Abstract
To address the challenges of information loss and noise interference in multi-focus image fusion, this paper presents a novel curvelet-domain fusion algorithm based on distance-weighted regional energy (DWRE) and fractal dimension. The proposed method first decomposes the source images using the curvelet transform, obtaining both low- and high-frequency sub-bands. For the high-frequency sub-bands, fusion is performed using DWRE and fractal dimension in conjunction with a consistency verification strategy, ensuring that salient details and structural information are effectively preserved. For the low-frequency sub-band, an averaging-based fusion rule is applied to maintain overall intensity information. Finally, the inverse curvelet transform is employed to reconstruct the fused image. To evaluate the effectiveness of the proposed algorithm, experiments are conducted on the Lytro and MFI-WHU benchmark datasets. The results demonstrate that our approach achieves superior fusion performance compared to several state-of-the-art (SOTA) methods, particularly in terms of detail preservation, noise suppression, and visual quality. Additionally, it demonstrates significant advantages in terms of the objective evaluation metrics \(Q_{AB/F}\), \(Q_{CB}\), \(Q_{FMI}\), \(Q_{G}\), \(Q_{MI}\), \(Q_{NCIE}\), \(Q_{P}\), \(Q_{MSE}\), \(Q_{PSNR}\) and \(Q_{Y}\).
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Data availability
The experimental datasets used in this study are all from open datasets, and the authors declare no conflicts of interest. The Lytro and MFI-WHU public datasets we used can be obtained from the following links, respectively: www.researchgate.net/publication/291522937_Lytro_Multi-focus_Image_Dataset; https://github.com/HaoZhang1018/MFI-WHU.
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Funding
This research was funded by the National Natural Science Foundation of China under Grant No. 62261053; the Tianshan Talent Training Project-Xinjiang Science and Technology Innovation Team Program (2023TSYCTD0012); the Research Project of Xinjiang Sky-Ground Integrated Intelligent Computing Technology Laboratory under Grant No.2025A05-1.
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The experiments and data collection were conducted by M.L., Z.J., W.L., L.L., and H.M. The manuscript was drafted by M.L., with contributions from the co-authors. All authors have read and agreed to the published version of the manuscript.
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Lv, M., Jia, Z., Le, W. et al. Fractal dimension-based multi-focus image fusion via distance-weighted regional energy in curvelet domain. Sci Rep (2026). https://doi.org/10.1038/s41598-026-44394-8
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DOI: https://doi.org/10.1038/s41598-026-44394-8
