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Jordan-Segmentable Masks: A Topology-Aware definition for characterizing Binary Image Segmentation

Image segmentation plays a central role in computer vision. However, widely used evaluation metrics, whether pixel-wise, region-based, or boundary-focused, often struggle to capture the structural and topological coherence of a segmentation. In many practical scenarios, such as medical imaging or object delineation, small inaccuracies in boundary, holes, or fragmented predictions can result in high metric scores, despite the fact that the resulting masks fail to preserve the object global shape or connectivity. This highlights a limitation of conventional metrics: they are unable to assess whether a predicted segmentation partitions the image into meaningful interior and exterior regions. In this work, we introduce a topology-aware notion of segmentation based on the Jordan Curve Theorem, and adapted for use in digital planes. We define the concept of a \emph{Jordan-segmentatable mask}, which is a binary segmentation whose structure ensures a topological separation of the image domain into two connected components. We analyze segmentation masks through the lens of digital topology and homology theory, extracting a $4$-curve candidate from the mask, verifying its topological validity using Betti numbers. A mask is considered Jordan-segmentatable when this candidate forms a digital 4-curve with $β_0 = β_1 = 1$, or equivalently when its complement splits into exactly two $8$-connected components. This framework provides a mathematically rigorous, unsupervised criterion with which to assess the structural coherence of segmentation masks. By combining digital Jordan theory and homological invariants, our approach provides a valuable alternative to standard evaluation metrics, especially in applications where topological correctness must be preserved.

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Improved Workflow for Unsupervised Multiphase Image Segmentation

Quantitative image analysis often depends on accurate classification of pixels through a segmentation process. However, imaging artifacts such as the partial volume effect and sensor noise complicate the classification process. These effects increase the pixel intensity variance of each constituent class, causing intensities from one class to overlap with another. This increased variance makes threshold based segmentation methods insufficient due to ambiguous overlap regions in the pixel intensity distributions. The class ambiguity becomes even more complex for systems with more than two constituents, such as unsaturated moist granular media. In this paper, we propose an image processing workflow that improves segmentation accuracy for multiphase systems. First, the ambiguous transition regions between classes are identified and removed, which allows for global thresholding of single-class regions. Then the transition regions are classified using a distance function, and finally both segmentations are combined into one classified image. This workflow includes three methodologies for identifying transition pixels and we demonstrate on a variety of synthetic images that these approaches are able to accurately separate the ambiguous transition pixels from the single-class regions. For situations with typical amounts of image noise, misclassification errors and area differences calculated between each class of the synthetic images and the resultant segmented images range from 0.69-1.48% and 0.01-0.74%, respectively, showing the segmentation accuracy of this approach. We demonstrate that we are able to accurately segment x-ray microtomography images of moist granular media using these computationally efficient methodologies.

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Clustering Approach Towards Image Segmentation: An Analytical Study

Image processing is an important research area in computer vision. Image segmentation plays the vital rule in image processing research. There exist so many methods for image segmentation. Clustering is an unsupervised study. Clustering can also be used for image segmentation. In this paper, an in-depth study is done on different clustering techniques that can be used for image segmentation with their pros and cons. An experiment for color image segmentation based on clustering with K-Means algorithm is performed to observe the accuracy of clustering technique for the segmentation purpose.

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DTC: A Deformable Transposed Convolution Module for Medical Image Segmentation

In medical image segmentation, particularly in UNet-like architectures, upsampling is primarily used to transform smaller feature maps into larger ones, enabling feature fusion between encoder and decoder features and supporting multi-scale prediction. Conventional upsampling methods, such as transposed convolution and linear interpolation, operate on fixed positions: transposed convolution applies kernel elements to predetermined pixel or voxel locations, while linear interpolation assigns values based on fixed coordinates in the original feature map. These fixed-position approaches may fail to capture structural information beyond predefined sampling positions and can lead to artifacts or loss of detail. Inspired by deformable convolutions, we propose a novel upsampling method, Deformable Transposed Convolution (DTC), which learns dynamic coordinates (i.e., sampling positions) to generate high-resolution feature maps for both 2D and 3D medical image segmentation tasks. Experiments on 3D (e.g., BTCV15) and 2D datasets (e.g., ISIC18, BUSI) demonstrate that DTC can be effectively integrated into existing medical image segmentation models, consistently improving the decoder's feature reconstruction and detail recovery capability.

