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Bharath, Karthik; Kurtek, Sebastian

Analysis of shape data: from landmarks to elastic curves. (English) Zbl 07909792

Wiley Interdiscip. Rev., WIREs Comput. Stat. 12, No. 3, Article ID e1495, 17 p. (2020).

Cited in 2 Documents

MSC:

62-08 Computational methods for problems pertaining to statistics

Keywords:

elastic curves; landmarks; non-Euclidean space; shape statistics
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Full Text: DOI

References:

[1] Almhdie, A., Léger, C., Deriche, M., & Lédée, R. (2007). 3D registration using a new implementation of the ICP algorithm based on a comprehensive lookup matrix: Application to medical imaging. Pattern Recognition Letters, 28(12), 1523-1533.
[2] Bardelli, E., & Mennucci, A. C. G. (2017). Probability measures on infinite‐dimensional Stiefel manifolds. Journal of Geometric Mechanics, 9, 291-316. · Zbl 1373.60022
[3] Bauer, M., Bruveris, M., Charon, N., & Moller‐Andersen, J. (2019). A relaxed approach for curve matching with elastic metrics. ESAIM: Control, Optimisation and Calculus of Variations, 25 (in press). · Zbl 07194611
[4] Bauer, M., Eslitzbichler, M., & Grasmair, M. (2017). Landmark‐guided elastic shape analysis of human character motions. Inverse Problems & Imaging, 11(4), 601-621. · Zbl 1368.65028
[5] Beg, M., Miller, M., Trouvé, A., & Younes, L. (2005). Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision, 61(2), 139-157. · Zbl 1477.68459
[6] Bharath, K., & Kurtek, S. (2019). Distribution on warp maps for alignment of closed and open curves. Journal of the American Statistical Association, 1708, 04891.
[7] Bharath, K., Kurtek, S., Rao, A., & Baladandayuthapani, V. (2018). Radiologic image‐based statistical shape analysis of brain tumours. Journal of the Royal Statistical Society, Series C, 67(5), 1357-1378.
[8] Bhattacharya, A. & Bhattacharya, R. (2012). Nonparametric inference on manifolds: With applications to shape spaces. IMS monographs. · Zbl 1273.62014
[9] Bookstein, F. L. (1984). A statistical method for biological shape comparisons. Journal of Theoretical Biology, 107(3), 475-520.
[10] Bookstein, F. L. (1992). Morphometric tools for landmark data: Geometry and biology. Cambridge, MA: Cambridge University Press. · Zbl 0770.92001
[11] Bookstein, F. L. (1996). Biometrics, biomathematics and the morphometric synthesis. Bulletin of Mathematical Biology, 58(2), 313-365. · Zbl 0855.92002
[12] Boothby, W. M. (1975). An introduction to differentiable manifolds and Riemannian geometry. In Pure and Applied Mathematics. Astermdam: Elsevier Science. · Zbl 0333.53001
[13] Bouix, S., Pruessner, J. C., Collins, D. L., & Siddiqi, K. (2001). Hippocampal shape analysis using medial surfaces. NeuroImage, 25, 1077-1089. · Zbl 1041.68567
[14] Charon, N., & Truové, A. (2013). The varifold representation of nonoriented shapes for diffeomorphic registration. SIAM Journal of Imaging Science, 6(4), 2547-2580. · Zbl 1279.68313
[15] Cheng, W., Dryden, I. L., & Huang, X. (2016). Bayesian registration of functions and curves. Bayesian Analysis, 11(2), 447-475. · Zbl 1357.62151
[16] Cho, M.‐H., Asiaee, A., & Kurtek, S. (2019). Elastic statistical shape analysis of biological structures with case studies: A tutorial. Bulletin of Mathematical Biology, 81(7), 2052-2073. · Zbl 1417.92016
[17] Crawford, L., Monod, A., Chen, A. X., Mukherjee, S., & Rabadán, R. (2019). Functional data analysis using a topological summary statistic: The smooth Euler characteristic transform. arXiv:1611.06818v4.
[18] doCarmo, M. P. (1992). Riemannian geometry. Basel: Birkhäuser.
[19] Dryden, I. L., & Mardia, K. V. (1993). Multivariate shape analysis. Sankhya, Series A, 55(3), 460-480. · Zbl 0806.62050
[20] Dryden, I. L., & Mardia, K. V. (2016). Statistical shape analysis: With applications in R (2nd ed.). New York, NY: Wiley. · Zbl 1381.62003
[21] Durrleman, S., Pennec, X., Trouvé, A., & Ayache, N. (2009). Statistical models of sets of curves and surfaces based on currents. Medical Image Analysis, 13(5), 793-808.
[22] Fletcher, P. T., Lu, C., Pizer, S. M., & Joshi, S. C. (2004). Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Transactions on Medical Imaging, 23(8), 995-1005.
[23] Fletcher, P. T., Venkatasubramanian, S., & Joshi, S. (2009). The geometric median on Riemannian manifolds with application to robust atlas estimation. NeuroImage, 45(1), S143-S152.
