Abstract
Shearlets are a relatively new and very effective multi-resolution framework for signal analysis able to capture efficiently the anisotropic information in multivariate problem classes. For this reason, Shearlets appear to be a valid choice for multi-resolution image processing and feature detection. In this paper we provide a brief review of the theory, referring in particular to the problem of enhancing signal discontinuities. We then discuss the specific application to corner detection, and provide a novel algorithm based on the concept of a cornerness measure. The appropriateness of the algorithm in detecting good matchable corners is evaluated on benchmark data including different image transformations.
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Aanes, H., Dahl, A.L., Pedersen, K.S.: Interesting interest points. IJCV (2011)
Candes, E.J., Donoho, D.L.: New tight frames of curvelets and optimal representations of objects with piecewise c2 singularities. Communications on Pure and Applied Mathematics 57(2), 219–266 (2004)
Chen, C.H., Lee, J.S., Sun, Y.N.: Wavelet transformation for gray-level corner detection. Pattern Recognition 28(6), 853–861 (1995)
Easley, G., Labate, D., Lim, W.Q.: Sparse directional image representations using the discrete shearlet transform. Applied and Computational Harmonic Analysis 25(1), 25–46 (2008)
Gao, X., Sattar, F., Venkateswarlu, R.: Multiscale corner detection of gray level images based on log-gabor wavelet transform. IEEE Transactions on Circuits and Systems for Video Technology 17(7), 868–875 (2007)
Guo, K., Labate, D.: Characterization and analysis of edges using the continuous shearlet transform. SIAM Journal on Imaging Sciences 2(3), 959–986 (2009)
Harris, C., Stephens, M.: A combined corner and edge detector. In: Alvey Vision Conference, Manchester, UK, vol. 15, p. 50 (1988)
Häuser, S., Steidl, G.: Fast finite shearlet transform: a tutorial. ArXiv (1202.1773) (2014)
Kitchen, L., Rosenfeld, A.: Gray-level corner detection. Pattern Recognition Letters 1(2), 95–102 (1982)
Kittipoom, P., Kutyniok, G., Lim, W.Q.: Construction of compactly supported shearlet frames. Constr. Approx. 35(1), 21–72 (2012)
Kutyniok, G., Labate, D.: Shearlets: Multiscale analysis for multivariate data. Springer (2012)
Kutyniok, G., Petersen, P.: Classification of edges using compactly supported shearlets. ArXi (1411.5657) (2014)
Labate, D., Lim, W.Q., Kutyniok, G., Weiss, G.: Sparse multidimensional representation using shearlets. In: Optics & Photonics 2005, pp. 59140U–59140U. International Society for Optics and Photonics (2005)
Mallat, S., Hwang, W.L.: Singularity detection and processing with wavelets. IEEE Transactions on Information Theory 38(2), 617–643 (1992)
Mallat, S., Zhong, S.: Characterization of signals from multiscale edges. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(7), 710–732 (1992)
Mikolajczyk, K., Tuytelaars, T., Schmid, C., Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., Van Gool, L.: A comparison of affine region detectors. International Journal of Computer Vision 65(1–2), 43–72 (2005)
Pedersini, F., Pozzoli, E., Sarti, A., Tubaro, S.: Multi-resolution corner detection. In: ICIP, pp. 881–884 (2000)
Po, D.D., Do, M.N.: Directional multiscale modeling of images using the contourlet transform. Image Processing 15(6), 1610–1620 (2006)
Rosten, E., Porter, R., Drummond, T.: Faster and better: A machine learning approach to corner detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(1), 105–119 (2010)
Selesnick, I.W., Baraniuk, R.G., Kingsbury, N.C.: The dual-tree complex wavelet transform. IEEE Signal Processing Magazine 22(6), 123–151 (2005)
Shi, J., Tomasi, C.: Good features to track. In: Proceedings of the 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 1994, pp. 593–600. IEEE (1994)
Yi, S., Labate, D., Easley, G.R., Krim, H.: A shearlet approach to edge analysis and detection. IEEE Transactions on Image Processing 18(5), 929–941 (2009)
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© 2015 Springer International Publishing Switzerland
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Duval-Poo, M.A., Odone, F., De Vito, E. (2015). Enhancing Signal Discontinuities with Shearlets: An Application to Corner Detection. In: Murino, V., Puppo, E. (eds) Image Analysis and Processing — ICIAP 2015. ICIAP 2015. Lecture Notes in Computer Science(), vol 9280. Springer, Cham. https://doi.org/10.1007/978-3-319-23234-8_11
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DOI: https://doi.org/10.1007/978-3-319-23234-8_11
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