Abstract
The Hilbert Transform (HT) and the analytic signal (AS) are widely used in their one-dimensional version for various applications. However, in the bi-dimensional (2D) case as occur for images, the definition of the 2D-HT is not unique and several approaches to it have been developed, having as one of the main goals to obtain a meaningful 2D-AS or analytic image, which can be used for various practical applications. In this work, one particular approach to the 2D-HT is introduced that allowed the calculation of analytic images which satisfy the basic properties that these functions have in the 1D case, and that produces a 2D spectrum equal to zero in one quadrant. The methods for calculation of the discrete version of the 2D-HT and the associated AS are presented and analyzed, as well as two applications, for edge detection and for envelope detection in a 2D AM modulated radial chirp.
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References
Gabor, D.: Theory of Communication. Journal of the IEE 93, 429–457 (1946)
Cohen, L.: Time Frequency Analysis. Prentice-Hall, Englewood Cliffs (1995)
Hahn, S.L.: Multidimensional complex signals with single-orthant spectra. Proc. IEEE 80(8), 1287–1300 (1992)
Bülow, T., Sommer, G.: Multi-dimensional signal processing using an algebraically extended signal representation. In: Sommer, G. (ed.) AFPAC 1997. LNCS, vol. 1315, pp. 148–163. Springer, Heidelberg (1997)
Kohlmann, K.: Corner detection in natural images based on the 2D Hilbert Transform. Signal Processing 48, 225–234 (1996)
Havlicek, J.P., Havlicek, J.W., Mamuya, N.D., Bovik, A.C.: Skewed 2D Hilbert Transforms and AM-FM models. In: ICIP 1998. Proc. International conference on Image Processing, October 4-7, 1998, vol. 1, pp. 602–606 (1998)
Havlicek, J.P., Havlicek, J.W., Bovik, A.C.: The analytic image. In: ICIP 1997. Proc. International conference on Image Processing, October 26-29, 1997, vol. 2, pp. 446–449 (1997)
Kovesi, P.: Image Features from Phase Congruency. Videre Journal of Computer Vision Research, vol. 1(3). MIT Press, Cambridge (1999)
Pei, S.-C., Ding, J.-J.: The generalized radial Hilbert Transform and its applications to 2-D edge detection (any direction or specified directions). In: ICASSP ’03. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, April 6-10, 2003, vol. 3, pp. 357–360 (2003)
Felsberg, M., Sommer, G.: The Monogenic Signal. IEEE Transactions on Signal Processing 49(12), 3136–3144 (2001)
Larkin, K.G., Bone, D.J., Oldfield, M.A.: Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. Journal of the Optical Society of America 18(8), 1862–1870 (2001)
Lawrence Marple Jr., S.: Computing the discrete-time analytic signal via FFT. IEEE Transactions on Signal Processing 47(9), 2600–2603 (1999)
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Lorenzo-Ginori, J.V. (2007). An Approach to the 2D Hilbert Transform for Image Processing Applications. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2007. Lecture Notes in Computer Science, vol 4633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74260-9_14
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DOI: https://doi.org/10.1007/978-3-540-74260-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74258-6
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