Abstract
Important new developments have appeared since the most recent direct survey on shape correspondence published almost a decade ago. Our survey covers the period from 2011, their stopping point, to 2019, inclusive. The goal is to present the recent updates on correspondence computation between surfaces or point clouds embedded in 3D. Two tables summarizing and classifying the prominent, to our knowledge, papers of this period, and a large section devoted to their discussion lay down the foundation of our survey. The discussion is carried out in chronological order to reveal the distribution of various types of correspondence methods per year. We also explain our classification criteria along with the most basic solution examples. We finish with conclusions and future research directions.
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Aflalo, Y., Dubrovina, A., Kimmel, R.: Spectral generalized multi-dimensional scaling. Int. J. Comput. Vis. 118(3), 380–392 (2016)
Aigerman, N., Kovalsky, S., Lipman, Y.: Spherical orbifold Tutte embeddings. ACM Trans. Graph. (Proc. SIGGRAPH) 36(4), 90 (2017)
Aigerman, N., Lipman, Y.: Orbifold Tutte embeddings. ACM Trans. Graph. 34(6), 190–1 (2015)
Aigerman, N., Lipman, Y.: Hyperbolic orbifold Tutte embeddings. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 35(6), 217 (2016)
Aigerman, N., Poranne, R., Lipman, Y.: Lifted bijections for low distortion surface mappings. ACM Trans. Graph. 33(4), 69 (2014)
Aigerman, N., Poranne, R., Lipman, Y.: Seamless surface mappings. ACM Trans. Graph. 34(4), 72 (2015)
Alhashim, I., Li, H., Xu, K., Cao, J., Ma, R., Zhang, H.: Topology-varying 3D shape creation via structural blending. ACM Trans. Graph. (TOG) 33(4), 158 (2014)
Alhashim, I., Xu, K., Zhuang, Y., Cao, J., Simari, P., Zhang, H.: Deformation-driven topology-varying 3D shape correspondence. ACM Trans. Graph. (TOG) 34(6), 236 (2015)
Azencot, O., Dubrovina, A., Guibas, L.: Consistent shape matching via coupled optimization. Comput. Graph. Forum 38(5), 13–25 (2019)
Azencot, O., Vantzos, O., Ben-Chen, M.: Advection-based function matching on surfaces. Comput. Graph. Forum 35(5), 55–64 (2016)
Biasotti, S., Cerri, A., Bronstein, A., Bronstein, M.: Recent trends, applications, and perspectives in 3D shape similarity assessment. Comput. Graph. Forum 35(6), 87–119 (2016)
Biasotti, S., Cerri, A., Bronstein, A.M., Bronstein, M.M.: Quantifying 3D shape similarity using maps: recent trends, applications and perspectives. Eurographics (State of the Art Reports), pp. 135–159 (2014)
Boscaini, D., Masci, J., Rodolà, E., Bronstein, M.: Learning shape correspondence with anisotropic convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 3189–3197 (2016)
Bronstein, M.M., Bruna, J., LeCun, Y., Szlam, A., Vandergheynst, P.: Geometric deep learning: going beyond euclidean data. IEEE Signal Process. Mag. 34(4), 18–42 (2017)
Brunton, A., Wand, M., Wuhrer, S., Seidel, H.-P., Weinkauf, T.: A low-dimensional representation for robust partial isometric correspondences computation. Graph. Models 76(2), 70–85 (2014)
Carrière, M., Oudot, S.Y., Ovsjanikov, M.: Stable topological signatures for points on 3D shapes. Comput. Graph. Forum 34(5), 1–12 (2015)
Chen, Q., Koltun, V.: Robust nonrigid registration by convex optimization. In: Proceedings of International Conference on Computer Vision, pp. 2039–2047 (2015)
