Abstract
The hypercomplex 2D analytic signal has been proposed by several authors with applications in color image processing. The analytic signal enables to extract local features from images. It has the fundamental property of splitting the identity, meaning that it separates qualitative and quantitative information of an image in form of the local phase and the local amplitude. The extension of analytic signal of linear canonical transform domain from 1D to 2D, covering also intrinsic 2D structures, has been proposed. We use this improved concept on envelope detector. The quaternion Fourier transform plays a vital role in the representation of multidimensional signals. The quaternion linear canonical transform (QLCT) is a well-known generalization of the quaternion Fourier transform. Some valuable properties of the two-sided QLCT are studied. Different approaches to the 2D quaternion Hilbert transforms are proposed that allow the calculation of the associated analytic signals, which can suppress the negative frequency components in the QLCT domains. As an application, examples of envelope detection demonstrate the effectiveness of our approach.
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Acknowledgments
The authors acknowledge financial support from the National Natural Science Funds for Young Scholars (Nos. 11401606, 11501015) and University of Macau Nos. MYRG2015-00058-FST, MYRG099(Y1-L2)-FST13-KKI and the Macao Science and Technology Development Fund FDCT/094/2011A, FDCT/099/2012/A3. The second author also acknowledges financial support from the Guangdong Natural Science Foundation (Grant Nos. 2014A030307016, 2014A030313422). The third author’s work is supported by the Asociación Mexicana de Cultura, A. C.
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Kou, K.I., Liu, MS., Morais, J.P. et al. Envelope detection using generalized analytic signal in 2D QLCT domains. Multidim Syst Sign Process 28, 1343–1366 (2017). https://doi.org/10.1007/s11045-016-0410-7
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DOI: https://doi.org/10.1007/s11045-016-0410-7
Keywords
- Quaternion Fourier transform
- Quaternion linear canonical transform
- Hilbert transform
- Analytic signal
- Instantaneous amplitude