Source-linked AI summary
3D Segmentation with Exponential Logarithmic Loss for Highly Unbalanced Object Sizes
Ken C. L. Wong, Mehdi Moradi, Hui Tang, Tanveer Syeda-Mahmood
TL;DR
Highly unbalanced object sizes and computational feasibility remain challenges for detailed 3D medical image segmentation, especially with more than 10 labels. The paper proposes an efficient network and exponential logarithmic loss, achieving strong 20-label brain segmentation with fast convergence and inference.
Problem
Detailed 3D segmentation remains challenging because most networks handle fewer than 10 labels, while small structures are disadvantaged by Dice-loss sensitivity and highly unbalanced object sizes.
Method
The paper combines a computationally efficient network using skip connections and deep supervision with an exponential logarithmic loss that balances label size and segmentation difficulty.
Results
The best exponential-loss setting, LExp(γ = 0.3), gave the best results with smaller standard deviations, while the proposed network converged better than V-Net and segmented volumes in about 0.4 s.
Takeaways & Limitations
The proposed architecture has about 1/14 of V-Net's parameters and is twice as fast, while logarithmic and exponential losses improve segmentation of very small structures.
Abstract
from arXiv · showhide
With the introduction of fully convolutional neural networks, deep learning has raised the benchmark for medical image segmentation on both speed and accuracy, and different networks have been proposed for 2D and 3D segmentation with promising results. Nevertheless, most networks only handle relatively small numbers of labels (<10), and there are very limited works on handling highly unbalanced object sizes especially in 3D segmentation. In this paper, we propose a network architecture and the corresponding loss function which improve segmentation of very small structures. By combining skip connections and deep supervision with respect to the computational feasibility of 3D segmentation, we propose a fast converging and computationally efficient network architecture for accurate segmentation. Furthermore, inspired by the concept of focal loss, we propose an exponential logarithmic loss which balances the labels not only by their relative sizes but also by their segmentation difficulties. We achieve an average Dice coefficient of 82% on brain segmentation with 20 labels, with the ratio of the smallest to largest object sizes as 0.14%. Less than 100 epochs are required to reach such accuracy, and segmenting a 128x128x128 volume only takes around 0.4 s.
1 Introduction
3D medical image segmentation remains challenging when many anatomical labels and highly unbalanced object sizes must be handled under computational constraints. The paper addresses these issues with a computationally efficient architecture and an exponential logarithmic loss.
- Most 3D segmentation networks were evaluated with fewer than 10 labels, limiting evidence for detailed multi-structure segmentation.
- Prior approaches included error-corrective weighting and generalized Dice loss, but they had limitations for Dice optimization or slice consistency.
- Dice loss is unfavorable to small structures because a few misclassified pixels can sharply reduce their coefficient.
- Frequency-based label weighting is nonoptimal for Dice losses because Dice sensitivity is unrelated to relative object sizes.
- The paper proposes exponential logarithmic loss and a fast, efficient architecture combining skip connections and deep supervision.The architecture is reported as having about 1/14 of V-Net’s parameters and twice its speed.
2 Methodology
The method combines a resource-conscious 3D encoder–decoder with skip connections and deep supervision, then uses exponential logarithmic losses to balance structure size and segmentation difficulty. The loss combines logarithmic Dice and weighted cross-entropy terms with tunable nonlinearities.
- 2.1 Proposed Network Architecture: The 3D encoder–decoder uses skip connections, additive branch fusion, and scale-dependent channel and layer allocation for efficient multi-scale processing.Adding branches instead of concatenating them reduces memory consumption.
- 2.1 Proposed Network Architecture: The network uses convolutional blocks, softmax output, augmentation, Adam optimization, batch size one, and 100 training epochs.Augmentation uses rigid rotations, shifting, and scaling; experiments run on a TITAN X GPU with 12 GB memory.
- 2.1 Proposed Network Architecture: Deep supervision provides more direct backpropagation for faster convergence and better accuracy, while omitting the largest block’s tensor limits memory use.The omission enables training on a GPU with 12 GB of memory.
- 2.2 Exponential Logarithmic Loss: The exponential loss combines logarithmic Dice loss and weighted exponential cross-entropy using separate component weights.The combined form is LExp = wDiceLDice + wCrossLCross.
- 2.2 Exponential Logarithmic Loss: The logarithmic Dice loss emphasizes less accurately segmented labels rather than relying only on size-based weighting.Label weights are used for cross-entropy, while the logarithmic Dice transformation addresses segmentation accuracy.
- 2.2 Exponential Logarithmic Loss: Exponents γDice and γCross control loss nonlinearities, with γ = 0.3 improving both low- and high-accuracy regions relative to γ ≥ 1.For γ = 0.3, the loss has an inflection point around x = 0.5 and avoids the over-suppression observed with γ = 2.
3 Experiments
Experiments on 43 brain MR images evaluated seven loss/network cases for 20-label segmentation with highly unbalanced structure sizes. The proposed network and exponential loss achieved favorable accuracy, convergence, qualitative segmentation, and efficiency.
- Dataset: 43 brain MR images provided expert-reviewed training and validation data with 20 labels, including background.The images were T1-weighted MP-RAGE scans with varied sizes and spacings, resampled before experimentation.
- Dataset: 0.14% was the ratio between the smallest and largest non-background structures, while background occupied 93.5% of each image on average.The smallest and largest structures occupied 0.07% and 50.24%, respectively.
- Loss comparison: LExp(γ = 0.3) produced the best results among the tested loss cases and had smaller standard deviations than LExp(γ = 1).LExp(γ = 2) was ineffective, consistent with over-suppression as accuracy increased.
- Network comparison: The proposed network outperformed V-Net on this problem when both used the best loss function.The V-Net comparison showed poorer performance for all but the linear Dice loss and LExp(γ = 2).
- Convergence: About 80 epochs were required for the logarithmic Dice loss, LExp(γ = 1), and LExp(γ = 0.3) to converge, with LExp(γ = 0.3) slightly better.The proposed network also converged better than V-Net, especially during earlier epochs.
- Qualitative results: The linear Dice loss missed small structures, whereas logarithmic Dice, LExp(γ = 1), and LExp(γ = 0.3) produced the best example segmentations.Weighted cross-entropy over-segmented some structures, while LExp(γ = 2) produced noisier segmentation.
- Efficiency: The proposed network used around 5 million parameters versus V-Net's 71 million and segmented a 128×128×128 volume in about 0.4 seconds versus 0.9 seconds.This corresponds to a 14-fold parameter difference and lower segmentation time.
4 Conclusion
The paper proposes a resource-efficient 3D segmentation network and exponential logarithmic loss for very small structures. The architecture is substantially smaller and faster than V-Net, while the combined loss improves segmentation accuracy and precision.
- Conclusion: The paper proposes a network architecture optimized for 3D image segmentation and a loss function for segmenting very small structures.The network has about 1/14 of V-Net's parameters and is twice as fast.
- Conclusion: The logarithmic Dice loss outperforms linear Dice loss, while its weighted sum with weighted cross-entropy outperforms the individual losses.The exponential form provides further control over loss nonlinearities to improve segmentation accuracy and precision.