[24] Glaunès, J., Qiu, A., Miller, M. I., & Younes, L. (2008). Large deformation diffeomorphic metric curve mapping. International Journal of Computer Vision, 80(3), 317-336. · Zbl 1477.68471
[25] Glaunès, J., Vaillant, M., & Miller, M. I. (2004). Landmark matching via large deformation diffeomorphisms on the sphere. Journal of Mathematical Imaging and Vision, 20(1), 179-200. · Zbl 1366.94052
[26] Gorczowski, K., Styner, M., Jeong, J. Y., Marron, J. S., Piven, J., Hazlett, H. C., … Gerig, G. (2010). Multi‐object analysis of volume, pose, and shape using statistical discrimination. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(4), 652-666.
[27] Grenander, U., & Miller, M. I. (1998). Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics, LVI, 4, 617-694. · Zbl 0952.92016
[28] Humeau‐Heurtier, A. (2019). Texture feature extraction methods: A survey. IEEE Access, 7, 8975-9000.
[29] Jermyn, I. H., Kurtek, S., Laga, H., & Srivastava, A. (2017). Elastic shape analysis of three‐dimensional objects. San Rafael, CA: Morgan & Claypool Publishers.
[30] Joshi, S. C., & Miller, M. I. (2000). Landmark matching via large deformation diffeomorphisms. IEEE Transactions on Image Processing, 9(8), 1357-1370. · Zbl 0965.37065
[31] Joshi, S. C., Miller, M. I., & Grenander, U. (1997). On the geometry and shape of brain sub‐manifolds. Pattern Recognition and Artificial Intelligence, 11, 1317-1343.
[32] Joshi, S. H., Klassen, E., Srivastava, A., & Jermyn, I. H. (2007). A novel representation for Riemannian analysis of elastic curves in ℝ^n. In IEEE Conference on Computer Vision and Pattern Recognition (pp. 1-7). New York, NY: IEEE.
[33] Joshi, S. H., & Srivastava, A. (2009). Intrinsic Bayesian active contours for extraction of object boundaries in images. International Journal of Computer Vision, 81(3), 331-355. · Zbl 1477.68379
[34] Kaziska, D., & Srivastava, A. (2006). Cyclostationary processes on shape spaces for gait‐based recognition. In European Conference on Computer Vision (Vol. 3952, pp. 442-453). Gratz, Austria: LNCS.
[35] Kendall, D. G. (1984). Shape manifolds, procrustean metrics and complex projective spaces. Bulletin of London Mathematical Society, 16, 81-121. · Zbl 0579.62100
[36] Klassen, E., & Srivastava, A. (2006). Geodesics between 3D closed curves using path‐straightening. In European Conference on Computer Vision (pp. 95-106). Gratz, Austria: LNCS.
[37] Klassen, E., Srivastava, A., Mio, W., & Joshi, S. H. (2004). Analysis of planar shapes using geodesic paths on shape spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(3), 372-383.
[38] Kurtek, S. (2017). A geometric approach to pairwise Bayesian alignment of functional data using importance sampling. Electronic Journal of Statistics, 11(1), 502-531. · Zbl 1362.62055
[39] Kurtek, S., Klassen, E., Ding, Z., Jacobson, S. W., Jacobson, J. L., Avison, M. J., & Srivastava, A. (2011). Parameterization‐invariant shape comparisons of anatomical surfaces. IEEE Transactions on Medical Imaging, 30(3), 849-858.
[40] Kurtek, S., & Needham, T. (2018). Simplifying transforms for general elastic metrics on the space of plane curves. arXiv:1803.10894v1.
[41] Kurtek, S., Srivastava, A., Klassen, E., & Ding, Z. (2012). Statistical modeling of curves using shapes and related features. Journal of the American Statistical Association, 107(499), 1152-1165. · Zbl 1443.62389
[42] Kurtek, S., Su, J., Grimm, C., Vaughan, M., Sowell, R., & Srivastava, A. (2013). Statistical analysis of manual segmentations of structures in medical images. Computer Vision and Image Understanding, 117, 1036-1050.
[43] Laga, H., Kurtek, S., Srivastava, A., & Miklavcic, S. J. (2014). Landmark‐free statistical analysis of the shape of plant leaves. Journal of Theoretical Biology, 363, 41-52. · Zbl 1309.92015
[44] Lang, S. (2001). Fundamentals of differential geometry. In Graduate texts in mathematics. Berlin: Springer. · Zbl 0995.53001
[45] Le, H. (2001). Locating Frechet means with application to shape spaces. Advances in Applied Probability, 33(2), 324-338. · Zbl 0990.60008
[46] Lu, Y., Herbei, R., & Kurtek, S. (2017). Bayesian registration of functions with a Gaussian process prior. Journal of Computational and Graphical Statistics, 26, 894-904.
