Source-linked AI summary
Steer the Sampling, Not the Kernel Grid: Geometry-Guided Sampling Operator for Volumetric Segmentation
Sizhe Wang, Himashi Peiris, Zhaolin Chen
TL;DR
Precise volumetric segmentation remains difficult for thin structures because fixed-grid operations can distort fine geometry and directional cues. GeoSample steers symmetric samples using local orientations and bounded step sizes while unifying refinement and downsampling, and it consistently improves segmentation quality across benchmarks and backbones while reducing U-Net parameters.
Problem
Fixed-grid refinement and downsampling can suppress or alias fine structures and distort boundary geometry, while existing adaptive offsets lack structured symmetry and orientation consistency.
Method
GeoSample predicts local rotation frames and adaptive step sizes for symmetric geometry-guided sampling, with a cross-scale consensus mechanism for encoder–decoder alignment.
Results
Across three public benchmarks and plug-in validation, GeoSample consistently improves segmentation quality, especially boundary metrics, while reducing U-Net parameters.
Takeaways & Limitations
The operator provides a plug-in alternative to fixed-grid convolution and pooling that can improve volumetric segmentation across backbones without redesigning their macro-architectures.
Takeaways & Limitations
Future work must reduce the memory and wall-clock overhead of interpolation-based sampling and improve early-training stability.
Abstract
from arXiv · showhide
Accurate 3D segmentation is central to quantitative lesion assessment and anatomy mapping for clinical planning and follow-up. Thin, elongated, and fine anatomical/pathological structures (e.g., vessels) are a particularly challenging case: a one-voxel boundary error can disconnect a branch and change clinically relevant topology. In encoder-decoder networks (e.g., U-Net), repeated downsampling and fixed-grid convolution blur or alias fine structures and weaken orientation cues, so early mistakes propagate across scales. We propose a geometry-guided local operator that steers where features are sampled, rather than deforming convolutional kernels, under a single formulation for both feature refinement (stride 1) and resolution reduction (stride > 1). At each voxel, it predicts a local orientation and bounded step sizes, samples symmetrically along these directions, and transforms paired samples into compact geometric and boundary cues with lightweight mixing; a cross-scale consensus aligns encoder and decoder features at skip connections to reduce geometric mismatch. Replacing all stride 1 and stride 2 operators in a 3D U-Net yields consistent improvements on BraTS, MSD Hepatic Vessel, and TDSC-ABUS, with notably better boundary metrics (e.g., BraTS Dice 86.1 to 88.9, HD95 7.1 to 6.2; TDSC-ABUS HD95 39.1 to 27.8) while reducing parameters from 2.3M to 0.8M. We further demonstrate that the operator can be integrated into other backbones (e.g., nnU-Net, Swin-UNETR, and MedNeXt) without changing their macro-architectures while providing consistent performance gains.
1 Introduction
Thin and anisotropic structures remain vulnerable to fixed-grid refinement and downsampling, motivating GeoSample’s geometry-guided, symmetric sampling and cross-scale alignment within existing encoder–decoder networks.
- Thin, elongated, or anisotropic structures can suffer continuity breaks and biased measurements from small boundary shifts.These targets often occupy only a few voxels, making precise boundary localisation clinically relevant.
- Fixed-grid refinement and downsampling can suppress high-frequency details, alias fine structures, and distort boundary geometry and directional cues.Orientation-agnostic antialiasing only partially addresses instability under downsampling.
- Existing adaptive sampling methods learn unconstrained offsets, lacking structured geometric regularisation, symmetry, and orientation consistency.The resulting sampling patterns may vary irregularly across neighbouring voxels.
- GeoSample predicts voxel-wise SO(3) rotation frames and adaptive step sizes to steer structured symmetric sampling instead of deforming convolutional kernels.It converts paired samples into compact gradient- and curvature-like cues with lightweight mixing.
