Geodesic
The determination of distances between images by de Rham currents method
Modelirovanie i analiz informacionnyh sistem, Tome 27 (2020) no. 1, pp. 96-107.

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The goal of the paper is to develop an algorithm for matching the shapes of images of objects based on the geometric method of de Rham currents and preliminary affine transformation of the source image shape. In the formation of the matching algorithm, the problems of ensuring invariance to geometric image transformations and ensuring the absence of a bijective correspondence requirement between images segments were solved. The algorithm of shapes matching based on the current method is resistant to changes of the topology of object shapes and reparametrization. When analyzing the data structures of an object, not only the geometric form is important, but also the signals associated with this form by functional dependence. To take these signals into account, it is proposed to expand de Rham currents with an additional component corresponding to the signal structure. To improve the accuracy of shapes matching of the source and terminal images we determine the functional on the basis of the formation of a squared distance between the shapes of the source and terminal images modeled by de Rham currents. The original image is subjected to preliminary affine transformation to minimize the squared distance between the deformed and terminal images.
Keywords: pattern recognition, image matching, de Rham current
Mots-clés : affine transformations. 
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S. N. Chukanov. The determination of distances between images by de Rham currents method. Modelirovanie i analiz informacionnyh sistem, Tome 27 (2020) no. 1, pp. 96-107. http://geodesic.mathdoc.fr/item/MAIS_2020_27_1_a7/

[1] K. Grauman, B. Leibe, “Visual object recognition”, Synthesis lectures on artificial intelligence and machine learning, 5:2 (2011), 1–181

[2] A. Goshtasby, Theory and applications of image registration, John Wiley Sons, 2017 | MR

[3] D. Zhang, G. Lu, L. Zhang, Advanced biometrics, Springer, 2018

[4] M. Miller, A. Trouvé, L. Younes, “Hamiltonian systems and optimal control in computational anatomy: 100 years since D'Arcy Thompson”, Annual review of biomedical engineering, 17 (2015), 447–509

[5] M. Deza, E. Deza, “Encyclopedia of distances”, Encyclopedia of distances, Springer-Verlag, Berlin–Heidelberg, 2016 | MR | Zbl

[6] L. Younes, Shapes and diffeomorphisms, Applied Mathematical Sciences, 171, Springer-Verlag, Berlin–Heidelberg, 2019 | MR | Zbl

[7] G. De Rham, F. Smith, S. Chern, Differentiable manifolds: forms, currents, harmonic forms, Grundlehren der mathematischen Wissenschaften, 266, Springer-Verlag, 1984 | MR | Zbl

[8] S. Chukanov, “A rotation, translation, and scaling invariant Fourier transform of 3D image function”, Optoelectronics, Instrumentation and Data Processing, 44:3 (2008), 249–255

[9] S. Chukanov, “Constructing invariants for visualization of vector fields defined by integral curves of dynamic systems”, Optoelectronics, Instrumentation and Data Processing, 47:2 (2011), 151–155

[10] S. Chukanov, “Comparison of objects' images based on computational topology methods”, Trudy SPIIRAN, 18:5 (2019), 1043–1065

[11] N. Aronszajn, “Theory of reproducing kernels”, Trans. Amer. Math. Soc., 68:3 (1950), 337–404 | MR | Zbl

[12] C. Micchelli, M. Pontil, “On learning vector-valued functions”, Neural computation, 17:1 (2005), 177–204 | MR | Zbl

[13] J. Glaunes, M. Micheli, “Matrix-valued kernels for shape deformation analysis. Geometry”, Imaging and Computing, 1:1 (2014), 57–139 | MR | Zbl

[14] S. Lejhter, S. Chukanov, “Matching of images based on their diffeomorphic mapping”, Computer optics, 42:1 (2018), 96–104

[15] S. Barahona, X. Gual-Arnau, M. Ibá{ n}ez, A. Simó, “Unsupervised classification of children's bodies using currents”, Advances in Data Analysis and Classification, 12:2 (2018), 365–397 | MR | Zbl

[16] I. Kaltenmark, B. Charlier, N. Charon, “A general framework for curve and surface comparison and registration with oriented varifolds”, Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, 3346–3355

[17] M. Vaillant, J. Glaunès, “Surface matching via currents”, Biennial international conference on information processing in medical imaging, Springer, 2005, 381–392

[18] D. Tang, Y. Cai, J. Zhao, Y. Xue, “A quantum-behaved particle swarm optimization with memetic algorithm and memory for continuous non-linear large scale problems”, Information Sciences, 289 (2014), 162–189

[19] J. Flusser, B. Zitova, T. Suk, Moments and moment invariants in pattern recognition, John Wiley Sons, 2009 | Zbl

[20] J. Kennedy, R. Eberhart, “Particle swarm optimization”, Proceedings of ICNN'95-international conference on neural networks, v. 4, IEEE, 1995, 1942–1948