perform morphological filtering

This work addresses the challenge of obtaining piecewise-constant images with sharp edges and homogeneous interior intensities for image segmentation preprocessing. To this end, a novel method based on nonlinear diffusion filtering is proposed. By constructing a new family of diffusion coefficients that satisfy scale-space theory, the approach integrates a semi-implicit numerical scheme within a forward nonlinear diffusion framework. This formulation effectively preserves edges while homogenizing intensities within regions, and it guarantees well-posedness in both semi-discrete and fully discrete scale-space settings. Experimental results demonstrate that the method efficiently produces high-quality piecewise-constant images, significantly enhancing the performance of subsequent segmentation tasks.

This paper addresses the mathematical morphological characterization of grayscale image stack operators. Methodologically, it introduces a rigorous algebraic framework based on the extension of binary image operators: a stack operator is formally defined as a mapping that commutes with section-wise averaging and admits a 1-Lipschitz extension from a binary lattice operator. The work establishes, for the first time, that such operators inherit the lattice structure of characteristic-set operators and derives kernel-, basis-, and characteristic-function representations for translation-invariant local stack operators—generalizing classical stack filtering to arbitrary stack operators. Key contributions include: (i) a complete algebraic characterization of stack operators; (ii) the insight that most grayscale morphological processing tasks reduce to binary operator design followed by Lipschitz extension; and (iii) a theoretical shortcut and systematic design paradigm for constructing morphological operators.

Traditional grayscale mathematical morphology exhibits poor robustness under illumination variations because its structuring function’s amplitude cannot adaptively adjust to local image intensity. To address this, we propose Logarithmic Mathematical Morphology (LMM), a novel framework integrating Logarithmic Image Processing (LIP) theory with nonlinear structuring function modeling. LMM is the first morphology framework enabling adaptive modulation of the structuring function’s amplitude in response to local image intensity, thereby overcoming the rigidity of additive structuring paradigms. Quantitative evaluation demonstrates that LMM outperforms classical morphological operators on images subject to uniform illumination changes. Moreover, in vessel segmentation from non-uniformly illuminated retinal fundus images, LMM achieves significantly higher robustness than three state-of-the-art methods. These results validate LMM’s effectiveness and practicality for illumination-invariant morphological analysis.

This work addresses the degradation of segmentation quality and reliability in quantitative analysis caused by topological errors—such as incorrect numbers or structures of connected components—in existing image segmentation models. To this end, we propose SCNP, a lightweight, general-purpose, and easily integrable topological refinement mechanism that enhances global topological accuracy by prioritizing local consistency. Specifically, SCNP penalizes the logits of each pixel relative to the worst-classified pixel within its same-class neighborhood, thereby guiding the model to correct local inconsistencies that often lead to topological defects. Notably, our method is agnostic to object morphology, imaging modality, segmentation architecture, and loss function, overcoming limitations of prior approaches in complexity, compatibility, and applicability. Experiments demonstrate that SCNP consistently improves topological accuracy across 13 diverse datasets and seamlessly integrates with three major segmentation frameworks.

To address the challenge of topological recovery in tubular structure extraction (e.g., vessels, roads), this paper proposes GraphMorph—a graph-level structural modeling approach that abandons conventional pixel-wise classification. Methodologically, it introduces a novel collaborative architecture integrating a graph neural decoder with a morphological deformation module; proposes SkeletonDijkstra, a geometric alignment algorithm that bridges graph topology and centerline probability maps; and employs centerline masks to guide post-processing segmentation, effectively suppressing false positives. By fusing multi-scale features and centerline-guided morphological deformation, GraphMorph achieves substantial improvements across multiple public benchmarks: topological accuracy increases by 5.2–9.8%, centerline extraction precision improves significantly, and the false positive rate decreases by an average of 37.6%, outperforming state-of-the-art segmentation and graph-generation methods.

This work addresses the challenge of effectively integrating local morphological and global topological features in persistent homology on cubical complexes. To this end, it introduces diverse mathematical morphology structuring elements into the persistent homology framework for the first time, constructing multiscale filtrations through erosion, dilation, opening, and closing operations to jointly extract morphological and topological information from digital images. Implemented using the GUDHI library, the proposed method unifies morphological image processing with topological data analysis, enabling a refined multiscale characterization of topological features—such as connected components and loops—on cubical complexes. This approach significantly enhances local geometric representation and provides richer spatial and morphological semantics compared to conventional methods.

This study addresses the challenge of fragmented predictions and topological discontinuities in deep learning-based 3D colon segmentation from abdominal CT scans, which frequently arise due to complex anatomical structures. To overcome this limitation, we propose a three-stage topology-preserving framework that sequentially performs initial segmentation, centerline extraction with bridging reconnection, and 3D reconstruction optimization. By explicitly introducing a centerline bridging mechanism, the method effectively repairs disconnected segments. Experimental validation on the TotalSegmentator and RAOS datasets demonstrates that the proposed approach significantly enhances the topological integrity and anatomical continuity of segmentation results. The framework outperforms existing baselines across key topological metrics, enabling more reliable clinical-grade colon segmentation.

This work addresses the limitation of existing graph analysis methods that often neglect geometric structure, thereby failing to capture the joint variation of topology and shape in shape graphs. To overcome this, the authors propose an explicit feature framework that integrates topological, geometric, and directional information to construct a multidimensional representation invariant to transformations such as rotation and translation. This approach transcends the traditional reliance on connectivity alone and enables effective grouping, clustering, and classification of shape graphs. Evaluated on real-world datasets—including urban road networks, neuronal trajectories, and astrocyte images—the method significantly outperforms both feature-based and non-feature baselines, demonstrating its efficacy for statistical analysis and pattern recognition in complex shape graphs.

This study addresses the high heterogeneity in material microstructure images caused by variations in processing and testing conditions, which severely limits the generalization of conventional methods and necessitates extensive manual annotation. To overcome these challenges, this work proposes a semi-automatic segmentation framework based on active learning, integrating a U-Net architecture, an interactive correction interface, and a novel image selection strategy termed SMILE—leveraging maximin Latin hypercube sampling in the embedding space. The SMILE strategy significantly outperforms both manual selection and uncertainty-based sampling, enhancing model performance while substantially reducing annotation costs. Experimental results demonstrate that the macro F1-score improves from 0.74 to 0.93, with approximately 65% reduction in manual labeling time, and successfully establish meaningful correlations between defect characteristics and additive manufacturing process parameters, offering an efficient, scalable, and robust solution for microstructure analysis.

研究通过调整轮廓初始化和数值停止条件，使用Otsu阈值等方法优化了皮肤镜图像分割中的Chan-Vese算法性能。