- A rotation-consistent Consensus Field aligns encoder and decoder geometry at skip connections, improving robustness across backbones.The mechanism addresses geometric mismatch during feature fusion.
- The operator unifies stride 1 refinement and stride > 1 downsampling while replacing fixed-grid convolution and pooling primitives.This provides one formulation for feature refinement and resolution reduction.
2 Methodology
GeoSample is a unified, geometry-guided operator for feature refinement and downsampling that steers symmetric sampling using local rotation frames and bounded step sizes. Consensus Field aligns encoder and decoder geometry at skip connections, while differential cues provide compact gradient- and curvature-like signals.
- GeoSample: GeoSample replaces stride-1 refinement blocks and stride > 1 downsampling with one geometry-guided local operator.It predicts a voxel-wise geometric field and uses it to steer symmetric sampling with lightweight mixing.
- Downsampling with directional-signal preservation: During downsampling, average pooling supplies a stable low-pass path while pooled directional magnitudes preserve odd-signal energy.A geometry-conditioned compensation term augments the pooled representation.
- Consensus Field: Consensus Field fuses decoder and encoder rotation fields and step sizes before skip concatenation to reduce geometric mismatch.Rotation fields are fused by quaternion spherical interpolation, while step sizes use the same consensus gate.
- Geometry field prediction: Each voxel predicts a local SO(3) rotation frame and bounded step sizes to define structured sampling directions.The frame is represented with a unit quaternion, and the first K rotated canonical axes provide the sampling directions.
- Symmetric sampling and oriented differentials: Symmetric samples are transformed into step-size-normalised even context, odd directional, and second-order curvature-like cues.Step-size normalisation makes the cues comparable across scales, while symmetric pairing exposes odd/even components.
- Compact differential tokens and mixing: The directional cue is sign-invariant because reversing a sampling direction also reverses its paired difference, preserving the tensor product.This design yields stable directional tokens without frame-sign jitter.
3 Experiments
Experiments evaluate the operator across three modalities and compare qualitative segmentation, operator-level performance, complexity, and plug-in performance across backbones.
- The evaluation uses BraTS, MSD HepaticVessel, and TDSC-ABUS with a fixed-seed 75/10/15 train/validation/test split and shared dataset-specific pipelines.
- Qualitative comparisons cover baseline U-Net, DCNv1/v2, Dynamic Downsampling, and the proposed operator, with red boxes marking noticeable errors reduced by the method.
- The U-Net replacement reduces Params from 2.3M to 0.8M and FLOPs from 194.8G to 108.9G.The efficiency comes from symmetric samples and compact token mixing rather than dense grids or heavy dynamic branches.
- Plug-in validation on TDSC-ABUS improves overlap and boundary metrics across nnU-Net, Swin-UNETR, and MedNeXt.Reported changes are Dice +1.8–+4.8, Sens. +2.9–+6.2, HD95 −2.5–−5.2, and ASSD −0.09–−0.49, with specificity ≥98.2%.
- The largest plug-in gain occurs on nnU-Net, where Dice changes from 68.0 to 72.8 while Params decrease from 30.8M to 17.4M and FLOPs from 1250G to 750G.
- Removing geometry-aware differentials reduces Dice/HD95/ASSD from 67.4/27.8/5.78 to 54.3/51.0/10.71, while removing Consensus Field reduces them to 58.4/48.2/8.52.
4 Conclusion
The conclusion presents GeoSample as a geometry-guided operator that improves segmentation quality, especially boundary metrics, across benchmarks and plug-in settings while reducing U-Net parameters. Future work targets interpolation-related memory and wall-clock overhead and early-training stability.
- GeoSample predicts local orientations to steer symmetric sampling and extract geometric signals for refinement and downsampling.
- Across three public benchmarks and plug-in validation, GeoSample consistently improves segmentation quality, especially boundary metrics, while reducing U-Net parameters.
- Future work will target memory and wall-clock overhead from interpolation-based sampling and improve early-training stability.