Corman, E., Ovsjanikov, M., Chambolle, A.: Supervised descriptor learning for non-rigid shape matching. In: European Conference on Computer Vision, pp. 283–298 (2014)
Corman, E., Ovsjanikov, M., Chambolle, A.: Continuous matching via vector field flow. Comput. Graph. Forum 34(5), 129–139 (2015)
Cosmo, L., Panine, M., Rampini, A., Ovsjanikov, M., Bronstein, M.M., Rodolà, E.: Isospectralization, or how to hear shape, style, and correspondence. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7529–7538 (2019)
Cosmo, L., Rodolà, E., Albarelli, A., Mémoli, F., Cremers, D.: Consistent partial matching of shape collections via sparse modeling. Comput. Graph. Forum 36(1), 209–221 (2017)
Denitto, M., Melzi, S., Bicego, M., Castellani, U., Farinelli, A., Figueiredo, M.A., Kleiman, Y., Ovsjanikov, M.: Region-based correspondence between 3d shapes via spatially smooth biclustering. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 4260–4269 (2017)
Dubrovina, A., Kimmel, R.: Approximately isometric shape correspondence by matching pointwise spectral features and global geodesic structures. Adv. Adapt. Data Anal. (AADA) 3, 203–228 (2011)
Dyke, R., Lai, Y.-K., Rosin, P., Tam, G.K.: Non-rigid registration under anisotropic deformations. Comput. Aided Geom. Des. 71, 142–156 (2019)
Dyke, R., Stride, C., Lai, Y., Rosin, P., Aubry, M., Boyarski, A., Bronstein, A., Bronstein, M., Cremers, D., Fisher, M., Groueix, T., Guo, D., Kim, V., Kimmel, R., Lahner, Z., Li, K., Litany, O., Remez, T., Rodolà, E., Russel, B., Sahillioğlu, Y., Slossberg, R., Tam, G., Vestner, M., Wu, Z., Yang, J.: Shape correspondence with isometric and non-isometric deformations. In: Eurographics Workshop on 3D Object Retrieval (2019)
Eisenberger, M., Lahner, Z., Cremers, D.: Divergence-free shape correspondence by deformation. Comput. Graph. Forum 38(5), 1–12 (2019)
Ezuz, D., Ben-Chen, M.: Deblurring and denoising of maps between shapes. Comput. Graph. Forum 36(5), 165–174 (2017)
Ezuz, D., Heeren, B., Azencot, O., Rumpf, M., Ben-Chen, M.: Elastic correspondence between triangle meshes. Comput. Graph. Forum 38(2), 121–134 (2019)
Ezuz, D., Solomon, J., Ben-Chen, M.: Reversible harmonic maps between discrete surfaces. ACM Trans. Graph. 38(2), 15 (2019)
Ezuz, D., Solomon, J., Kim, V., Ben-Chen, M.: Gwcnn: a metric alignment layer for deep shape analysis. Comput. Graph. Forum (Proc. SGP) 36(5), 49–57 (2017)
Fish, N., van Kaick, O., Bermano, A., Cohen-Or, D.: Structure-oriented networks of shape collections. ACM Trans. Graph. 35(6), 171 (2016)
Ganapathi-Subramanian, V., Thibert, B., Ovsjanikov, M., Guibas, L.: Stable region correspondences between non-isometric shapes. Comput. Graph. Forum 35(5), 121–133 (2016)
Gehre, A., Bronstein, M., Kobbelt, L., Solomon, J.: Interactive curve constrained functional maps. Comput. Graph. Forum 37(5), 1–12 (2018)
Groueix, T., Fisher, M., Kim, V.G., Russell, B., Aubry, M.: Unsupervised cycle-consistent deformation for shape matching. Comput. Graph. Forum 38(5), 123–133 (2019)
Groueix, T., Fisher, M., Kim, V.G., Russell, B.C., Aubry, M.: 3D-coded: 3D correspondences by deep deformation. In: Proceedings of the European Conference on Computer Vision (ECCV), pp. 230–246 (2018)
Guo, H., Zhu, D., Mordohai, P.: Correspondence estimation for non-rigid point clouds with automatic part discovery. Vis. Comput. 32(12), 1511–1524 (2016)