[47] Malladi, R., Sethian, J. A., & Vemuri, B. C. (1996). A fast level set based algorithm for topology‐independent shape modeling. Journal of Mathematical Imaging and Vision, 6, 269-290. · Zbl 1490.68251
[48] Mardia, K. V., & Dryden, I. L. (1989). The statistical analysis of shape data. Biometrika, 76(2), 271-281. · Zbl 0666.62056
[49] Materka, A. (2004). Texture analysis methodologies for magnetic resonance imaging. Dialogues in Clinical Neuroscience, 6(2), 243-250.
[50] Miller, M. I., & Younes, L. (2001). Group actions, homeomorphisms, and matching: A general framework. International Journal of Computer Vision, 41(1-2), 61-84. · Zbl 1012.68714
[51] Mio, W., Srivastava, A., & Joshi, S. H. (2007). On shape of plane elastic curves. International Journal of Computer Vision, 73(3), 307-324. · Zbl 1477.68398
[52] O’Higgins, P., & Dryden, I. L. (1992). Studies of craniofacial development and evolution. Archaeology and Physical Anthropology in Oceania, 27, 105-112.
[53] Pennec, X. (2006). Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. Journal of Mathematical Imaging and Vision, 25(1), 127-154. · Zbl 1478.94072
[54] Robinson, D. T. (2012). Functional data analysis and partial shape matching in the square root velocity framework (PhD thesis). Florida State University.
[55] Samir, C., Kurtek, S., Srivastava, A., & Canis, M. (2014). Elastic shape analysis of cylindrical surfaces for 3D/2D registration in endometrial tissue characterization. IEEE Transactions on Medical Imaging, 33(5), 1035-1043.
[56] Samir, C., Srivastava, A., Daoudi, M., & Klassen, E. (2009). An intrinsic framework for analysis of facial surfaces. International Journal of Computer Vision, 82(1), 80-95.
[57] Siddiqi, K., & Pizer, S. (2008). Medial representations: Mathematics, algorithms and applications. Berlin: Springer. · Zbl 1151.00014
[58] Small, C. G. (1996). The statistical theory of shape. Berlin: Springer. · Zbl 0859.62087
[59] Srivastava, A., Klassen, E., Joshi, S. H., & Jermyn, I. H. (2011). Shape analysis of elastic curves in Euclidean spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33, 1415-1428.
[60] Srivastava, A., & Klassen, E. P. (2016). Functional and shape data analysis. Berlin: Springer‐Verlag. · Zbl 1376.62003
[61] Srivastava, A., Samir, C., Joshi, S. H., & Daoudi, M. (2009). Elastic shape models for face analysis using curvilinear coordinates. Journal of Mathematical Imaging and Vision, 33(2), 253-265. · Zbl 1523.68164
[62] Strait, J., Chkrebtii, O., & Kurtek, S. (2019). Automatic detection and uncertainty quantification of landmarks on elastic curves. Journal of the American Statistical Association, 114, 1002-1017. https://doi.org/10.1080/01621459.2018.1527224 · Zbl 1423.68401 · doi:10.1080/01621459.2018.1527224
[63] Strait, J., Kurtek, S., Bartha, E., & MacEachern, S. N. (2017). Landmark‐constrained elastic shape analysis of planar curves. Journal of the American Statistical Association, 112(518), 521-533.
[64] Su, J., Kurtek, S., Klassen, E., & Srivastava, A. (2014). Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance. Annals of Applied Statistics, 8(1), 530-552. · Zbl 1454.62554
[65] Thompson, D. (1917). On growth and form. Cambridge, MA: Cambridge University Press.
[66] Vaillant, M., & Glaunès, J. (2005). Surface matching via currents. In Information processing in medical imaging (pp. 381-392). Berlin, Heidelberg: Springer Berlin Heidelberg.
[67] Younes, L. (1998). Computable elastic distance between shapes. SIAM Journal of Applied Mathematics, 58(2), 565-586. · Zbl 0907.68158
[68] Younes, L. (2018). Elastic distance between curves under the metamorphosis viewpoint. arXiv:1804.10155.
[69] Younes, L., Michor, P. W., Shah, J., Mumford, D., & Lincei, R. (2008). A metric on shape space with explicit geodesics. Matematica E Applicazioni, 19(1), 25-57. · Zbl 1142.58013
[70] Zahn, C. T., & Roskies, R. Z. (1972). Fourier descriptors for plane closed curves. IEEE Transactions on Computers, 21(3), 269-281. · Zbl 0231.68042
[71] Zhang, M., & Fletcher, P. T. (2013). Probabilistic principal geodesic analysis. In Neural information processing systems (pp. 1178-1186).
[72] Zhang, M., & Fletcher, P. T. (2014). Bayesian principal geodesic analysis in diffeomorphic image registration. In Medical image computing and computer‐assisted intervention (pp. 121-128). Springer International Publishing.
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