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FMG-Net and W-Net: Multigrid Inspired Deep Learning Architectures For Medical Imaging Segmentation

Accurate medical imaging segmentation is critical for precise and effective medical interventions. However, despite the success of convolutional neural networks (CNNs) in medical image segmentation, they still face challenges in handling fine-scale features and variations in image scales. These challenges are particularly evident in complex and challenging segmentation tasks, such as the BraTS multi-label brain tumor segmentation challenge. In this task, accurately segmenting the various tumor sub-components, which vary significantly in size and shape, remains a significant challenge, with even state-of-the-art methods producing substantial errors. Therefore, we propose two architectures, FMG-Net and W-Net, that incorporate the principles of geometric multigrid methods for solving linear systems of equations into CNNs to address these challenges. Our experiments on the BraTS 2020 dataset demonstrate that both FMG-Net and W-Net outperform the widely used U-Net architecture regarding tumor subcomponent segmentation accuracy and training efficiency. These findings highlight the potential of incorporating the principles of multigrid methods into CNNs to improve the accuracy and efficiency of medical imaging segmentation.

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Spatial-Frequency Dual Progressive Attention Network For Medical Image Segmentation

In medical images, various types of lesions often manifest significant differences in their shape and texture. Accurate medical image segmentation demands deep learning models with robust capabilities in multi-scale and boundary feature learning. However, previous networks still have limitations in addressing the above issues. Firstly, previous networks simultaneously fuse multi-level features or employ deep supervision to enhance multi-scale learning. However, this may lead to feature redundancy and excessive computational overhead, which is not conducive to network training and clinical deployment. Secondly, the majority of medical image segmentation networks exclusively learn features in the spatial domain, disregarding the abundant global information in the frequency domain. This results in a bias towards low-frequency components, neglecting crucial high-frequency information. To address these problems, we introduce SF-UNet, a spatial-frequency dual-domain attention network. It comprises two main components: the Multi-scale Progressive Channel Attention (MPCA) block, which progressively extract multi-scale features across adjacent encoder layers, and the lightweight Frequency-Spatial Attention (FSA) block, with only 0.05M parameters, enabling concurrent learning of texture and boundary features from both spatial and frequency domains. We validate the effectiveness of the proposed SF-UNet on three public datasets. Experimental results show that compared to previous state-of-the-art (SOTA) medical image segmentation networks, SF-UNet achieves the best performance, and achieves up to 9.4\% and 10.78\% improvement in DSC and IOU. Codes will be released at https://github.com/nkicsl/SF-UNet.

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SPEGC: Continual Test-Time Adaptation via Semantic-Prompt-Enhanced Graph Clustering for Medical Image Segmentation

In medical image segmentation tasks, the domain gap caused by the difference in data collection between training and testing data seriously hinders the deployment of pre-trained models in clinical practice. Continual Test-Time Adaptation (CTTA) aims to enable pre-trained models to adapt to continuously changing unlabeled domains, providing an effective approach to solving this problem. However, existing CTTA methods often rely on unreliable supervisory signals, igniting a self-reinforcing cycle of error accumulation that culminates in catastrophic performance degradation. To overcome these challenges, we propose a CTTA via Semantic-Prompt-Enhanced Graph Clustering (SPEGC) for medical image segmentation. First, we design a semantic prompt feature enhancement mechanism that utilizes decoupled commonality and heterogeneity prompt pools to inject global contextual information into local features, alleviating their susceptibility to noise interference under domain shift. Second, based on these enhanced features, we design a differentiable graph clustering solver. This solver reframes global edge sparsification as an optimal transport problem, allowing it to distill a raw similarity matrix into a refined and high-order structural representation in an end-to-end manner. Finally, this robust structural representation is used to guide model adaptation, ensuring predictions are consistent at a cluster-level and dynamically adjusting decision boundaries. Extensive experiments demonstrate that SPEGC outperforms other state-of-the-art CTTA methods on two medical image segmentation benchmarks. The source code is available at https://github.com/Jwei-Z/SPEGC-for-MIS.