Halimi, O., Litany, O., Rodola, E., Bronstein, A.M., Kimmel, R.: Unsupervised learning of dense shape correspondence. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4370–4379 (2019)
Hu, R., Savva, M., van Kaick, O.: Functionality representations and applications for shape analysis. Comput. Graph. Forum 37(2), 603–624 (2018)
Huang, Q., Guibas, L.: Consistent shape maps via semidefinite programming. Comput. Graph. Forum (Proc. SGP) 32(5), 177–186 (2013)
Huang, Q., Wang, F., Guibas, L.: Functional map networks for analyzing and exploring large shape collections. ACM Trans. Graph. (TOG) 33(4), 36 (2014)
Huang, Q., Zhang, G., Gao, L., Hu, S., Bustcher, A., Guibas, L.: An optimization approach for extracting and encoding consistent maps in a shape collection. ACM Trans. Graph. (TOG) Proc. SIGGRAPH Asia 31(6), 167 (2012)
Huang, R., Achlioptas, P., Guibas, L., Ovsjanikov, M.: Limit shapes—a tool for understanding shape differences and variability in 3D model collections. Comput. Graph. Forum 38(5), 187–202 (2019)
Huang, R., Ovsjanikov, M.: Adjoint map representation for shape analysis and matching. Comput. Graph. Forum 36(5), 151–163 (2017)
Jacobson, A., Deng, Z., Kavan, L., Lewis, J.P.: Skinning: real-time shape deformation. In: ACM SIGGRAPH 2014 Courses, vol. 24 (2014)
Kim, V., Li, W., Mitra, N., DiVerdi, S., Funkhouser, T.: Exploring collections of 3D models using fuzzy correspondences. Proc. SIGGRAPH 31, 54-1 (2012)
Kim, V., Lipman, Y., Funkhouser, T.: Blended intrinsic maps. ACM Trans. Graph. 30(4), 79 (2011)
Kim, V.G., Chaudhuri, S., Guibas, L., Funkhouser, T.: Shape2pose: human-centric shape analysis. ACM Trans. Graph. (TOG) 33(4), 120 (2014)
Kim, V.G., Li, W., Mitra, N.J., Chaudhuri, S., DiVerdi, S., Funkhouser, T.: Learning part-based templates from large collections of 3D shapes. ACM Trans. Graph. (TOG) 32(4), 70 (2013)
Kovnatsky, A., Bronstein, M., Bresson, X., Vandergheynst, P.: Functional correspondence by matrix completion. In: Proceedings of Computer Vision and Pattern Recognition, pp. 905–914 (2015)
Küpçü, E., Yemez, Y.: Diffusion-based isometric depth correspondence. Comput. Vis. Image Underst. (2019) (in press)
Lahner, Z., Rodolà, E., Bronstein, M., Cremers, D., Burghard, O., Cosmo, L., Dieckmann, A., Klein, R., Sahillioğlu, Y.: Shrec’16: matching of deformable shapes with topological noise. In: Proceedings of Eurographics Workshop on 3D Object Retrieval (2016)
Lee, S., Kazhdan, M.: Dense point-to-point correspondences between genus-zero shapes. Comput. Graph. Forum 38(5), 27–37 (2019)
Li, X., Iyengar, S.S.: On computing mapping of 3D objects: a survey. ACM Comput. Surv. 47(2), 34:1–34:45 (2014)
Lian, Z., Godil, A., Bustos, B., Daoudi, M., Hermans, J., Kawamura, S., Kurita, Y., Lavoué, G., Van Nguyen, H., Ohbuchi, R., et al.: A comparison of methods for non-rigid 3D shape retrieval. Pattern Recognit. 46(1), 449–461 (2013)
Lim, I., Dielen, A., Campen, M., Kobbelt, L.: A simple approach to intrinsic correspondence learning on unstructured 3D meshes. In: Proceedings of the European Conference on Computer Vision (ECCV) (2018)
Litany, O., Remez, T., Rodolà, E., Bronstein, A.M., Bronstein, M.M.: Deep functional maps: structured prediction for dense shape correspondence. In: Proceedings of International Conference on Computer Vision (2017)
