Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 5 Sayı: 4, 183 - 189, 01.12.2022
https://doi.org/10.33205/cma.1181174

Öz

Proje Numarası

FA9550-21-1-0275

Kaynakça

  • B. Hurat, Z. Alvarado and J. Gilles: The Empirical Watershed Wavelet, Journal of Imaging, 6 (12) (2020), 140.
  • J. Gilles: Continuous empirical wavelets systems, Advances in Data Science and Adaptive Analysis, 12 (03n04) (2020), 2050006.
  • K. Bui, J. Fauman, D. Kes, L.Torres Mandiola, A. Ciomaga, R. Salazar, A.L. Bertozzi, J. Gilles, D. P. Goronzy, A. I. Guttentag and P. S. Weiss: Segmentation of Scanning Tunneling Microscopy Images Using Variational Methods and Empirical Wavelets, Pattern Analysis and Applications, 23 (2020), 625–651.
  • Y. Huang, F. Zhou and J. Gilles: Empirical curvelet based Fully Convolutional Network for supervised texture image segmentation, Neurocomputing, 349 (2019), 31–43.
  • Y. Huang, V. De Bortoli, F. Zhou and J. Gilles: Review of wavelet-based unsupervised texture segmentation, advantage of adaptive wavelets, IET Image Processing Journal, 12 (9) (2018), 1626–1638.
  • J. Gilles, K. Heal: A parameterless scale-space approach to find meaningful modes in histograms - Application to image and spectrum segmentation, International Journal of Wavelets, Multiresolution and Information Processing, 12 (6) (2014), 1450044-1–1450044-17.
  • J. Gilles, G. Tran and S. Osher: 2D Empirical transforms. Wavelets, Ridgelets and Curvelets Revisited, SIAM Journal on Imaging Sciences, 7 (1) (2014), 157–186.
  • J. Gilles: Empirical Wavelet Transform, IEEE Transactions on Signal Processing, 61 (16) (2013), 3999–4010.
  • N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N-C. Yen, C. C. Tung and H. H. Liu: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. Royal Society London A., 454 (1998), 903–995.
  • W. Liu, S. Cao and Y. Chen: Seismic TimeFrequency Analysis via Empirical Wavelet Transform, IEEE Geoscience and Remote Sensing Letters, 13 (1) (2016), 28–32.
  • X. Zhang, X. Li and Y. Feng: Image fusion based on simultaneous empirical wavelet transform, Multimedia Tools and Applications, 76 (2017), 8175–8193.
  • N. Otsu: A threshold selection method from gray-level histograms, IEEE Trans on Systems, Man and Cybernetics, 9 (1) (1979), 62–66.
  • S. Beucher, C. Lantuéjoul: Use of Watersheds in Contour Detection, International Workshop on Image Processing: Real-time edge and motion detection-estimation, Rennes, France, 2.1–2.12.
  • F. Meyer: Topographic distance and watershed lines, Signal Processing, 38 (1) (1994), 113-125.
  • F. Meyer, S. Beucher: Morphological segmentation, Journal of Visual Communication and Image Representation, 1 (1) (1990), 21–46.
  • F. Aurenhammer, R. Klein and D.-T. Lee: Voronoi Diagrams and Delaunay Triangulations,World Scientific, (2013).

Empirical Voronoi wavelets

Yıl 2022, Cilt: 5 Sayı: 4, 183 - 189, 01.12.2022
https://doi.org/10.33205/cma.1181174

Öz

Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is desirable to keep a certain level of regularity in the geometry of the obtained partitions. In this paper, we propose to build such partition using Voronoi diagrams. This solution allows us to keep a high level of adaptability while guaranteeing a minimum level of geometric regularity in the detected partition.

