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Efficient Connectivity-Preserving Instance Segmentation with Supervoxel-Based Loss Function
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Extends digital-topology simple voxels to supervoxels (connected sets) and proposes a linear-time, connectivity-preserving loss that penalizes critical false split/merge components for topology-aware segmentation.
Problem
Topological errors (splits and merges) in instance segmentation of curvilinear, filamentous structures such as neuronal arbors; existing topology-aware losses are computationally expensive (n log n to n^2).
Approach
Generalize simple voxels to supervoxels by defining "critical" false-positive and false-negative connected components whose addition or removal changes the number of connected components; penalize them with a loss term computed in linear time via BFS and hash-table checks on precomputed component labels.
Key results
- On DRIVE the proposed loss reaches Dice 0.809 and ARI 0.943 with VOI 0.48, the best among compared methods.
- On EXASPIM the method achieves the best normalized ERL (0.784) and lowest splits per neuron (2.63) while running in linear time (20.12 s/epoch vs 50.68 s for MALIS).
- On ISBI12 it reaches Dice 0.983, the highest, but ARI 0.934 is below DMT's 0.953.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the supervoxel-based topological loss to U-Net | U-Net · DRIVE | VOI: 1.08$\pm$0.01 -> 0.48$\pm$0.01 | Helped |
| Add the supervoxel-based topological loss to U-Net | U-Net · ISBI12 | Dice: 0.980$\pm$0.003 -> 0.983$\pm$0.001 | Helped |
| Add the supervoxel-based topological loss to U-Net | U-Net · CrackTree | Betti Error: 0.52$\pm$0.19 -> 0.51$\pm$0.06 | Helped |
| Add the supervoxel-based topological loss to U-Net | U-Net · EXASPIM | Normalized ERL: 0.719$\pm$0.098 -> 0.784$\pm$0.099 | Helped |
| Add the supervoxel-based topological loss to U-Net | U-Net · EXASPIM | Runtime/Epoch: 10.03$\pm$0.23 sec -> 20.12$\pm$1.15 sec | Hurt |
| Use a positive α in the topological loss (ablation) | U-Net with the proposed loss · Segmentation datasets | Topological accuracy | Helped |
| Tune α and β by dataset (approximately 0.5 and 0.5 on ISBI12; 0.9 and 0.8 on EXASPIM) (ablation) | U-Net with the proposed loss · ISBI12 and EXASPIM | ARI | Mixed |
Surprising findings
- On the EXASPIM 3-d dataset, MALIS achieves higher Dice (0.794) than the proposed method (0.770).
- On CrackTree and ISBI12 the proposed method does not win on every metric; DMT attains better Dice on CrackTree and better ARI/VOI on ISBI12.
Limitations
- Theoretical linear-time algorithm is restricted to tree-structured objects; the general case is super-linear.
- Hyperparameters alpha and beta were set to 0.5 for 2-D datasets and tuned differently for sparse 3-D data.
- Performance gains are mixed across metrics and datasets, with some baselines (DMT, MALIS) winning individual metrics.
Experimental setup
Datasets: DRIVE ISBI12 CrackTree EXASPIM
Benchmarks: DRIVE ISBI12 CrackTree EXASPIM
Metrics: Dice ARI VOI Betti error accuracy splits per neuron edge accuracy normalized ERL runtime per epoch
Baselines: U-Net DIVE Mosin. TopoLoss DMT Gornet clDice MALIS
Builds on: clDice MALIS TopoLoss simple points digital topology
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