Abstract
We present a method for detecting and describing features in vector flow fields. Our method models flow fields locally using a linear combination of complex monomials. These monomials form an orthogonal basis for analytic flows with respect to a correlation-based inner-product. We investigate the invariance properties of the coefficients of the approximation polynomials under both rotation and scaling operators. We then propose a descriptor for local flow patterns, and developed a method for comparing them invariantly against rigid transformations. Additionally, we propose a SIFT-like detector that can automatically detect singular flow patterns at different scales and orientations. Promising detection results are obtained on different fluid flow data.
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Bronshtein, I., Semendyayev, K., Musiol, G., Muehlig, H.: Handbook of mathematics. Springer, Berlin (1997)
Bruhn, A., Weickert, J., Schnörr, C.: Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods. Int. J. Comp. Vis. 61(3), 211–231 (2005)
Carlier, J.: Second set of fluid mechanics image sequences. In: European Project ’Fluid image analysis and description, FLUID (2005), http://www.fluid.irisa.fr/
Corpetti, T., Mémin, E., Pérez, P.: Extraction of singular points from dense motion fields: An analytic approach. J. Math. Imaging Vis. 19(3), 175–198 (2003)
Davies, B.: Integral Transforms and Their Applications. Springer, Heidelberg (2002)
Fan, L., Wang, S., Wang, H., Guo, T.: Singular points detection based on zero-pole model in fingerprint images. Trans. Patt. Anal. Mach. Intell. 30(6), 929–940 (2008)
Florack, L.: Scale-space theories for scalar and vector images. In: Scale-Space 2001, London, UK, 2001, pp. 193–204. Springer, London (2001)
Ford, R.M., Strickland, R.N., Thomas, B.A.: Image models for 2-D flow visualization and compression. Graph. Models Image Process. 56(1), 75–93 (1994)
Forray, M.J.: Approximation Theory and Methods. Cambridge Univ. Press, Cambridge (1981)
Hoey, J., Little, J.J.: Bayesian clustering of optical flow fields. ICCVÂ 2, 1086 (2003)
Kihl, O., Tremblais, B., Augereau, B.: Multivariate orthogonal polynomials to extract singular points. In: ICIP, pp. 857–860 (2008)
Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A., Eyink, G.: A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. Journal of Turbulence 9(31), 1–29 (2008)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 60(2), 91–110 (2004)
Nilsson, K., Bigun, J.: Localization of corresponding points in fingerprints by complex filtering. Pattern Recogn. Lett. 24(13), 2135–2144 (2003)
Nogawa, H., Nakajima, Y., Sato, Y., Tamura, S.: Acquisition of symbolic description from flow fields: a new approach based on a fluid model. IEEE Trans. Patt. Anal. Mach. Intell. 19(1), 58–63 (1997)
Rao, A.R., Jain, R.C.: Computerized flow field analysis: Oriented texture fields. IEEE Trans. Pattern Anal. Mach. Intell. 14(7), 693–709 (1992)
Schlemmer, M., Heringer, M., Morr, F., Hotz, I., Hering-Bertram, M., Garth, C., Kollmann, W., Hamann, B., Hagen, H.: Moment invariants for the analysis of 2D flow fields. IEEE Trans. on Vis. and Comp. Graph 13(6), 1743–1750 (2007)
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Liu, W., Ribeiro, E. (2010). Scale and Rotation Invariant Detection of Singular Patterns in Vector Flow Fields. In: Hancock, E.R., Wilson, R.C., Windeatt, T., Ulusoy, I., Escolano, F. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2010. Lecture Notes in Computer Science, vol 6218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14980-1_51
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DOI: https://doi.org/10.1007/978-3-642-14980-1_51
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