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Efficient Connectivity-Preserving Instance Segmentation with Supervoxel-Based Loss Function

Anna Grim, Jayaram Chandrashekar, Uygar Sumbul

TL;DR

The paper tackles topological errors in 3D neuron instance segmentation by extending simple voxels to connected supervoxels and introducing a differentiable, topology-preserving loss with linear-time complexity. A key contribution is the notion of critical components, generalizing non-simple voxels to supervoxels, along with an $\mathcal{O}(n)$ method to identify and penalize splits and merges during training. The framework augments a standard voxel loss with structure-level penalties and is architecture-agnostic, showing state-of-the-art performance on topology-relevant metrics across 2D and 3D datasets, including a new public mouse-brain benchmark. This approach enables scalable, connectivity-preserving neuron reconstructions, reducing manual proofreading and facilitating large-scale connectomics analysis.

Abstract

Reconstructing the intricate local morphology of neurons and their long-range projecting axons can address many connectivity related questions in neuroscience. The main bottleneck in connectomics pipelines is correcting topological errors, as multiple entangled neuronal arbors is a challenging instance segmentation problem. More broadly, segmentation of curvilinear, filamentous structures continues to pose significant challenges. To address this problem, we extend the notion of simple points from digital topology to connected sets of voxels (i.e. supervoxels) and propose a topology-aware neural network segmentation method with minimal computational overhead. We demonstrate its effectiveness on a new public dataset of 3-d light microscopy images of mouse brains, along with the benchmark datasets DRIVE, ISBI12, and CrackTree.

Efficient Connectivity-Preserving Instance Segmentation with Supervoxel-Based Loss Function

TL;DR

The paper tackles topological errors in 3D neuron instance segmentation by extending simple voxels to connected supervoxels and introducing a differentiable, topology-preserving loss with linear-time complexity. A key contribution is the notion of critical components, generalizing non-simple voxels to supervoxels, along with an method to identify and penalize splits and merges during training. The framework augments a standard voxel loss with structure-level penalties and is architecture-agnostic, showing state-of-the-art performance on topology-relevant metrics across 2D and 3D datasets, including a new public mouse-brain benchmark. This approach enables scalable, connectivity-preserving neuron reconstructions, reducing manual proofreading and facilitating large-scale connectomics analysis.

Abstract

Reconstructing the intricate local morphology of neurons and their long-range projecting axons can address many connectivity related questions in neuroscience. The main bottleneck in connectomics pipelines is correcting topological errors, as multiple entangled neuronal arbors is a challenging instance segmentation problem. More broadly, segmentation of curvilinear, filamentous structures continues to pose significant challenges. To address this problem, we extend the notion of simple points from digital topology to connected sets of voxels (i.e. supervoxels) and propose a topology-aware neural network segmentation method with minimal computational overhead. We demonstrate its effectiveness on a new public dataset of 3-d light microscopy images of mouse brains, along with the benchmark datasets DRIVE, ISBI12, and CrackTree.
Paper Structure (20 sections, 16 theorems, 20 equations, 13 figures, 4 tables)

This paper contains 20 sections, 16 theorems, 20 equations, 13 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Method
  4. Critical Components
  5. False Splits
  6. False Merges
  7. Computing Critical Components
  8. Penalizing Critical Topological Mistakes
  9. Experiments
  10. Conclusion
  11. Characterizations of Critical Components
  12. General Case
  13. Special Case
  14. Computation
  15. Extension to Affinity Models
  16. ...and 5 more sections

Key Result

Theorem 1

A component $C\in\mathcal{S}_y(\hat{y}_\shortminus)$ is negatively critical if and only if there exists an $A\in\mathcal{S}(y\cap N(C))$ with $A\supseteq C$ such that either $(1)$$A=C$ or $(2)$$\exists\, v_0, v_k\in A\setminus C$ such that there does not exist a path $(v_0,\ldots, v_k)\subseteq N(C)

Figures (13)

  • Figure 1: Top: Image patches of ground truth and predicted segmentations. Bottom: False negative mask with the component $C$ highlighted in red. $C$ is negatively critical since its removal changes the connectivity of the ground truth.
  • Figure 2: Top: Image patches of ground truth and predicted segmentations. Bottom: False positive mask with a single component $C$ highlighted. $C$ is positively critical since its removal changes the number of connected components.
  • Figure 3: Segmentation of a 512x512 image from the ISBI12 dataset. The critical components of this prediction were computed in 1.41 seconds using code at https://github.com/AllenNeuralDynamics/supervoxel-loss.
  • Figure 4: Visualization of the loss in the prediction in Fig. \ref{['fig:runtime']}.Left: As $\alpha$ varies from 0 to 1, the loss places higher penalties on critical components. Right: As $\beta$ varies from 0 to 1, the loss shifts from assigning higher penalties to negatively critical to positively critically components.
  • Figure 5: Qualitative results on three 2d datasets.
  • ...and 8 more figures

Theorems & Definitions (30)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Corollary 1
  • Definition 3
  • Theorem 2
  • Corollary 2
  • Corollary 3
  • Theorem 3
  • Lemma 1
  • ...and 20 more