Litany, O., Rodolà, E., Bronstein, A., Bronstein, M.: Fully spectral partial shape matching. Comput. Graph. Forum 36(2), 247–258 (2017)
Litany, O., Rodolà, E., Bronstein, A., Bronstein, M., Cremers, D.: Non-rigid puzzles. Comput. Graph. Forum (Proc. SGP) 35(5), 135–143 (2016)
Litman, R., Bronstein, A.M.: Learning spectral descriptors for deformable shape correspondence. IEEE Trans. Pattern Anal. Mach. Intell. 36(1), 171–180 (2014)
Liu, T., Kim, V.G., Funkhouser, T.: Finding surface correspondences using symmetry axis curves. Comput. Graph. Forum (Proc. SGP) 31(5), 1607–1616 (2012)
Liu, Z.-B., Bu, S.-H., Zhou, K., Gao, S.-M., Han, J.-W., Wu, J.: A survey on partial retrieval of 3D shapes. J. Comput. Sci. Technol. 28(5), 836–851 (2013)
Mandad, M., Cohen-Steiner, D., Kobbelt, L., Alliez, P., Desbrun, M.: Variance-minimizing transport plans for inter-surface mapping. ACM Trans. Graph. (TOG) 36(4), 39 (2017)
Maron, H., Dym, N., Kezurer, I., Kovalsky, S., Lipman, Y.: Point registration via efficient convex relaxation. ACM Trans. Graph. 35(4), 73 (2016)
Maron, H., Galun, M., Aigerman, N., Trope, M., Dym, N., Yumer, E., Kim, V.G., Lipman, Y.: Convolutional neural networks on surfaces via seamless toric covers. ACM Trans. Graph. 36(4), 71–1 (2017)
Melzi, S., Ovsjanikov, M., Roffo, G., Cristani, M., Castellani, U.: Discrete time evolution process descriptor for shape analysis and matching. ACM Trans. Graph. (TOG) 37(1), 4 (2018)
Melzi, S., Rodolà, E., Castellani, U., Bronstein, M.M.: Localized manifold harmonics for spectral shape analysis. Comput. Graph. Forum 37(6), 20–34 (2018)
Nguyen, A., Ben-Chen, M., Welnicka, K., Ye, Y., Guibas, L.: An optimization approach to improving collections of shape maps. Comput. Graph. Forum (Proc. SGP) 30(5), 1481–1491 (2011)
Nogneng, D., Melzi, S., Rodolà, E., Castellani, U., Bronstein, M., Ovsjanikov, M.: Improved functional mappings via product preservation. Comput. Graph. Forum 37(2), 179–190 (2018)
Nogneng, D., Ovsjanikov, M.: Informative descriptor preservation via commutativity for shape matching. Comput. Graph. Forum (Proc. Eurographics) 36(2), 259–267 (2017)
Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.: Functional maps: a flexible representation of maps between shapes. ACM Trans. Graph. (TOG) Proc. SIGGRAPH 31, 30 (2012)
Ovsjanikov, M., Huang, Q., Guibas, L.: A condition number for non-rigid shape matching. Comput. Graph. Forum (Proc. SGP) 30(5), 1503–1512 (2011)
Ovsjanikov, M., Mérigot, Q., Pătrucean, V., Guibas, L.: Shape matching via quotient spaces. In: Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing, pp. 1–11 (2013)
Panozzo, D., Baran, I., Diamanti, O., Sorkine-Hornung, O.: Weighted averages on surfaces. ACM Trans. Graph. (TOG) Proc. SIGGRAPH 32, 60 (2013)
Pokrass, J., Bronstein, A., Bronstein, M., Sprechmann, P., Sapiro, G.: Sparse modeling of intrinsic correspondences. Comput. Graph. Forum 32(2), 459–468 (2013)
Pokrass, J., Bronstein, A.M., Bronstein, M.M.: A correspondence-less approach to matching of deformable shapes. In: Proceedings of Scale Space and Variational Methods (2011)
Poulenard, A., Skraba, P., Ovsjanikov, M.: Topological function optimization for continuous shape matching. Comput. Graph. Forum 37(5), 13–25 (2018)
Ren, J., Panine, M., Wonka, P., Ovsjanikov, M.: Structured regularization of functional map computations. Comput. Graph. Forum 38(5), 39–53 (2019)
