GraphCL: Graph-based Clustering for Semi-Supervised Medical Image Segmentation

Thank you for your thorough review and constructive feedback on our manuscript. We are grateful for your positive remarks and are pleased that you found our work to be a valuable contribution to the field of semi-supervised medical image segmentation.

Q1: The standard deviation of the performance is missing, however. The authors would benefit by showing standard deviation and conducting t-test to determine if the performance improvement is statistically significant or not.

A1: Thank you for your valuable feedback. We appreciate your suggestion regarding the inclusion of standard deviation and statistical significance analysis. Since we have four metrics: Dice, Jaccard, 95HD, and ASD, where Dice and Jaccard indicate that higher values are better, while 95HD and ASD indicate that lower values are better, it is not possible to compute the standard deviation as suggested by the reviewer because these four metrics represent different meanings. Consequently, since the standard deviation cannot be computed, the t-value also cannot be calculated. We sincerely appreciate the reviewer’s suggestion from a statistical perspective. Thank you for this constructive suggestion that has helped improve our work.

Q1: About the novelty

A1: For the importance of graph structural information, our method leverages two types of graph structural information: spatial relationships between voxels/pixels and semantic relationships based on feature similarity. Specifically, we construct dense instance graphs to capture structural information from CNN features, propagate this information through GCNs, and employ correlation clustering to group similar nodes. These mechanisms collectively enhance the model's expressive capability, allowing it to better utilize the structural information within images. Meanwhile, medical images inherently exhibit topological relationships in anatomical structures, such as organ connectivity and tissue continuity. Given the limited availability of labeled data, leveraging these structural priors is crucial for semi-supervised learning.

For the novelty of the graph-based perspective, unlike Sun et al [1], our method does not merely use graph cuts as a post-processing step. Instead, it integrates graph learning in an end-to-end manner, modeling both local and global structural relationships while leveraging graph clustering to refine feature representations, rather than focusing solely on boundary optimization. Compared to Li et al [2], we are the first to introduce correlation clustering for SSMIS and propose a k-less clustering strategy, which automatically determines the number of clusters, eliminating the reliance on hyper-parameter selection. Existing graph-based methods are primarily used for regularization (e.g., graph cuts) or consistency enforcement. In contrast, our work is the first to model data structure as a learnable component, utilizing graph clustering to discover latent semantic relationships.

Q2: About SGM

A2: The Structural Graph Model (SGM) mentioned in the paper serves as a fundamental framework for semi-supervised medical image segmentation (SSMIS), designed to effectively integrate both labeled and unlabeled medical image data. Although Figure 2 does not explicitly label the SGM module, it is embedded within the model—for instance, as a graph-structured processing layer following feature extraction or incorporated into the design of graph-based loss functions. The core working principle of SGM relies on constructing a graph structure to enable semi-supervised learning, where pixels or regions of an image are represented as nodes, and their similarities form the edges. Labeled data nodes act as "anchor points," providing supervised information, while unlabeled nodes receive semantic information through graph convolution or message-passing mechanisms, thereby facilitating label propagation. This approach leverages the relational structure of the graph to propagate knowledge from limited labeled data to unlabeled samples.

Q3: About internal spatial structure

A3: We recognize that our original description may have been unclear - the "internal spatial structure" we refer to does not originate directly from the CNN feature maps themselves, but rather emerges from the graph representation of sample relationships. Specifically, in our framework: (1) each node in the instance graph represents a feature vector extracted by a standard CNN from an individual sample; (2) the spatial relationships are then constructed at the graph level through learned connectivity patterns between these node features; and (3) the structure scores quantify similarity based on these graph topological relationships rather than direct spatial correlations in the CNN features.

Q4: About the Data Structure Analyzer

A4: The Data Structure Analyzer (DSA) is primarily responsible for computing structure scores, which quantify the similarity between different samples and guide the GCN in graph construction. In Figure 2 , this component is positioned between the CNN feature extraction stage and the GCN processing stage. In Eq. (12), $\mathbf{X}$ represents the features extracted by the CNN, serving as the graph signal. In Eq. (13), $\mathbf{X}\_{\text{sa}}$ denotes the structure scores. Specifically, $\mathbf{X}\_{\text{sa}}$ is computed from $\mathbf{X}$ and is utilized to construct the adjacency matrix $\hat{\mathbf{A}}$, which models the relationships between samples.

