Abstract
We consider the estimation of diffeomorphic deformations aligning a known binary shape and its distorted observation. The classical solution consists in extracting landmarks, establishing correspondences and then the aligning transformation is obtained via a complex optimization procedure. Herein we present an alternative solution which works without landmark correspondences, is independent of the magnitude of transformation, easy to implement, and has a linear time complexity. The proposed universal framework is capable of recovering linear as well as nonlinear deformations.
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References
Holden, M.: A review of geometric transformations for nonrigid body registration. IEEE Trans. Med. Imaging 27, 111–128 (2008)
Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape context. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 509–522 (2002)
Heikkilä, J.: Pattern matching with affine moment descriptors. Pattern Recognition 37, 1825–1834 (2004)
Hagege, R., Francos, J.M.: Parametric estimation of multi-dimensional affine transformations:an exact linear solution. In: Proceedings of International Conference on Acoustics, Speech, and Signal Processing, vol. 2, Philadelphia, USA, pp. 861–864. IEEE (2005)
Domokos, C., Kato, Z.: Parametric estimation of affine deformations of planar shapes. Pattern Recognition 43, 569–578 (2010)
Tanács, A., Domokos, C., Sladoje, N., Lindblad, J., Kato, Z.: Recovering Affine Deformations of Fuzzy Shapes. In: Salberg, A.-B., Hardeberg, J.Y., Jenssen, R. (eds.) SCIA 2009. LNCS, vol. 5575, pp. 735–744. Springer, Heidelberg (2009)
Tanács, A., Sladoje, N., Lindblad, J., Kato, Z.: Estimation of linear deformations of 3D objects. In: Proceedings of International Conference on Image Processing, Hong Kong, China, pp. 153–156. IEEE (2010)
Tanacs, A., Kato, Z.: Fast linear registration of 3D objects segmented from medical images. In: Proceedings of International Conference on BioMedical Engineering and Informatics, Shanghai, China, pp. 299–303. IEEE (2011)
Domokos, C., Kato, Z.: Affine Puzzle: Realigning Deformed Object Fragments without Correspondences. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part II. LNCS, vol. 6312, pp. 777–790. Springer, Heidelberg (2010)
Domokos, C., Nemeth, J., Kato, Z.: Nonlinear shape registration without correspondences. IEEE Transactions on Pattern Analysis and Machine Intelligence 34, 943–958 (2012)
Hagege, R., Francos, J.M.: Parametric estimation of affine transformations: An exact linear solution. Journal of Mathematical Imaging and Vision 37, 1–16 (2010)
Nemeth, J., Domokos, C., Kato, Z.: Recovering planar homographies between 2D shapes. In: Proceedings of International Conference on Computer Vision, Kyoto, Japan, pp. 2170–2176. IEEE (2009)
Bookstein, F.L.: Principal warps: Thin-Plate Splines and the Decomposition of deformations. IEEE Trans. Pattern Anal. Mach. Intell. 11, 567–585 (1989)
Zagorchev, L., Goshtasby, A.: A comparative study of transformation functions for nonrigid image registration. IEEE Transactions on Image Processing 15, 529–538 (2006)
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Kato, Z. (2013). Linear and Nonlinear Shape Alignment without Correspondences. In: Csurka, G., Kraus, M., Laramee, R.S., Richard, P., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Application. Communications in Computer and Information Science, vol 359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38241-3_1
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DOI: https://doi.org/10.1007/978-3-642-38241-3_1
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