Ren, J., Poulenard, A., Wonka, P., Ovsjanikov, M.: Continuous and orientation-preserving correspondences via functional maps. In: SIGGRAPH Asia 2018 Technical Papers, p. 248 (2018)
Rodolà, E., Bronstein, A., Albarelli, A., Bergamasco, F., Torsello, A.: A game-theoretic approach to deformable shape matching. In: Proceedings of Computer Vision and Pattern Recognition, pp. 182–189 (2012)
Rodolà, S. Bulo, E., Windheuser, T., Vestner, M., Cremers, D.: Dense non-rigid shape correspondence using random forests. In: Proceedings of Computer Vision and Pattern Recognition, pp. 4177–4184 (2014)
Rodolà, E., Cosmo, L., Bronstein, M.M., Torsello, A., Cremers, D.: Partial functional correspondence. Comput. Graph. Forum 36(1), 222–236 (2017)
Rodolà, E., Möller, M., Cremers, D.: Regularized pointwise map recovery from functional correspondence. Comput. Graph. Forum 36(8), 700–711 (2017)
Rustamov, R., Ovsjanikov, M., Azencot, O., Ben-Chen, M., Chazal, F., Guibas, L.: Map-based exploration of intrinsic shape differences and variability. ACM Trans. Graph. 32(4), 72 (2013)
Sahillioğlu, Y.: A genetic isometric shape correspondence algorithm with adaptive sampling. ACM Trans. Graph. (TOG) 37(5), 175 (2018)
Sahillioğlu, Y.: A shape deformation algorithm for constrained multidimensional scaling. Comput. Graph. 53, 156–165 (2015)
Sahillioğlu, Y., Kavan, L.: Skuller: a volumetric shape registration algorithm for modeling skull deformities. Med. Image Anal. 23(1), 15–27 (2015)
Sahillioğlu, Y., Yemez, Y.: Coarse-to-fine combinatorial matching for dense isometric shape correspondence. Comput. Graph. Forum (Proc. SGP) 30(5), 1461–1470 (2011)
Sahillioğlu, Y., Yemez, Y.: Minimum-distortion isometric shape correspondence using EM algorithm. IEEE Trans. PAMI 34(11), 2203–2215 (2012)
Sahillioğlu, Y., Yemez, Y.: Scale normalization for isometric shape matching. Comput. Graph. Forum (Proc. Pac. Graph.) 31(7), 2233–2240 (2012)
Sahillioğlu, Y., Yemez, Y.: Coarse-to-fine isometric shape correspondence by tracking symmetric flips. Comput. Graph. Forum 32(1), 177–189 (2013)
Sahillioğlu, Y., Yemez, Y.: Multiple shape correspondence by dynamic programming. Comput. Graph. Forum (Proc. Pac. Graph.) 33(7), 121–130 (2014)
Sahillioğlu, Y., Yemez, Y.: Partial 3D correspondence from shape extremities. Comput. Graph. Forum 33(6), 63–76 (2014)
Shapira, N., Ben-Chen, M.: Cross-collection map inference by intrinsic alignment of shape spaces. Comput. Graph. Forum 33(5), 281–290 (2014)
Shoham, M., Vaxman, A., Ben-Chen, M.: Hierarchical functional maps between subdivision surfaces. Comput. Graph. Forum 38(5), 55–73 (2019)
Shtern, A., Kimmel, R.: Spectral gradient fields embedding for nonrigid shape matching. Comput. Vis. Image Underst. 140, 21–29 (2015)
Solomon, J., Nguyen, A., Butscher, A., Ben-Chen, M., Guibas, L.: Soft maps between surfaces. Comput. Graph. Forum 31(5), 1617–1626 (2012)
Solomon, J., Peyre, G., Kim, V., Sra, S.: Entropic metric alignment for correspondence problems. ACM Trans. Graph. 35(4), 72 (2016)
Tam, G., Cheng, Z., Lai, Y., Langbein, F., Liu, Y., Marshall, D., Martin, R., Sun, X., Rosin, P.: Registration of 3D point clouds and meshes: a survey from rigid to non-rigid. IEEE Trans. Vis. Comput. Graph. 19(7), 1199–1217 (2013)