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Structure-Aware Stylized Image Synthesis for Robust Medical Image Segmentation

Accurate medical image segmentation is essential for effective diagnosis and treatment planning but is often challenged by domain shifts caused by variations in imaging devices, acquisition conditions, and patient-specific attributes. Traditional domain generalization methods typically require inclusion of parts of the test domain within the training set, which is not always feasible in clinical settings with limited diverse data. Additionally, although diffusion models have demonstrated strong capabilities in image generation and style transfer, they often fail to preserve the critical structural information necessary for precise medical analysis. To address these issues, we propose a novel medical image segmentation method that combines diffusion models and Structure-Preserving Network for structure-aware one-shot image stylization. Our approach effectively mitigates domain shifts by transforming images from various sources into a consistent style while maintaining the location, size, and shape of lesions. This ensures robust and accurate segmentation even when the target domain is absent from the training data. Experimental evaluations on colonoscopy polyp segmentation and skin lesion segmentation datasets show that our method enhances the robustness and accuracy of segmentation models, achieving superior performance metrics compared to baseline models without style transfer. This structure-aware stylization framework offers a practical solution for improving medical image segmentation across diverse domains, facilitating more reliable clinical diagnoses.

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Certification of Deep Learning Models for Medical Image Segmentation

In medical imaging, segmentation models have known a significant improvement in the past decade and are now used daily in clinical practice. However, similar to classification models, segmentation models are affected by adversarial attacks. In a safety-critical field like healthcare, certifying model predictions is of the utmost importance. Randomized smoothing has been introduced lately and provides a framework to certify models and obtain theoretical guarantees. In this paper, we present for the first time a certified segmentation baseline for medical imaging based on randomized smoothing and diffusion models. Our results show that leveraging the power of denoising diffusion probabilistic models helps us overcome the limits of randomized smoothing. We conduct extensive experiments on five public datasets of chest X-rays, skin lesions, and colonoscopies, and empirically show that we are able to maintain high certified Dice scores even for highly perturbed images. Our work represents the first attempt to certify medical image segmentation models, and we aspire for it to set a foundation for future benchmarks in this crucial and largely uncharted area.

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FAS-UNet: A Novel FAS-driven Unet to Learn Variational Image Segmentation

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (denoted as FAS-Unet) that exploits the model and algorithm priors to extract the multi-scale features. The proposed model-informed network integrates image data and mathematical models, and implements them through learning a few convolution kernels. Based on the variational theory and FAS algorithm, we first design a feature extraction sub-network (FAS-Solution module) to solve the model-driven nonlinear systems, where a skip-connection is employed to fuse the multi-scale features. Secondly, we further design a convolution block to fuse the extracted features from the previous stage, resulting in the final segmentation possibility. Experimental results on three different medical image segmentation tasks show that the proposed FAS-Unet is very competitive with other state-of-the-art methods in qualitative, quantitative and model complexity evaluations. Moreover, it may also be possible to train specialized network architectures that automatically satisfy some of the mathematical and physical laws in other image problems for better accuracy, faster training and improved generalization.The code is available at \url{https://github.com/zhuhui100/FASUNet}.

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A Novel Approach Towards Clustering Based Image Segmentation

In computer vision, image segmentation is always selected as a major research topic by researchers. Due to its vital rule in image processing, there always arises the need of a better image segmentation method. Clustering is an unsupervised study with its application in almost every field of science and engineering. Many researchers used clustering in image segmentation process. But still there requires improvement of such approaches. In this paper, a novel approach for clustering based image segmentation is proposed. Here, we give importance on color space and choose lab for this task. The famous hard clustering algorithm K-means is used, but as its performance is dependent on choosing a proper distance measure, so, we go for cosine distance measure. Then the segmented image is filtered with sobel filter. The filtered image is analyzed with marker watershed algorithm to have the final segmented result of our original image. The MSE and PSNR values are evaluated to observe the performance.

