[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84991-en":3,"doc-seo-84991-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84991,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","VCDP Variation-Conditioned Distributional Proxy Learning for Semi-Supervised Medical Image Segmentation","Semi-supervised 3D medical image segmentation reduces reliance on costly voxel-level annotations by leveraging unlabeled volumes. Existing approaches improve prediction robustness via consistency regularization, pseudo-labeling, or co-training, yet often fail to structure feature space for anatomically complex targets, particularly small organs and ambiguous boundaries with large intra-class variation. VCDP introduces a plug-and-play training-only regularizer that models class semantics with learnable Gaussians and variation prototypes, aligning voxel embeddings to global identity and local patterns.","VCDP: Variation-Conditioned Distributional Proxy Learning for Semi-Supervised Medical Image  \nSegmentation  \nZimu Zhang2 , Yiheng Zhong 1 , Zhuoru Zhang2 ,  \nYingzhen Hu2 , Yanan He 1 , Fanliang Meng 1 , Xiaofeng Liu 1,†  \n1Yale University, United States  \n2Xi’an Jiaotong-Liverpool University, China  \nEmail: [xiaofeng.liu@yale.edu](xiaofeng.liu@yale.edu)  \narXiv :2607 .074 16v 1 [ cs .CV] 8 Jul 2026  \nAbstract—Semi-supervised 3D medical image segmentation reduces the need for dense voxel-level annotations by exploiting unlabeled volumes. Although existing methods such as consistency regularization, pseudo-labeling, and co-training improve prediction-level robustness, they often provide insufficient feature-space organization for anatomically complex structures, especially small organs and ambiguous boundary regions with large intra-class variations. To address this issue, we propose Variation-Conditioned Distributional Proxy Learning (VCDP), a plug-and-play training-only regularization module for semisupervised 3D medical image segmentation. VCDP represents each class with a learnable Gaussian distribution for shared class semantics and multiple variation prototypes for fine-grained intra-class patterns. A unified variation-conditioned compatibility score is further formulated to fuse distributional similarity and soft variation aggregation, guiding voxel embeddings to align with both global organ identity and local anatomical variations. VCDP is attached to decoder features during training and removed during inference, introducing no additional inference cost. Experiments on multi-organ segmentation benchmarks show that VCDP improves most evaluated baselines, particularly for small, ambiguous, and highly variable organs. Our anonymous code is released at [https://anonymous.4open.science/r/VCDP_](https://anonymous.4open.science/r/VCDP_)code-41ED.  \nIndex Terms—Semi-Supervised Segmentation, Medical Image Segmentation, Proxy Learning, Intra-Class Variation, Representation Learning  \nI. INTRODUCTION  \nMedical image segmentation is a fundamental task in medical image analysis and plays an important role in clinical applications such as disease diagnosis, treatment planning, preoperative assessment, and therapy monitoring [1], [2] . In 3D multi-organ segmentation, models are required to delineate multiple anatomical structures from volumetric CT or MRI scans, where accurate voxel-wise predictions are essential for reliable clinical decision-making. Despite the remarkable progress of deep learning-based segmentation methods, their success typically relies on dense voxel-level annotations, which are expensive and time-consuming to acquire and require substantial expertise from trained clinicians [3]–[5] .  \n†Corresponding author.  \nTo mitigate the limitations caused by insufficient annotations, semi-supervised medical image segmentation has received increasing attention in recent years. It aims to reduce annotation cost by learning from a small set of labeled volumes together with abundant unlabeled data [6]–[9] . Representative methods include consistency regularization [10]–[12], pseudolabeling [13], and co-training [14], [15], which encourage models to learn from unlabeled images by enforcing stable or mutually agreed predictions. As illustrated in Fig. 1(a), a typical co-training framework feeds the same unlabeled image into two student networks and encourages their predicted masks to be consistent with each other. In this way, unlabeled data provides additional supervision through crossmodel agreement, making the model less dependent on dense voxel-level annotations. Despite promising results, most of them primarily improve prediction-level robustness by enforcing consistency in the output space, while leaving the feature space insufficiently organized with respect to the complex anatomical variations within each semantic class.  \nThis limitation is particularly pronounced for small organs and ambiguous boundary regions. Anatomi","cbCaioqEwHg3T9Wo","https://ap.wps.com/l/cbCaioqEwHg3T9Wo","pdf",1801570,1,9,"English","en",105,"# Introduction\n## Background on 3D multi-organ segmentation\n## Semi-supervised segmentation approaches\n## Motivation: feature-space organization for intra-class variation\n## Proposed VCDP concept","[{\"question\":\"What problem does VCDP address in semi-supervised 3D medical image segmentation?\",\"answer\":\"VCDP targets insufficient feature-space organization for anatomically complex classes, especially small organs and ambiguous boundary regions where intra-class variation is large.\"},{\"question\":\"How does VCDP represent classes and variations during training?\",\"answer\":\"VCDP represents each class with a learnable Gaussian distribution for shared semantics and uses multiple variation prototypes to capture fine-grained intra-class patterns.\"},{\"question\":\"Does VCDP add inference-time computation?\",\"answer\":\"VCDP is attached to decoder features during training 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