Abstract
Rigid transformations are involved in a wide variety of image processing applications, including image registration. In this context, we recently proposed to deal with the associated optimization problem from a purely discrete point of view, using the notion of discrete rigid transformation (DRT) graph. In particular, a local search scheme within the DRT graph to compute a locally optimal solution without any numerical approximation was formerly proposed. In this article, we extend this study, with the purpose to reduce the algorithmic complexity of the proposed optimization scheme. To this end, we propose a novel algorithmic framework for just-in-time computation of sub-graphs of interest within the DRT graph. Experimental results illustrate the potential usefulness of our approach for image registration.
Keywords
- image registration
- discrete rigid transformation
- discrete optimization
- DRT graph
The research leading to these results has received funding from the French Agence Nationale de la Recherche (Grant Agreement ANR-2010-BLAN-0205).
Download conference paper PDF
References
Nouvel, B., Rémila, É.: Characterization of bijective discretized rotations. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 248–259. Springer, Heidelberg (2004)
Nouvel, B., Rémila, E.: Configurations induced by discrete rotations: Periodicity and quasi-periodicity properties. Discrete Appl. Math. 147, 325–343 (2005)
Berthé, V., Nouvel, B.: Discrete rotations and symbolic dynamics. Theor. Comput. Sci. 380, 276–285 (2007)
Nouvel, B.: Self-similar discrete rotation configurations and interlaced Sturmian words. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 250–261. Springer, Heidelberg (2008)
Jacob, M.A., Andres, E.: On discrete rotations. In: Proc. DGCI, pp. 161–174 (1995)
Amir, A., Kapah, O., Tsur, D.: Faster two-dimensional pattern matching with rotations. Theor. Comput. Sci. 368, 196–204 (2006)
Reveillès, J.P.: Géométrie discrète, calcul en nombres entiers et algorithmique. Thèse d’État, Université Strasbourg 1 (1991)
Andres, E.: The quasi-shear rotation. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 307–314. Springer, Heidelberg (1996)
Richman, M.S.: Understanding discrete rotations. In: Proc. ICASSP, vol. 3, pp. 2057–2060. IEEE (1997)
Andres, E., Fernandez-Maloigne, C.: Discrete rotation for directional orthogonal wavelet packets. In: Proc. ICIP, vol. 2, pp. 257–260. IEEE (2001)
Ngo, P., Passat, N., Kenmochi, Y., Talbot, H.: Topology-preserving rigid transformation of 2D digital images. IEEE T. Image Process. 23, 885–897 (2014)
Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Combinatorial structure of rigid transformations in 2D digital images. Comput. Vis. Image Und. 117, 393–408 (2013)
Nouvel, B.: Rotations discrètes et automates cellulaires. PhD thesis, École Normale Supérieure de Lyon (2006)
Nouvel, B., Rémila, É.: Incremental and transitive discrete rotations. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 199–213. Springer, Heidelberg (2006)
Thibault, Y., Kenmochi, Y., Sugimoto, A.: Computing upper and lower bounds of rotation angles from digital images. Pattern Recogn. 42, 1708–1717 (2009)
Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: On 2D constrained discrete rigid transformations. Ann. Math. Artif. Intell. (in press), doi:10.1007/s10472-014-9406-x
Ngo, P., Kenmochi, Y., Passat, N., Talbot, H.: Topology-preserving conditions for 2D digital images under rigid transformations. J. Math. Imaging Vis. 49, 418–433 (2014)
Ngo, P., Sugimoto, A., Kenmochi, Y., Passat, N., Talbot, H.: Discrete rigid transformation graph search for 2D image registration. In: Huang, F., Sugimoto, A. (eds.) PSIVT 2013. LNCS, vol. 8334, pp. 228–239. Springer, Heidelberg (2014)
Zitová, B., Flusser, J.: Image registration methods: A survey. Image Vision Comput. 21, 977–1000 (2003)
Schowengerdt, R.A.: Remote Sensing: Models and Methods for Image Processing, 3rd edn. Elsevier Academic Press (2007)
Noblet, V., Heinrich, C., Heitz, F., Armspach, J.P.: Recalage d’images médicales. Tech Ing (MED910) (2014)
Edelsbrunner, H., Guibas, L.J.: Topologically sweeping an arrangement. Journal Comput. Syst. Sci. 38, 165–194 (1989); Corrig. 42, 249–251 (1991)
Hoare, C.A.R.: Algorithm 65: find. Commun. ACM 4, 321–322 (1961)
Boykov, Y., Kolmogorov, V., Cremers, D., Delong, A.: An integral solution to surface evolution PDEs via geo-cuts. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 409–422. Springer, Heidelberg (2006)
Flusser, J., Zitová, B., Suk, T.: Moments and Moment Invariants in Pattern Recognition. Wiley (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Kenmochi, Y., Ngo, P., Talbot, H., Passat, N. (2014). Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2014. Lecture Notes in Computer Science, vol 8668. Springer, Cham. https://doi.org/10.1007/978-3-319-09955-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-09955-2_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09954-5
Online ISBN: 978-3-319-09955-2
eBook Packages: Computer ScienceComputer Science (R0)
-
Published in cooperation with
http://www.iapr.org/
