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Spline Interpolation on Shape Space

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Regression and Fitting on Manifold-valued Data
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Abstract

For many applications in several branches of science, involving medical imaging, computer vision, Human Biometrics and Nanomanufacturing, it is desirable to be able to characterize objects for detection, recognition and prediction of their behavior at unobserved times or in the future.

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References

  1. Grenander, U. and Miller, M.I. and Klassen, E. and Le, H. and Srivastava, A.: Computational anatomy: an emerging discipline, Quarterly of applied Mathematics, 4, 617-694, 1998.

    MathSciNet  Google Scholar 

  2. Kendall, D.G: Shape manifolds, Procrustean metrics and complex projective spaces, Bulletin of the London Mathematical Society, 16, 81–121, 1984.

    Google Scholar 

  3. Le, H. and Kume, A.: Detection of Shape changes in biological features, Journal of Microscopy, 200, 140–147, 2000.

    Google Scholar 

  4. Kenobi, K. and Dryden, I. L. and Le, H.: Shape curves and geodesic modelling, Biometrika, 97, 567–584, 2010.

    MathSciNet  Google Scholar 

  5. Kim, K.R and Dryden, I.L and Le, H.: Smoothing splines on Riemannian manifolds, with applications to 3D shape space, 2018.

    Google Scholar 

  6. Jupp, P. E. and Kent, J. T.: Fitting smooth path to spherical data, Journal of Applied Statistics, 36, 34–46, 1987.

    MathSciNet  Google Scholar 

  7. Srivastava, A. and Klassen, E. and Joshi, S. H. and Jermyn, I. H. : Shape Analysis of Elastic Curves in Euclidean Spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 33, 1415–1428, 2011.

    Google Scholar 

  8. Joshi, S.H. and Klassen, E. and Srivastava, A. and Jermyn, I.: Removing shape-preserving transformations in square-root elastic (SRE) framework for shape analysis of curves, 387–398, EMMCVPR, 2007.

    Google Scholar 

  9. Klassen, E. and Srivastava, A. and Mio, W. and Joshi, S.H: Analysis of planar shapes using geodesic paths on shape spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 3 (26), 372–383, 2004.

    Google Scholar 

  10. Glaunes, J. and Qiu, A. and Miller, M. and Younes, L.: Large deformation diffeomorphic metric curve mapping, International Journal of Computer Vision, 80, 317–336, 2008.

    Google Scholar 

  11. Michor, P. W. and Mumford, D.: Riemannian Geometries on Spaces of Plane Curves, Journal of the European Mathematical Society, 8, 1–48, 2006.

    MathSciNet  Google Scholar 

  12. Younes, L. :Computable elastic distance between shapes, SIAM Journal of Applied Mathematics, 58 (2), 565–586, 1998.

    MathSciNet  Google Scholar 

  13. Hohmeyer, M. and Barsky, B.: Skinning rational B-spline curves to construct an interpolatory surface, Comput. Vision. Gruph. and Image Process. Graph. Mod and Image Process, 53(6), 511–521, 1991.

    Google Scholar 

  14. Hoschek, J.: Automatic conversion of spline curves, Comput Aided Geom, 4, 171–181, 1991.

    Google Scholar 

  15. Patrikalakis, N.M.: Approximate conversion of rational splines, Comput Aided Geom, 4, 155–165, 1989.

    MathSciNet  Google Scholar 

  16. Piegl, L. and Tiller, W.: Surface skinning revisited, The Visual Computer, 18, 273–283, 2002.

    Google Scholar 

  17. Woodward, C.D.: Skinning techniques for interactive B-spline surface interpolation, Computer-Aided Design, 20(8), 441–451, 1988.

    Google Scholar 

  18. Keppel, E.: Approximating complex surface by triangulation of contour lines, IBM Journal of Research and Development, 19, 2–11, 1975.

    MathSciNet  Google Scholar 

  19. Fuchs, H. and Kedem, Z.M. and Uselton, S.P.: Optimal surface reconstruction from planar contours, Communications of the ACM, 20(10), 1977.

    Google Scholar 

  20. Boissonnat, J.D.: Shape reconstruction from planar cross sections, Computer Vision, Graphics, and Image Processing, 44(1), 1–29, 1988.

    MathSciNet  Google Scholar 

  21. Barequet, G. and Sharir, M.: Piecewise-linear interpolation between polygonal slices, Computer Vision and Image Understanding, 63, 251–272, 1996.

    Google Scholar 

  22. Salvatore C., and Ardelio G., and Giulio G., and Alfredo S.: Surface Reconstruction from Scattered Point via RBF Interpolation on GPU, CoRR, abs/1305.5179, 2013.

    Google Scholar 

  23. Zhao, H.K and Osher, S. and Fedkiw, R. :Fast surface reconstruction using the level set method, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision, 194–201, 2001.

    Google Scholar 

  24. Rouhani, M. and Sappa, A.D.: Relaxing the 3L algorithm for an accurate implicit polynomial fitting, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 3066–3072, 2010.

    Google Scholar 

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Correspondence to Chafik Samir .

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Adouani, I., Samir, C. (2024). Spline Interpolation on Shape Space. In: Regression and Fitting on Manifold-valued Data. Springer, Cham. https://doi.org/10.1007/978-3-031-61712-6_8

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