Redundant Wavelet Transform by Range-Fourier Series Expansion
##article.authors##
- Kohei Hayashi Graduate School of Engineering, Nagoya Institute of Technology
- Soichiro Honda Graduate School of Engineering, Nagoya Institute of Technology
- Hirokazu Kamei Graduate School of Engineering, Nagoya Institute of Technology
-
Yoshihiro Maeda
College of Engineering, Shibaura Institute of Technology
https://researchmap.jp/yoshihiromaeda
-
Norishige Fukushima
Graduate School of Engineering, Nagoya Institute of Technology
https://researchmap.jp/read0153731/
DOI:
https://doi.org/10.51094/jxiv.761Keywords:
edge-preserving smoothing, edge-aware enhancement, wavelet transfrom, scale-spaceAbstract
スケールスペースフィルタリングは，スケールに応じて画像をベース信号と詳細信号に分解する画像解析の基本的な処理の一つである．このスケールスペースフィルタリングを画像強調に用いるには，詳細信号の係数を増幅させて再構成すればよい．しかしながら急峻なエッジ付近では詳細係数が大きくなるため，その係数を線形に増幅するとオーバーフロー・アンダーフローが発生し，それが halo と呼ばれる「もや」として生じる．
古典的方法として，様々な非線形変換により詳細信号の増幅を抑える方法が取られてきたが輪郭のエッジ付近の応答は非常に大きいため完全な halo 抑制は難しい．そこでエッジ保存平滑化フィルタを用いた分解や，ローカルラプラシアンフィルタなどの局所コントラスト変換を用いたピラミッド分解が提案されてきた．
しかし，局所コントラスト手法で取り扱うことができる現状のピラミッド表現だけでは多様な信号をとらえて解析することは難しい．そこで本論文では，信号解析の中核となるウェーブレット変換を対象として，局所コントラストアダプティブなウェーブレット変換（local contrast adaptive wavelet transform; LCA-WT）を提案する．そして，LCA-WTを値域のフーリエ級数展開を用いた冗長ウェーブレット変換で表す高速化計算方法を提案し，それは画像固有のウェーブレット変換であり，パラメータに依存しない変換であるその形式が新しいウェーブレット変換表現の一つであることを示す．実験の結果，提案手法は少ない回数のウェーブレット変換の線形結合により実現できることを示すとともに，LCA-WTによる係数操作により，方向性画像強調，ガイド付き処理，ウェーブレット合成などのいくつかの画像処理応用が可能なことが示された．
Conflicts of Interest Disclosure
The authors have no conflicts of interest to report.Downloads *Displays the aggregated results up to the previous day.
References
飯島泰蔵, “パターン観測に関する基礎理論,” 電気通信学会オートマトンと自動制御研究会, 1959.
A. Witkin, “Scale-space filtering,” in International Joint Conferences on Artificial Intelligence (IJCAI), 1983.
D. Marr and E. Hildreth, “Theory of edge detection,” Proceedings of the Royal Society of London. Series B. Biological Sciences, vol. 207, no. 1167, pp. 187–217, 1980.
P. J. Burt and E. H. Adelson, “The laplacian pyramid as a compact image code,” IEEE Transactions on Communications, vol. 31, no. 4, pp. 532–540, 1983.
A. Grossmann and J. Morlet, “Decomposition of hardy functions into square integrable wavelets of constant shape,” SIAM journal on mathematical analysis, vol. 15, no. 4, pp. 723–736, 1984.
P. Vuylsteke and E. P. Schoeters, “Multiscale image contrast amplification (musica),” in Proceedings of SPIE, vol. 2167, 1994, pp. 551–560.
S. Dippel, M. Stahl, R. Wiemker, and T. Blaffert, “Multiscale contrast enhancement for radiographies: Laplacian pyramid versus fast wavelet transform,” IEEE Transactions on Medical Imaging, vol. 21, no. 4, 2002.
Y. Li, L. Sharan, and E. H. Adelson, “Compressing and companding high dynamic range images with subband architectures,” ACM Transactions on Graphics, vol. 24, no. 3, pp. 836–844, 2005.
R. Fattal, D. Lischinski, and M. Werman, “Gradient domain high dynamic range compression,” ACM Transactions on Graphics, vol. 21, no. 3, pp. 249–256, 2002.
