Steer the Sampling, Not the Kernel Grid: Geometry-Guided Sampling Operator for Volumetric Segmentation

Sizhe Wang; Himashi Peiris; Zhaolin Chen

cs.CVAug 26, 2026

Steer the Sampling, Not the Kernel Grid: Geometry-Guided Sampling Operator for Volumetric Segmentation

Authors: Sizhe Wang, Himashi Peiris, Zhaolin Chen

Organizations: Department of Data Science & AI, Faculty of Information Technology, Monash University, Clayton, VIC, Australia

Abstract

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.

Figures & tables

Figure 1: Overall workflow of the proposed modules. (a) GeoSample : per-voxel geometry field, symmetric sampling, and differential-token mixing. (b) Consensus Field : rotation-consistent fusion of geometry fields from the encoder skip and upsampled decoder features for pre-skip alignment. Shown on a U-Net, GeoSample replaces stride- $1$ blocks and stride- $2$ downsampling; Consensus Field is applied at skip connection.

Figure 2: Qualitative comparison on representative cases from BraTS (top), MSD Hepatic Vessel (middle), and TDSC-ABUS (bottom). Shown are input, ground truth, and predictions from the baseline U-Net, DCNv1/v2, Dynamic Downsampling (DCD), and the proposed operator; red boxes mark noticeable segmentation errors reduced by our method.

	MSD Hepatic Vessel			BraTS			TDSC-ABUS			Mean
Model	Dice $\uparrow$	HD95 $\downarrow$	ASSD $\downarrow$	Dice $\uparrow$	HD95 $\downarrow$	ASSD $\downarrow$	Dice $\uparrow$	HD95 $\downarrow$	ASSD $\downarrow$	Dice $\uparrow$	HD95 $\downarrow$	ASSD $\downarrow$
Baseline U-Net	53.5	42.8	8.87	86.1	7.1	1.15	64.4	39.1	7.31	68.0	29.7	5.78
Deformable Conv v1	57.2	37.3	7.93	88.3	6.4	1.07	67.5	33.1	5.83	71.0	25.6	4.94
Deformable Conv v2	56.7	36.3	8.21	88.3	6.5	1.33	66.3	35.4	6.06	70.4	26.1	5.20
Dynamic Downsampling	56.4	34.9	7.40	88.4	6.8	1.14	67.2	33.9	6.87	70.6	25.2	5.13
Proposed	58.2	34.3	7.43	88.9	6.2	0.95	67.4	27.8	5.78	71.5	22.8	4.72

Table 1: Operator-level comparison across datasets (top: Dice/HD95/ASSD). Bottom: model complexity (Params/FLOPs) under evaluation patch sizes.

Backbone	Variant	Overlap			Boundary		Efficiency
		Dice $\uparrow$	Sensitivity $\uparrow$	Specificity $\uparrow$	HD95 $\downarrow$	ASSD $\downarrow$	Params (M) $\downarrow$	FLOPs (G) $\downarrow$
nnU-Net	Baseline	$68.0$	$72.4$	$98.8$	$28.4$	$5.24$	$30.8$	$1250$
nnU-Net	+ Proposed	72.8	$75.3$	$98.5$	25.6	5.03	$17.4$	$750.2$
Swin-UNETR	Baseline	$69.1$	$68.0$	$98.6$	$30.2$	$4.97$	$63.5$	$751.5$
Swin-UNETR	+ Proposed	70.9	$74.2$	$98.7$	27.7	4.88	$64.8$	$802.7$
MedNeXt	Baseline	$66.8$	$69.5$	$99.1$	$29.4$	$5.38$	$2.71$	$50.1$

Table 2: Architecture-level plug-in validation on TDSC-ABUS dataset.

Figure 3: Qualitative plug-in results on TDSC-ABUS (red boxes: improved regions).

Figure 4: Volumetric agreement on TDSC-ABUS. Left: relative volume error (RVE) distributions for different backbones. Right: predicted vs. ground-truth tumour volumes (log scale) for baseline and +Proposed; dashed line denotes $y=x$ .

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Abstract

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