Boundary loss for highly unbalanced segmentation (1812.07032v4)

Abstract: Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy, are based on integrals over the segmentation regions. Unfortunately, for highly unbalanced segmentations, such regional summations have values that differ by several orders of magnitude across classes, which affects training performance and stability. We propose a boundary loss, which takes the form of a distance metric on the space of contours, not regions. This can mitigate the difficulties of highly unbalanced problems because it uses integrals over the interface between regions instead of unbalanced integrals over the regions. Furthermore, a boundary loss complements regional information. Inspired by graph-based optimization techniques for computing active-contour flows, we express a non-symmetric $L_2$ distance on the space of contours as a regional integral, which avoids completely local differential computations involving contour points. This yields a boundary loss expressed with the regional softmax probability outputs of the network, which can be easily combined with standard regional losses and implemented with any existing deep network architecture for N-D segmentation. We report comprehensive evaluations and comparisons on different unbalanced problems, showing that our boundary loss can yield significant increases in performances while improving training stability. Our code is publicly available: https://github.com/LIVIAETS/surface-loss .

• The paper introduces a boundary loss that shifts segmentation from region-based to contour-based analysis, effectively addressing data imbalance.
• It demonstrates improved metrics, notably boosting the Dice coefficient in ISLES and WMH tasks by reducing error bias.
• The method enhances training stability and spatial regularization, ensuring more accurate lesion delineation in challenging medical images.

Boundary Loss for Highly Unbalanced Segmentation: An Overview

The paper, "Boundary Loss for Highly Unbalanced Segmentation," addresses a critical problem in semantic segmentation, particularly within medical imaging: the training instabilities caused by highly imbalanced data. Traditional loss functions like Dice and cross-entropy, though prevalent, often falter when dealing with imbalance, as they rely on integrals across the segmentation regions that vary considerably in magnitude across classes.

Core Contribution

The authors introduce a boundary loss that functions within a contour space rather than a regional space. This approach leverages distances over region interfaces instead of within unbalanced regions themselves. The boundary loss is integrated seamlessly with standard convolutional neural networks (CNNs) used for N-D segmentation tasks, enabling its straightforward application across different architectures and datasets.

Theoretical Underpinnings

The proposed boundary loss takes inspiration from graph-based optimization techniques that are used in active-contour models. By expressing a non-symmetric $L_2$ distance in terms of regional integrals, the method bypasses the complexities of local differential computations, connecting directly with regional softmax probabilities. This allows for a simple combination with conventional regional losses.

Empirical Investigations

The authors validate their method on two challenging tasks: Ischemic Stroke Lesion segmentation (ISLES) and White Matter Hyperintensities segmentation (WMH). They demonstrate that incorporating boundary loss yields improved performance, with notable gains in Dice and Hausdorff metrics compared to using standard losses independently.

1. Performance Metrics: The boundary loss led to substantial improvements in performance. For instance, in ISLES, it increased the Dice coefficient when added to Generalized Dice Loss (GDL), significantly reducing the error bias encountered with highly imbalanced class distributions.
2. Training Stability: The boundary loss not only enhanced the accuracy but also stabilized the training process. This is particularly important in medical image segmentation, where the precise delineation of small structures such as lesions is critical.

Practical and Theoretical Implications

The introduction of a boundary loss offers pragmatic advantages for segmentation tasks with imbalanced datasets, prevalent in medical imaging scenarios. By providing complementary information to standard regional losses, this method enhances model robustness and accuracy without adding computational complexity.

• Spatial Regularization: The integration of distance-to-boundary information inherently adds a form of spatial regularization, smoothing the approximated contours and potentially providing more accurate boundary predictions in noisy imaging conditions.
• Future Directions: Extending this approach to multi-region segmentation could be valuable, addressing constraints involving multiple competing structures and class-specific delineation challenges.

Final Thoughts

This paper contributes a significant advancement in the domain of semantic segmentation by handling imbalance more effectively. It opens pathways for developing more refined segmentation models that are not only performance-efficient but also computationally considerate. For future research, examining how this boundary loss interacts with complex topologies and how it could be adapted for multi-class segmentation challenges would be beneficial pursuits, potentially enriching its applicability in diverse real-world scenarios.