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DeSAM: Decoupled Segment Anything Model for Generalizable Medical Image Segmentation

Deep learning-based medical image segmentation models often suffer from domain shift, where the models trained on a source domain do not generalize well to other unseen domains. As a prompt-driven foundation model with powerful generalization capabilities, the Segment Anything Model (SAM) shows potential for improving the cross-domain robustness of medical image segmentation. However, SAM performs significantly worse in automatic segmentation scenarios than when manually prompted, hindering its direct application to domain generalization. Upon further investigation, we discovered that the degradation in performance was related to the coupling effect of inevitable poor prompts and mask generation. To address the coupling effect, we propose the Decoupled SAM (DeSAM). DeSAM modifies SAM's mask decoder by introducing two new modules: a prompt-relevant IoU module (PRIM) and a prompt-decoupled mask module (PDMM). PRIM predicts the IoU score and generates mask embeddings, while PDMM extracts multi-scale features from the intermediate layers of the image encoder and fuses them with the mask embeddings from PRIM to generate the final segmentation mask. This decoupled design allows DeSAM to leverage the pre-trained weights while minimizing the performance degradation caused by poor prompts. We conducted experiments on publicly available cross-site prostate and cross-modality abdominal image segmentation datasets. The results show that our DeSAM leads to a substantial performance improvement over previous state-of-theart domain generalization methods. The code is publicly available at https://github.com/yifangao112/DeSAM.

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Cutting-Splicing data augmentation: A novel technology for medical image segmentation

Background: Medical images are more difficult to acquire and annotate than natural images, which results in data augmentation technologies often being used in medical image segmentation tasks. Most data augmentation technologies used in medical segmentation were originally developed on natural images and do not take into account the characteristic that the overall layout of medical images is standard and fixed. Methods: Based on the characteristics of medical images, we developed the cutting-splicing data augmentation (CS-DA) method, a novel data augmentation technology for medical image segmentation. CS-DA augments the dataset by splicing different position components cut from different original medical images into a new image. The characteristics of the medical image result in the new image having the same layout as and similar appearance to the original image. Compared with classical data augmentation technologies, CS-DA is simpler and more robust. Moreover, CS-DA does not introduce any noise or fake information into the newly created image. Results: To explore the properties of CS-DA, many experiments are conducted on eight diverse datasets. On the training dataset with the small sample size, CS-DA can effectively increase the performance of the segmentation model. When CS-DA is used together with classical data augmentation technologies, the performance of the segmentation model can be further improved and is much better than that of CS-DA and classical data augmentation separately. We also explored the influence of the number of components, the position of the cutting line, and the splicing method on the CS-DA performance. Conclusions: The excellent performance of CS-DA in the experiment has confirmed the effectiveness of CS-DA, and provides a new data augmentation idea for the small sample segmentation task.

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CAMEL: A Weakly Supervised Learning Framework for Histopathology Image Segmentation

Histopathology image analysis plays a critical role in cancer diagnosis and treatment. To automatically segment the cancerous regions, fully supervised segmentation algorithms require labor-intensive and time-consuming labeling at the pixel level. In this research, we propose CAMEL, a weakly supervised learning framework for histopathology image segmentation using only image-level labels. Using multiple instance learning (MIL)-based label enrichment, CAMEL splits the image into latticed instances and automatically generates instance-level labels. After label enrichment, the instance-level labels are further assigned to the corresponding pixels, producing the approximate pixel-level labels and making fully supervised training of segmentation models possible. CAMEL achieves comparable performance with the fully supervised approaches in both instance-level classification and pixel-level segmentation on CAMELYON16 and a colorectal adenoma dataset. Moreover, the generality of the automatic labeling methodology may benefit future weakly supervised learning studies for histopathology image analysis.

