Abstract
Monogenic signal is regarded as a generalization of analytic signal from one dimensional to higher dimensional space, which has been received considerable attention in the literature. It is defined by an original signal with its isotropic Hilbert transform (the combination of Riesz transform). Similar to analytic signal, the monogenic signal can be written in the polar form. Then it provides the signal features representation, such as the local attenuation and the local phase vector. The aim of the paper is twofold: first, to analyze the relationship between the local phase vector and the local attenuation in the higher dimensional spaces. Secondly, a study on image edge detection using modified differential phase congruency is presented. Comparisons with competing methods on real-world images consistently show the superiority of the proposed methods.
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References
Babaud, J., Witkin, A. P., Baudin, M., & Duda, R. O. (1986). Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(1), 26–33.
Brackx, F., Delanghe, R., & Sommen, F. (1982). Clifford analysis (Vol. 76). Boston-London-Melbourne: Pitman.
Cohen, L. (1995). Time-frequency analysis: Theory and applications. Upper Saddle River, NJ: Prentice Hall.
Delanghe, R., Sommen, F., & Soucek, V. (1992). Clifford algebra and spinor valued functions. Dordrecht-Boston-London: Kluwer.
Felsberg, M. (2002). Low-level image processing with the structure multivector. Institut Fur Informatik Und Praktische Mathmatik, Christian-Alberchis-Universitat Kiel.
Felsberg, M., Duits, R., & Florack, L. (2005). The monogenic scale space on a rectanular domain and it features. Internertional Journal of Computer Vision, 64(2/3), 187–201.
Felsberg, M., & Sommer, G. (2001). The monogenic signal. IEEE Transactions on Signal Processing, 49(12), 3136–3144.
Felsberg, M., & Sommer, G. (2004). The monogenic scale-space: A unifying approach to phase-based image processing in scale-space. Journal of Mathematical Imaging and Vision, 21(1), 5–26.
Garnet, J. (1981). Bounded analytic functions. New York: Academic Press.
Hahn, S. L. (1996). Hilbert transforms in signal processing. Norwood, MD: Artech House.
Iijima, T. (1959). Basic theory of pattern obsercation. In Papers of Technical Group on Automata and Automatic Control. IECE, Japan
Kou, K.-I., & Qian, T. (2002). The Paley–Wiener theorem in \({{\bf R}^m}\) with the Clifford analysis setting. Journal of Functional Analysis, 189, 227–241.
Kovesi, P. (1999). Image features from phase congruency. Videre: A Journal of Computer Vision Research,1(3), 1–30.
Kovesi, P. (2013). Phase congruency detects corners and edges. In Proceedings DICTA.
Li, C., Mcintosh, A., & Qian, T. (1994). Clifford algebras, Fourier transforms, and singular convolution operators on Lipschitz surfaces. Revista Matemática Iberoamericana, 10, 665–721.
Lindeberg, T. (1994). Scale-space theory in computer vision, The Kluwer international series in engineering and computer science. Kluwer Academic Publishers, Boston.
Nussenzveig, H. M. (1972). Causality and dispersion relations. London: Academic Press.
Pei, S., Huang, J., Ding, J., & Guo, G. (2008). Short response Hilbert transform for edge detection. IEEE Asia Pacific conference on circuits and systems (pp. 340–343).
Yang, Y., Dang, P., & Qian, T. (2015). Space-frequency analysis in higher dimensions and applications. Annali di Mathematica, 194(4), 953–968.
Yang, Y., & Kou, K.-I. (2014). Uncertainty principles for hypercomplex signals in the linear canonical transform domains. Signal Processing, 95, 67–75.
Yang, Y., Qian, T., & Sommen, F. (2012). Phase derivative of monogenic functions in higher dimensional spaces. Complex Analysis and Operator Theory, 6(5), 987–1010.
Zhang, L., & Zhang, D. (2016a). Visual understanding via multi-feature shared learning with global consistency. IEEE Transactions on Multimedia, 18(2), 247–259.
Zhang, L., & Zhang, D. (2016b). Robust visual knowledge transfer via extreme learning machine-based domain adaptation. IEEE Transactions on Image Processing, 25(10), 4959–4973.
Zhang, L., Zuo, W., & Zhang, D. (2016). LSDT: latent sparse domain transfer learning for visual adaptation. IEEE Transactions on Image Processing, 25(3), 247–259.
Acknowledgements
The authors acknowledge financial support from the National Natural Science Funds (No. 11401606) and University of Macau (No. MYRG2015-00058-L2-FST) and the Macao Science and Technology Development Fund (FDCT/099/2012/A3 and FDCT/031/2016/A1).
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Yang, Y., Kou, K.I. & Zou, C. Edge detection methods based on modified differential phase congruency of monogenic signal. Multidim Syst Sign Process 29, 339–359 (2018). https://doi.org/10.1007/s11045-016-0468-2
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DOI: https://doi.org/10.1007/s11045-016-0468-2