Multi-focus image fusion is an important method for obtaining fully focused information. In this paper, a novel multi-focus image fusion method based on fractal dimension (FD) and parameter adaptive unit-linking dual-channel pulse-coupled neural network (PAUDPCNN) in the curvelet transform (CVT) domain is proposed. The source images are decomposed into low-frequency and high-frequency sub-bands by CVT, respectively. The FD and PAUDPCNN models, along with consistency verification, are employed to fuse the high-frequency sub-bands, the average method is used to fuse the low-frequency sub-band, and the final fused image is generated by inverse CVT. The experimental results demonstrate that the proposed method shows superior performance in multi-focus image fusion on Lytro, MFFW, and MFI-WHU datasets.

Fuzzy clustering is an essential algorithm in image segmentation, and most of them are based on fuzzy c-mean (FCM) algorithms. However, it is sensitive to noise, center point selection, cluster number, and distance metric. To address this problem, we propose a new fuzzy clustering method based on low-rank representation (LRR) for image segmentation, which integrates low-rank structure with fuzzy theory. First, we improve the morphological reconstruction super-pixel method based on edge detection by introducing anisotropy to enhance the image edge. Thus, on the one hand, the improved morphological reconstruction super-pixel method can improve its noise-resistance performance; on the other hand, the complexity of the subsequent low-rank computation can be reduced by enhancing the superpixels constructed by the edges. Second, inspired by the fact that rank can represent correlation, we propose the concept of fuzzy low-rank structure, which is not dealing with data directly but with the relationship between data. Specifically, we perform rank minimization on the constructed membership matrix to obtain the optimal matrix. To obtain better clustering results, we added the Frobenius norm of the fuzzy matrix as a fuzzy regularization term in the LRR model to achieve global convergence and obtain a membership matrix with a strong element correlation. Finally, we obtain the final clustering results by clustering the processed membership matrix using a subspace clustering with a lowrank structure constraint. Experiments performed on artificial and real-world images show that the proposed method is more effective and efficient than the current state-of-the-art methods.

In multi-focus image fusion, accurately detecting and extracting focused regions remains a key challenge. Some existing methods suffer from misjudgment of focus areas, resulting in incorrect focus information or the unintended retention of blurred regions in the fused image. To address these issues, this paper proposes a novel multi-focus image fusion method that leverages a dual-channel Rybak neural network combined with consistency verification in the nonsubsampled contourlet transform (NSCT) domain. Specifically, the high-frequency sub-bands produced by NSCT decomposition are processed using the dual-channel Rybak neural network and a consistency verification strategy, allowing for more accurate extraction and integration of salient details. Meanwhile, the low-frequency sub-bands are fused using a simple averaging approach to preserve the overall structure and brightness information. The effectiveness of the proposed method has been thoroughly evaluated through comprehensive qualitative and quantitative experiments conducted on three widely used public datasets: Lytro, MFFW, and MFI-WHU. Experimental results show that our method consistently outperforms several state-of-the-art image fusion techniques, including both traditional algorithms and deep learning-based approaches, in terms of visual quality and objective performance metrics ($Q_{AB/F}$, $Q_{CB}$, $Q_E$, $Q_{FMI}$, $Q_{MI}$, $Q_{MSE}$, $Q_{NCIE}$, $Q_{NMI}$, $Q_P$, and $Q_{PSNR}$). These results clearly demonstrate the robustness and superiority of the proposed fusion framework in handling multi-focus image fusion tasks.

Due to more or less deviations in the imaging system, there will be noise in the image, which makes the image segmentation inaccurate. To divide a natural image into a more accurate binary image, the target and background of the image are effectively separated to achieve a more effective segmentation result. Therefore, this paper proposes an image segmentation algorithm combining a saliency map and neutrosophic set (NS) theory. First, to overcome the problem of weak edges in the image, we highlight the details and use the guided filter to filter the various channels of the natural image. Then, the initial saliency map is generated. After the weighted superposition of the initial saliency map, the local entropy map and the gray scale map, the final saliency map can be generated using the nonlinear function, and it can effectively highlight the foreground information of the image. Second, the saliency map is transformed to the NS domain and interpreted by three subsets: true (T), indeterminate (I), and false (F). According to NS theory, the indeterminacy is reduced, and the segmentation results are finally obtained by using the method of threshold. Various experiments were done and compared with other state-of-the-art approaches. These experiments demonstrate the effect of the proposed work, which is fast and effective for de-noising.

Small object detection in remote sensing imagery is inherently constrained by several persistent factors within the conventional spatial domain. On one hand, the small proportion of tiny targets in the entire image results in sparse spatial feature representations that are easily submerged by complex background noise. On the other hand, effectively capturing long-range dependencies in dense-object scenarios remains difficult, which limits the model's capacity for global context modeling. Collectively, these factors represent significant performance bottlenecks for existing spatial-based object detection algorithms. To remedy these shortcomings, TSF-DETR, a novel detection framework anchored by a Two-Stage Frequency-Domain Enhancement strategy, is proposed in this study. Specifically, a Remote Sensing Frequency Enhancement Module (RSEM) is integrated within the backbone as the first stage to implement a hierarchical differentiated mechanism for frequency-domain feature refinement. In the subsequent neck stage, a Multi-Scale Frequency Domain (MSFD) module is leveraged to execute multi-scale and multi-orientational Gabor filtering, establishing a robust “Global FFT Enhancement – Local Gabor Optimization” synergy to suppress background noise. Furthermore, to fortify the model's global perception, a tailored Linear Multi-Head Self-Attention (LMSA) mechanism is incorporated. Distinguishable from standard linear attention designs, this modified LMSA enhances the model's ability to capture long-range dependencies and aggregate global semantic context, thereby improving detection precision while maintaining high computational efficiency. Extensive evaluations on four benchmark datasets—VisDrone2019, DIOR, RSOD and USOD—demonstrate that TSF-DETR outperforms the RT-DETR baseline and several state-of-the-art methods, validating its efficacy in strengthening small object representations and enhancing detection accuracy across diverse remote sensing scenarios.