Destekleyen Kurum

Air Force Office of Scientific Research

Proje Numarası

FA9550-21-1-0275

Kaynakça

  • B. Hurat, Z. Alvarado and J. Gilles: The Empirical Watershed Wavelet, Journal of Imaging, 6 (12) (2020), 140.
  • J. Gilles: Continuous empirical wavelets systems, Advances in Data Science and Adaptive Analysis, 12 (03n04) (2020), 2050006.
  • K. Bui, J. Fauman, D. Kes, L.Torres Mandiola, A. Ciomaga, R. Salazar, A.L. Bertozzi, J. Gilles, D. P. Goronzy, A. I. Guttentag and P. S. Weiss: Segmentation of Scanning Tunneling Microscopy Images Using Variational Methods and Empirical Wavelets, Pattern Analysis and Applications, 23 (2020), 625–651.
  • Y. Huang, F. Zhou and J. Gilles: Empirical curvelet based Fully Convolutional Network for supervised texture image segmentation, Neurocomputing, 349 (2019), 31–43.
  • Y. Huang, V. De Bortoli, F. Zhou and J. Gilles: Review of wavelet-based unsupervised texture segmentation, advantage of adaptive wavelets, IET Image Processing Journal, 12 (9) (2018), 1626–1638.
  • J. Gilles, K. Heal: A parameterless scale-space approach to find meaningful modes in histograms - Application to image and spectrum segmentation, International Journal of Wavelets, Multiresolution and Information Processing, 12 (6) (2014), 1450044-1–1450044-17.
  • J. Gilles, G. Tran and S. Osher: 2D Empirical transforms. Wavelets, Ridgelets and Curvelets Revisited, SIAM Journal on Imaging Sciences, 7 (1) (2014), 157–186.
  • J. Gilles: Empirical Wavelet Transform, IEEE Transactions on Signal Processing, 61 (16) (2013), 3999–4010.
  • N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N-C. Yen, C. C. Tung and H. H. Liu: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. Royal Society London A., 454 (1998), 903–995.
  • W. Liu, S. Cao and Y. Chen: Seismic TimeFrequency Analysis via Empirical Wavelet Transform, IEEE Geoscience and Remote Sensing Letters, 13 (1) (2016), 28–32.
  • X. Zhang, X. Li and Y. Feng: Image fusion based on simultaneous empirical wavelet transform, Multimedia Tools and Applications, 76 (2017), 8175–8193.
  • N. Otsu: A threshold selection method from gray-level histograms, IEEE Trans on Systems, Man and Cybernetics, 9 (1) (1979), 62–66.
  • S. Beucher, C. Lantuéjoul: Use of Watersheds in Contour Detection, International Workshop on Image Processing: Real-time edge and motion detection-estimation, Rennes, France, 2.1–2.12.
  • F. Meyer: Topographic distance and watershed lines, Signal Processing, 38 (1) (1994), 113-125.
  • F. Meyer, S. Beucher: Morphological segmentation, Journal of Visual Communication and Image Representation, 1 (1) (1990), 21–46.
  • F. Aurenhammer, R. Klein and D.-T. Lee: Voronoi Diagrams and Delaunay Triangulations,World Scientific, (2013).
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Makaleler
Yazarlar

Jerome Gilles 0000-0002-5626-8386

Proje Numarası FA9550-21-1-0275
Yayımlanma Tarihi 1 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 4

Kaynak Göster

APA Gilles, J. (2022). Empirical Voronoi wavelets. Constructive Mathematical Analysis, 5(4), 183-189. https://doi.org/10.33205/cma.1181174
AMA Gilles J. Empirical Voronoi wavelets. CMA. Aralık 2022;5(4):183-189. doi:10.33205/cma.1181174
Chicago Gilles, Jerome. “Empirical Voronoi Wavelets”. Constructive Mathematical Analysis 5, sy. 4 (Aralık 2022): 183-89. https://doi.org/10.33205/cma.1181174.
EndNote Gilles J (01 Aralık 2022) Empirical Voronoi wavelets. Constructive Mathematical Analysis 5 4 183–189.
IEEE J. Gilles, “Empirical Voronoi wavelets”, CMA, c. 5, sy. 4, ss. 183–189, 2022, doi: 10.33205/cma.1181174.
ISNAD Gilles, Jerome. “Empirical Voronoi Wavelets”. Constructive Mathematical Analysis 5/4 (Aralık 2022), 183-189. https://doi.org/10.33205/cma.1181174.
JAMA Gilles J. Empirical Voronoi wavelets. CMA. 2022;5:183–189.
MLA Gilles, Jerome. “Empirical Voronoi Wavelets”. Constructive Mathematical Analysis, c. 5, sy. 4, 2022, ss. 183-9, doi:10.33205/cma.1181174.
Vancouver Gilles J. Empirical Voronoi wavelets. CMA. 2022;5(4):183-9.