X. Deng, Y. Zhang, X. Zhao, and H. Li, “Halo-free image enhancement through multi-scale detail sharpening and single-scale contrast stretching,” Signal Processing: Image Communication, vol. 113, p. 116923, 2023.
C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of IEEE International Conference on Computer Vision (ICCV), 1998, pp. 839–846.
R. Fattal, M. Agrawala, and S. Rusinkiewicz, “Multiscale shape and detail enhancement from multi-light image collections,” ACM Transactions on Graphics, vol. 26, no. 3, p. 51, 2007.
K. Sugimoto, N. Fukushima, and S. Kamata, “200 fps constant-time bilateral filter using svd and tiling strategy,” in Proceedings of IEEE International Conference on Image Processing (ICIP), 2019.
S. Paris, W. Hasinoff, and J. Kautz, “Local laplacian filters: Edge-aware image processing with a laplacian pyramid,” ACM Transactions on Graphics, vol. 30, no. 4, 2011.
M. Aubry, S. Paris, J. Kautz, and F. Durand, “Fast local laplacian filters: Theory and applications,” ACM Transactions on Graphics, vol. 33, no. 5, 2014.
Y. Sumiya, T. Otsuka, Y. Maeda, and N. Fukushima, “Gaussian fourier pyramid for local laplacian filter,” IEEE Signal Processing Letters, vol. 29, pp. 11–15, 2022.
K. Hayashi, Y. Maeda, and N. Fukushima, “Local contrast enhancement with multiscale filtering,” in Proceedings of Asia Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), 2023, pp. 765–770.
H. Du, X. Jin, and P. J. Willis, “Two-level joint local laplacian texture filtering,” Visual Computer, vol. 32, pp. 1537–1548, 2016.
R. Fattal, “Edge-avoiding wavelets and their applications,” ACM Transactions on Graphics, vol. 28, no. 3, pp. 22: 1–10, 2009.
Y. Sumiya, H. Kamei, K. Ishikawa, and N. Fukushima, “Vectorized computing for edge-avoiding wavelet,” in International Workshop on Advanced Image Technology (IWAIT), vol. 12177, 2022, pp. 23–28.
Y. Sumiya, N. Fukushima, K. Sugimoto, and S. Kamata, “Extending compressive bilateral filtering for arbitrary range kernel,” in Proceedings of IEEE International Conference on Image Processing (ICIP), 2020.
Y. Maeda, N. Fukushima, and H. Matsuo, “Effective implementation of edge-preserving filtering on cpu microarchitectures,” Applied Sciences, vol. 8, no. 10, 2018.
A. D. Sappa, J. A. Carvajal, C. A. Aguilera, M. Oliveira, D. Romero, and B. X. Vintimilla, “Wavelet-based visible and infrared image fusion: a comparative study,” Sensors, vol. 16, no. 6, p. 861, 2016.
H. Xu, J. Ma, Z. Le, J. Jiang, and X. Guo, “Fusiondn: A unified densely connected network for image fusion,” in Proceedings of AAAI Conference on Artificial Intelligence, 2020.
L. Tang, J. Yuan, and J. Ma, “Image fusion in the loop of high-level vision tasks: A semantic-aware real-time infrared and visible image fusion network,” Information Fusion, vol. 82, pp. 28–42, 2022.
P. Singh, M. Diwakar, X. Cheng, and A. Shankar, “A new wavelet-based multi-focus image fusion technique using method noise and anisotropic diffusion for real-time surveillance application,” Journal of Real-Time Image Processing, vol. 8, no. 4, pp. 1051–1068, 2021.
白井啓一郎, 野村和史, 池原雅章, “ウェーブレット変換による合焦画像の作成,” 電子情報通信学会論文誌 A, vol. 88, no. 10, pp. 1154–1162, 2005.
M. Nejati, S. Samavi, and S. Shirani, “Multi-focus image fusion using dictionary-based sparse representation,” Information Fusion, vol. 25, pp. 72–84, 2015.
Downloads
Posted
Submitted: 2024-06-20 17:39:49 UTC
Published: 2024-06-28 05:40:55 UTC
License
Copyright (c) 2024
Kohei Hayashi
Soichiro Honda
Hirokazu Kamei
Yoshihiro Maeda
Norishige Fukushima
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