Q5: About the larger dataset

A5: To further validate the effectiveness of our model, we conducted experiments on the BraTS 2019 dataset. The BraTS 2019 dataset comprises multi-institutional pre-operative MRI scans from 335 patients. It can be observed that our method achieves a significant improvement on the large-scale BraTS 2019 dataset, particularly with the Dice score increasing from 78.11% to 82.02%, demonstrating the superiority of our approach on the large-scale datasets.

Q1: Essential References Not Discussed

A1: We acknowledge the relevance of works like GraphSAGE (neighborhood aggregation)[1], GAT (attention mechanisms)[2], Graph U-Nets (hierarchical pooling)[3] and MixMatch (unifiy dominant approaches)[4]. Different from this methods, GraphL uniquely address semi-supervised medical image segmentation by constructing dense instance graphs for structural similarity learning and k-less clustering, leveraging both labeled and unlabeled data. We will incorporate these comparisons in the revised manuscript to improve our work.

Q2: Lack insightful discussion of data structure information

A2: Medical images exhibit strong geometric regularity in organ/lesion morphology (e.g., topological connectivity of cardiac chambers). Our graph-based approach leverages this by enforcing structural consistency constraints on segmentation boundaries when annotations are scarce and propagating anatomical knowledge from labeled to unlabeled regions through graph convolutional message passing. From the ablation study in Table 4, our method achieves significant performance improvement by incorporating graph structural information into the CNN framework, as it effectively preserves the tree-like branching patterns of capillaries at local scales while simultaneously maintaining the spatial constraints between vessels and organs at global scales.

Q3: Computational complexity

A3: To empirically assess the computational cost of our approach, we conduct experiments on the BraTS2019 dataset using an NVIDIA RTX 3090 GPU. During the training phase, we set the batch size to 4, following previous studies, and observe a memory consumption of only 3697 MiB for GPU and 9 GiB for system memory. In the inference phase, the GPU memory consumption further reduces to 2745 MiB, while the system memory remains at 9 GiB. Additionally, our model exhibits a computational complexity of 119.512G FLOPs, which is considered moderate, and a parameter count of 15.747M, indicating a lightweight architecture. These results demonstrate that our method maintains computational feasibility even on large-scale datasets, addressing potential concerns regarding scalability. Furthermore, the total training time is 2 hours, further confirming the efficiency of our approach.

Q4:Discussing potential limitations in GCNs

A4: Compared to traditional methods, GCN-based approaches require additional matrix multiplications and neighborhood aggregation steps, which can increase computational complexity, especially for large-scale datasets. To mitigate this issue, existing optimization techniques such as mini-batch training, efficient sparse matrix operations, and model pruning can be employed. Moreover, exploring lightweight graph neural network variants or hybrid approaches could further reduce computational costs while maintaining performance.

Q5:Visualize the graph structures and clustering results

A5: To enhance the clarity and intuitiveness of our method, we have added t-SNE visualizations at https://anonymous.4open.science/r/tsne-E479/Visualization.pdf.

Q6: Clarify the impact of different dataset sizes on performance improvements

A6: To further validate the effectiveness of our model, we conducted additional experiments on the BraTS 2019 dataset (Labeled 10% and Unlabeled 90%). It can be observed that our method achieves a significant improvement on the large-scale BraTS 2019 dataset, particularly with the Dice score increasing from 78.11% to 82.02%, demonstrating the superiority of our approach on large-scale datasets.

Q7: Performance on imbalanced class distribution

A7: The ACDC dataset is a classic class-imbalanced dataset, where the pixel distribution differences between the myocardium and ventricular cavities provide a real-world scenario for studying imbalanced segmentation problems. As shown in Table 2, our method demonstrates a significant improvement, which validates its effectiveness on imbalanced data.

Q8: Considering the very limited number of labeled data

A8: We consider the very limited number of 20% labeled data in Table 1 and and one labeled data (1/70) in Table 2, experimental results demonstrate that our method achieves significant performance improvement even with limited training data.