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Self-Learning AI Framework for Skin Lesion Image Segmentation and Classification

Image segmentation and classification are the two main fundamental steps in pattern recognition. To perform medical image segmentation or classification with deep learning models, it requires training on large image dataset with annotation. The dermoscopy images (ISIC archive) considered for this work does not have ground truth information for lesion segmentation. Performing manual labelling on this dataset is time-consuming. To overcome this issue, self-learning annotation scheme was proposed in the two-stage deep learning algorithm. The two-stage deep learning algorithm consists of U-Net segmentation model with the annotation scheme and CNN classifier model. The annotation scheme uses a K-means clustering algorithm along with merging conditions to achieve initial labelling information for training the U-Net model. The classifier models namely ResNet-50 and LeNet-5 were trained and tested on the image dataset without segmentation for comparison and with the U-Net segmentation for implementing the proposed self-learning Artificial Intelligence (AI) framework. The classification results of the proposed AI framework achieved training accuracy of 93.8% and testing accuracy of 82.42% when compared with the two classifier models directly trained on the input images.

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Quantum Image Segmentation Based on Grayscale Morphology

The classical image segmentation algorithm based on grayscale morphology can effectively segment images with uneven illumination, but with the increase of the image data, the real-time problem will emerge. In order to solve this problem, a quantum image segmentation algorithm is proposed in this paper, which can use quantum mechanism to simultaneously perform morphological operations on all pixels in a grayscale image, and then quickly segment the image into a binary image. In addition, several quantum circuit units, including dilation, erosion, bottom hat transformation, top hat transformation, etc., are designed in detail, and then they are combined together to construct the complete quantum circuits for segmenting the NEQR images. For a 2^n * 2^n image with q grayscale levels, the complexity of our algorithm can be reduced to O(n^2+q), which is an exponential speedup than the classic counterparts. Finally, the experiment is conducted on IBM Q to show the feasibility of our algorithm in the noisy intermediate-scale quantum (NISQ) era.

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SwinTextUNet: Integrating CLIP-Based Text Guidance into Swin Transformer U-Nets for Medical Image Segmentation

Precise medical image segmentation is fundamental for enabling computer aided diagnosis and effective treatment planning. Traditional models that rely solely on visual features often struggle when confronted with ambiguous or low contrast patterns. To overcome these limitations, we introduce SwinTextUNet, a multimodal segmentation framework that incorporates Contrastive Language Image Pretraining (CLIP), derived textual embeddings into a Swin Transformer UNet backbone. By integrating cross attention and convolutional fusion, the model effectively aligns semantic text guidance with hierarchical visual representations, enhancing robustness and accuracy. We evaluate our approach on the QaTaCOV19 dataset, where the proposed four stage variant achieves an optimal balance between performance and complexity, yielding Dice and IoU scores of 86.47% and 78.2%, respectively. Ablation studies further validate the importance of text guidance and multimodal fusion. These findings underscore the promise of vision language integration in advancing medical image segmentation and supporting clinically meaningful diagnostic tools.

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Total Variation and Tight Frame Image Segmentation with Intensity Inhomogeneity

Image segmentation is an important task in the domain of computer vision and medical imaging. In natural and medical images, intensity inhomogeneity, i.e. the varying image intensity, occurs often and it poses considerable challenges for image segmentation. In this paper, we propose an efficient variational method for segmenting images with intensity inhomogeneity. The method is inspired by previous works on two-stage segmentation and variational Retinex. Our method consists of two stages. In the first stage, we decouple the image into reflection and illumination parts by solving a convex energy minimization model with either total variation or tight-frame regularisation. In the second stage, we segment the original image by thresholding on the reflection part, and the inhomogeneous intensity is estimated by the smoothly varying illumination part. We adopt a primal dual algorithm to solve the convex model in the first stage, and the convergence is guaranteed. Numerical experiments clearly show that our method is robust and efficient to segment both natural and medical images.

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