clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation (2003.07311v7)

Abstract: Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.

• The paper introduces clDice as a connectivity-aware metric that preserves topological properties in tubular segmentation through centerline overlap.
• The study develops a differentiable soft-clDice variant enabling neural networks like U-Net to achieve improved topological accuracy over traditional loss functions.
• Experimental validation across multiple datasets shows enhanced precision and recall for maintaining connected structures and reducing segmentation errors.

Analyzing clDice: A Novel Loss Function for Tubular Structure Segmentation

The segmentation of tubular and network-like structures, such as blood vessels, neurons, and road networks, plays a vital role in various fields including medical imaging, remote sensing, and industrial quality control. The paper "clDice - a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation" introduces a novel methodology, centerlineDice (clDice), which emphasizes the preservation of topological properties, particularly connectivity, in segmenting such structures. This paper provides both theoretical insights and practical applications, demonstrating the efficacy of clDice in maintaining the integrity of segmented networks.

Overview of clDice

The authors propose clDice as a connectivity-aware metric designed to evaluate the segmentation of tubular and linear structures by measuring the intersection of the segmentation masks and their morphological skeleta. The approach aims to ensure topologically accurate segmentations, which is essential in preventing errors that could significantly affect downstream analytical tasks, such as simulating hemodynamics or planning navigational routes. The clDice measure guarantees topology preservation up to homotopy equivalence, making it distinct from traditional overlap-based measures such as the Dice coefficient that fail to adequately capture topological discrepancies.

To further integrate clDice into machine learning for segmentation, the authors introduce a differentiable variant known as soft-clDice, which allows neural networks to be trained to prioritize topologically consistent segmentations. The paper demonstrates the effectiveness of soft-clDice across multiple datasets, highlighting improvements in connectivity accuracy and graph similarity metrics.

Theoretical Foundations

Central to the clDice metric is its theoretical foundation, proving that it ensures topological preservation by satisfying homotopy equivalence between the predicted and true segmentation masks in both 2D and 3D domains. The paper's proofs are rigorous, leveraging fundamental concepts from algebraic topology, such as Betti numbers and the Euler characteristic, to ensure that segmentation alterations do not lead to incorrect topology, which could manifest as disconnected components or unwarranted holes.

Experimental Validation

The empirical evaluation of soft-clDice spans five public datasets, including applications in medical imaging and remote sensing. The quantitative results indicate that training models with soft-clDice outperforms baseline models trained on traditional loss functions, such as cross-entropy or soft-Dice, in terms of both volumetric and topological accuracy. Specifically, models optimized with soft-clDice achieve a better balance between precision and recall for connected structures, thereby reducing both false positives (ghosts) and false negatives (misses) post-skeletonization.

The methodology is validated against state-of-the-art networks, such as U-Net and fully convolutional networks (FCNs), in both 2D and 3D contexts. The improvements are most notable in complex datasets characterized by significant topological variation, underscoring the loss function's robustness and versatility.

Practical Implications and Future Directions

The introduction of clDice and its soft variant offers a significant advancement in the segmentation of tubular structures, with potential applications extending beyond those demonstrated in the paper. The ability to incorporate topological constraints into the loss function directly contributes to more reliable and clinically relevant segmentations, potentially impacting fields such as biomedical research, urban planning, and automated cartography.

Future developments could refine the differentiable skeletonization process and extend the methodology to multiclass segmentation tasks, further broadening clDice's applicability. Additionally, integrating clDice into real-time systems could facilitate on-the-fly analysis in clinical and field settings, offering immediate feedback and segmentation refinement.

In summary, this paper delivers a well-founded and practically potent method for enhancing the topological fidelity of tubular structure segmentation, providing a useful tool for researchers and practitioners in computer vision and allied disciplines.