Abstract
We propose to employ scale spaces of mathematical morphology to hierarchically simplify fracture surfaces of complementarily fitting archaeological fragments. This representation preserves complementarity and is insensitive to different kinds of abrasion affecting the exact fitting of the original fragments. We present a pipeline for morphologically simplifying fracture surfaces, based on their Lipschitz nature; its core is a new embedding of fracture surfaces to simultaneously compute both closing and opening morphological operations, using distance transforms.
This research was funded by the GRAVITATE project under EU2020-REFLECTIVE-7-2014 Research and Innovation Action, grant no. 665155.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
van den Boomgaard, R., Dorst, L.: The morphological equivalent of Gaussian scale space. In: Proceedings of Gaussian Scale-Space Theory, pp. 203–220. Kluwer (1997)
Bosworth, J.H., Acton, S.T.: Morphological scale-space in image processing. Digit. Signal Process. 13(2), 338–367 (2003)
Calderon, S., Boubekeur, T.: Point morphology. ACM Trans. Graph. 33(4), 1–13 (2014)
Chen, M.H., Yan, P.-F.: A multiscaling approach based on morphological filtering. IEEE Trans. PAMI 11(7), 694–700 (1989)
Crane, K., de Goes, F., Desbrun, M., Schröder, P.: Digital geometry processing with discrete exterior calculus. In: ACM SIGGRAPH 2013 Courses, SIGGRAPH 2013. ACM, New York (2013)
ElNaghy, H., Dorst, L.: Geometry based faceting of 3D digitized archaeological fragments. In: 2017 IEEE ICCV Workshops, pp. 2934–2942 (2017)
Fitzgibbon, A.: Robust registration of 2D and 3D point sets. Image Vis. Comput. 21, 1145–1153 (2003)
Funkhouser, T., et al.: Learning how to match fresco fragments. J. Comput. Cult. Herit. 4(2), 1–13 (2011)
Hachenberger, P.: 3D Minkowski sum of polyhedra. In: CGAL User and Reference Manual. CGAL Editorial Board, 4.11.1 edn. (2018)
Huang, Q.X., Flöry, S., Gelfand, N., Hofer, M., Pottmann, H.: Reassembling fractured objects by geometric matching. In: ACM SIGGRAPH Papers, SIGGRAPH 2006, pp. 569–578. ACM, New York (2006)
Jackway, P.T., Deriche, M.: Scale-space properties of the multiscale morphological dilation-erosion. IEEE Trans. PAMI 18(1), 38–51 (1996)
Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: Proceedings of the Fourth Eurographics Symposium on Geometry Processing, SGP 2006, pp. 61–70. Eurographics Association, Aire-la-Ville (2006)
Maurer, C.R., Qi, R., Raghavan, V.: A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. PAMI 25(2), 265–270 (2003)
McBride, J.C., Kimia, B.B.: Archaeological fragment reconstruction using curve-matching. In: IEEE CVPR Workshops, vol. 1, p. 3 (2003)
Palmas, G., Pietroni, N., Cignoni, P., Scopigno, R.: A computer-assisted constraint-based system for assembling fragmented objects. In: 2013 Digital Heritage International Congress (DigitalHeritage), vol. 1, pp. 529–536 (2013)
Salinas, D., Lafarge, F., Alliez, P.: Structure-aware mesh decimation. Comput. Graph. Forum 34, 211–227 (2015)
Serra, J.C.: Lipschitz lattices and numerical morphology. In: SPIE Conference on Image Algebra and Morphological Image Processing II, vol. 1568, pp. 54–56 (1991)
Sethian, J.: Fast marching methods and level set methods for propagating interfaces. In: Computational Fluid Dynamics. 29th Annual Lecture Series (1998)
Toler-Franklin, C., Brown, B., Weyrich, T., Funkhouser, T., Rusinkiewicz, S.: Multi-feature matching of fresco fragments. ACM Trans. Graph. 29(6), 1–12 (2010)
Wu, Z., et al.: 3D shapenets: a deep representation for volumetric shapes. In: IEEE CVPR, pp. 1912–1920 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
ElNaghy, H., Dorst, L. (2019). Complementarity-Preserving Fracture Morphology for Archaeological Fragments. In: Burgeth, B., Kleefeld, A., Naegel, B., Passat, N., Perret, B. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2019. Lecture Notes in Computer Science(), vol 11564. Springer, Cham. https://doi.org/10.1007/978-3-030-20867-7_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-20867-7_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20866-0
Online ISBN: 978-3-030-20867-7
eBook Packages: Computer ScienceComputer Science (R0)