Complementarity-Preserving Fracture Morphology for Archaeological Fragments

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.

[1]  Tim Weyrich,et al.  Multi-feature matching of fresco fragments , 2010, ACM Trans. Graph..

[2]  J. Sethian.  Advances in fast marching and level set methods for propagating interfaces , 1999 .

[3]  Scott T. Acton,et al.  Morphological scale-space in image processing , 2003, Digit. Signal Process..

[4]  Keenan Crane,et al.  Digital geometry processing with discrete exterior calculus , 2013, SIGGRAPH '13.

[5]  Andrew W. Fitzgibbon,et al.  Robust Registration of 2D and 3D Point Sets , 2003, BMVC.

[6]  Jianxiong Xiao,et al.  3D ShapeNets: A deep representation for volumetric shapes , 2014, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[7]  Tim Weyrich,et al.  Learning how to match fresco fragments , 2011, JOCCH.

[8]  Leo Dorst,et al.  The Morphological Equivalent of Gaussian Scale-Space , 1997, Gaussian Scale-Space Theory.

[9]  James A. Sethian,et al.  Fast marching methods and level set methods for propagating interfaces , 1998 .

[10]  Michael M. Kazhdan,et al.  Poisson surface reconstruction , 2006, SGP '06.

[11]  Hans-Peter Seidel,et al.  Animating deformable objects using sparse spacetime constraints , 2014, ACM Trans. Graph..

[12]  Mohamed A. Deriche,et al.  Scale-Space Properties of the Multiscale Morphological Dilation-Erosion , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Paolo Cignoni,et al.  A computer-assisted constraint-based system for assembling fragmented objects , 2013, 2013 Digital Heritage International Congress (DigitalHeritage).

[14]  Florent Lafarge,et al.  Structure‐Aware Mesh Decimation , 2015, Comput. Graph. Forum.

[15]  Calvin R. Maurer,et al.  A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Benjamin B. Kimia,et al.  Archaeological Fragment Reconstruction Using Curve-Matching , 2003, 2003 Conference on Computer Vision and Pattern Recognition Workshop.

[17]  Leo Dorst,et al.  Geometry Based Faceting of 3D Digitized Archaeological Fragments , 2017, 2017 IEEE International Conference on Computer Vision Workshops (ICCVW).

[18]  Jean Serra.  Lipschitz lattices and numerical morphology , 1991, Optics & Photonics.

[19]  Helmut Pottmann,et al.  Reassembling fractured objects by geometric matching , 2006, ACM Trans. Graph..

[20]  M.-H. Chen,et al.  A Multiscanning Approach Based on Morphological Filtering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  Hans-Peter Seidel,et al.  MovieReshape: tracking and reshaping of humans in videos , 2010, SIGGRAPH 2010.

[22]  Tamy Boubekeur,et al.  Point morphology , 2014, ACM Trans. Graph..