and Analysis Using the Pseudo-polar Fourier Transform. Int. Journal of Computer Vision 90, 2 (2010), 166-182. 2 – reference: Huang Q., Koltun V., Guibas L.: Joint shape segmentation with linear programming. ACM Trans. Graph. 30, 6 (Dec. 2011), 125:1-125:12. 8 – reference: Harary G., Tal A., Grinspun E.: Feature-preserving surface completion using four points. Computer Graphics Forum 33, 5 (2014), 45-54. 2 – reference: Mitra N.J., Pauly M., Wand M., Ceylan D.: Symmetry in 3D Geometry: Extraction and Applications. Computer Graphics Forum 32, 6 (2013), 1-23. 2, 3 – reference: Li H., Adams B., Guibas L.J., Pauly M.: Robust single-view geometry and motion reconstruction. ACM Trans. Graph. 28, 5 (Dec. 2009), 175:1-175:10. 2 – reference: Jiang W., Xu K., Cheng Z.-Q., Zhang H.: Skeleton-based intrinsic symmetry detection on point clouds. Graphical Models 75, 4 (2013), 177-188. 2 – reference: Sipiran I., Gregor R., Schreck T.: Approximate symmetry detection in partial 3d meshes. Computer Graphics Forum (proc. Pacific Graphics) 33 (2014), 131-140. 2, 6, 7 – reference: Xu K., Zhang H., Jiang W., Dyer R., Cheng Z., Liu L., Chen B.: Multi-scale Partial Intrinsic Symmetry Detection. ACM Trans. Graph. 31, 6 (Nov. 2012), 181:1-181:11. 2 – reference: Thrun S., Wegbreit B.: Shape from symmetry. In Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on (Oct 2005), vol. 2, pp. 1824-1831 Vol. 2. 2 – reference: Huang Q.-X., Flöry S., Gelfand N., Hofer M., Pottmann H.: Reassembling Fractured Objects by Geometric Matching. ACM Trans. Graph. 25, 3 (July 2006), 569-578. 1 – reference: Harary G., Tal A., Grinspun E.: Context-based coherent surface completion. ACM Trans. Graph. 33, 1 (Feb. 2014), 5:1-5:12. 2 – reference: Chen Y., Medioni G.: Object modelling by registration of multiple range images. Image and vision computing 10, 3 (1992), 145-155. 5 – reference: Zabrodsky H., Peleg S., Avnir D.: Symmetry as a continuous feature. Pattern Analysis and Machine Intelligence, IEEE Transactions on 17, 12 (Dec 1995), 1154-1166. 2 – reference: Li H., Sumner R.W., Pauly M.: Global correspondence optimization for non-rigid registration of depth scans. Computer Graphics Forum (Proc. SGP'08) 27, 5 (July 2008). 5 – reference: Mellado N., Aiger D., Mitra N.J.: Super 4pcs fast global pointcloud registration via smart indexing. Computer Graphics Forum 33, 5 (2014), 205-215. 3 – reference: Eggert D.W., Lorusso A., Fisher R.B.: Estimating 3-D rigid body transformations: a comparison of four major algorithms. Machine Vision and Applications 9, 5-6 (1997), 272-290. 3 – reference: Zheng Q., Sharf A., Wan G., Li Y., Mitra N.J., Cohen-Or D., Chen B.: Non-local scan consolidation for 3d urban scenes. ACM Trans. Graph. 29, 4 (July 2010), 94:1-94:9. 2 – reference: Huang H., Gong M., Cohen-Or D., Ouyang Y., Tan F., Zhang H.: Field-guided registration for feature-conforming shape composition. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2012) 31 (2012), 171:1-171:11. 2 – reference: Xu K., Zhang H., Tagliasacchi A., Liu L., Li G., Meng M., Xiong Y.: Partial Intrinsic Reflectional Symmetry of 3D Shapes. ACM Trans. Graph. 28, 5 (2009), 138:1- 138:10. 2 – reference: Guy E., Thiery J.-M., Boubekeur T.: Simselect: similarity-based selection for 3d surfaces. Computer Graphics Forum (Proc. EUROGRAPHICS 2014) 33, 2 (2014), 165. 8 – reference: Umeyama S.: Least-squares estimation of transformation parameters between two point patterns. IEEE Transactions on pattern analysis and machine intelligence 13, 4 (1991), 376-380. 3 – reference: Korman S., Litman R., Avidan S., Bronstein A.: Probably approximately symmetric: Fast rigid symmetry detection with global guarantees. Computer Graphics Forum 34, 1 (2015), 2-13. 2 – start-page: 249 year: 2013 end-page: 256 – volume: 28 start-page: 175:1 issue: 5 year: 2009 end-page: 175:10 article-title: Robust single‐view geometry and motion reconstruction publication-title: ACM Trans. Graph – volume: 9 start-page: 5 year: 1997 end-page: 6 article-title: Estimating 3‐D rigid body transformations: a comparison of four major algorithms publication-title: Machine Vision and Applications – year: 2005 – volume: 29 start-page: 103:1 issue: 4 year: 2010 end-page: 103:12 article-title: Symmetry Factored Embedding and Distance publication-title: ACM Trans. Graph – volume: 29 start-page: 94:1 issue: 4 year: 2010 end-page: 94:9 article-title: Non‐local scan consolidation for 3d urban scenes publication-title: ACM Trans. Graph – volume: 27 issue: 5 year: 2008 article-title: Global correspondence optimization for non‐rigid registration of depth scans publication-title: Computer Graphics Forum (Proc. SGP'08) – start-page: 1 year: 2014 end-page: 26 – volume: 33 start-page: 45 issue: 5 year: 2014 end-page: 54 article-title: Feature‐preserving surface completion using four points publication-title: Computer Graphics Forum – volume: 17 start-page: 1154 issue: 12 year: 1995 end-page: 1166 article-title: Symmetry as a continuous feature publication-title: Pattern Analysis and Machine Intelligence, IEEE Transactions on – volume: 25 start-page: 560 issue: 3 year: 2006 end-page: 568 article-title: Partial and Approximate Symmetry Detection for 3D Geometry publication-title: ACM Trans. Graph – volume: 28 issue: 5 year: 2009 article-title: A Concise and Provably Informative Multi‐Scale Signature Based on Heat Diffusion publication-title: Comput. Graph. Forum – start-page: 115 year: 2004 end-page: 123 – volume: 28 start-page: 138:1 issue: 5 year: 2009 end-page: 138:10 article-title: Partial Intrinsic Reflectional Symmetry of 3D Shapes publication-title: ACM Trans. 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| SubjectTerms | 3-D graphics Algorithms and object representations Approximation Categories and Subject Descriptors (according to ACM CCS) Computer science Cultural heritage Cultural resources Errors Handles I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations Image processing systems Maximization Optimization techniques solid Studies surface Symmetry Three dimensional |
| Title | Object Completion using k-Sparse Optimization |
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