Tam, G.K., Martin, R.R., Rosin, P.L., Lai, Y.: Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry. ACM Trans. Graph. 33(1), 1–17 (2014)
Tam, G.K., Martin, R.R., Rosin, P.L., Lai, Y.-K.: An efficient approach to correspondences between multiple non-rigid parts. Comput. Graph. Forum 33, 137–146 (2014)
Tevs, A., Berner, A., Wand, M., Ihrke, I., Seidel, H.-P.: Intrinsic shape matching by planned landmark sampling. Comput. Graph. Forum (Proc. Eurographics) 30(2), 543–552 (2011)
van Kaick, O., Tagliasacchi, A., Sidi, O., Zhang, H., Cohen-Or, D., Wolf, L., Hamarneh, G.: Prior knowledge for part correspondence. Comput. Graph. Forum 30(2), 553–562 (2011)
van Kaick, O., Zhang, H., Hamarneh, G.: Bilateral maps for partial matching. Comput. Graph. Forum 32(6), 189–200 (2013)
van Kaick, O., Zhang, H., Hamarneh, G., Cohen-Or, D.: A survey on shape correspondence. In: Proceedings of Eurographics State-of-the-Art Report, pp. 1–24 (2010)
van Kaick, O., Zhang, H., Hamarneh, G., Cohen-Or, D.: A survey on shape correspondence. Comput. Graph. Forum 30(6), 1681–1707 (2011)
Vestner, M., Lähner, Z., Boyarski, A., Litany, O., Slossberg, R., Remez, T., Rodola, E., Bronstein, A., Bronstein, M., Kimmel, R., et al.: Efficient deformable shape correspondence via kernel matching. In: 2017 International Conference on 3D Vision (3DV), pp. 517–526 (2017)
Vestner, M., Litman, R., Rodolà, E., Bronstein, A., Cremers, D.: Product manifold filter: non-rigid shape correspondence via kernel density estimation in the product space. In: Proceedings of Computer Vision and Pattern Recognition (2017)
Wang, L., Gehre, A., Bronstein, M.M., Solomon, J.: Kernel functional maps. Comput. Graph. Forum 37(5), 27–36 (2018)
Wei, L., Huang, Q., Ceylan, D., Vouga, E., Li, H.: Dense human body correspondences using convolutional networks. In: IEEE Conference on Computer Vision and Pattern Recognition (2016)
Yoshiyasu, Y., Yoshida, E., Guibas, L.: Symmetry aware embedding for shape correspondence. Comput. Graph. 60, 9–22 (2016)
Zeng, A., Song, S., Nießner, M., Fisher, M., Xiao, J., Funkhouser, T.: 3DMATCH: learning local geometric descriptors from RGB-D reconstructions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1802–1811 (2017)
Zhang, Z., Yin, K., Foong, K.: Symmetry robust descriptor for non-rigid surface matching. Comput. Graph. Forum 32(7), 355–362 (2013)
Zheng, X., Wen, C., Lei, N., Ma, M., Gu, X.: Surface registration via foliation. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 938–947 (2017)
Zheng, Y., Cohen-Or, D., Averkiou, M., Mitra, N.J.: Recurring part arrangements in shape collections. Comput. Graph. Forum 33(2), 115–124 (2014)
Zhou, T., Krahenbuhl, P., Aubry, M., Huang, Q., Efros, A.A.: Learning dense correspondence via 3D-guided cycle consistency. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 117–126 (2016)
Zhu, C., Yi, R., Lira, W., Alhashim, I., Xu, K., Zhang, H.: Deformation-driven shape correspondence via shape recognition. ACM Trans. Graph. 36(4), 51 (2017)
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This work has been supported by TUBITAK under the Project EEEAG-115E471.
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Sahillioğlu, Y. Recent advances in shape correspondence. Vis Comput 36, 1705–1721 (2020). https://doi.org/10.1007/s00371-019-01760-0
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DOI: https://doi.org/10.1007/s00371-019-01760-0