Reducing the Gap Between Spatial and Space-Filling Curve Neighbors in 3D Point Cloud Segmentation

Konan Sasaki; Junya Komori; Kazuhiro Hotta

cs.CVOct 14, 2026

Reducing the Gap Between Spatial and Space-Filling Curve Neighbors in 3D Point Cloud Segmentation

Authors: Konan Sasaki, Junya Komori, Kazuhiro Hotta

Organizations: Meijo University, 1-501 Shiogamaguchi, Tempaku-ku, Nagoya, Aichi 468-8502, Japan · Asia Air Survey Co., Ltd., Shinyuri 21 Bldg., 1-2-2 Manpukuji, Asao-ku, Kawasaki, Kanagawa 215-0004, Japan

Abstract

As a lightweight and highly accurate method for nearest-neighbor search in 3D point clouds, approaches based on space-filling curves (SFC) have been proposed. However, due to the inherent properties of SFC, a gap arises between proximity relationships along the SFC and those in the original Euclidean space. In this study, we propose a loss function that reduces the influence of this gap. Specifically, we compute the distances between adjacent points along the SFC and train the model to optimize feature similarity between pairs of points that are distant from each other in the original 3D space. We incorporate the proposed method into a high-performing 3D point cloud segmentation model and evaluate its effectiveness on three datasets. The results demonstrate that the proposed method outperforms conventional methods on both indoor and outdoor point cloud datasets.

Figures & tables

Figure 1: The gap between neighboring points in the original 3D space and those on the SFC. SFC-based serialization enables efficient neighborhood selection without performing the large number of distance calculations required by KNN. However, due to the characteristics of the SFC, points that are far apart in the original 3D space may be treated as neighboring points on the SFC (upper right). Conversely, points that are close to each other in the original 3D space may be treated as distant points on the SFC (lower right).

Figure 2: Visualization of adjacent points on the SFC that are spatially distant from each other. Point pairs whose distances exceed the threshold in Eq. 2 of the proposed method are visualized by connecting them with black lines. Since this point cloud is taken from S3DIS dataset during the training of Point Transformer V3, data augmentation has been applied.

Figure 3: Overview of DAS Loss. The loss is adopted when the distance between adjacent points on the SFC exceeds the sum of the mean and standard deviation of all adjacent-point distances. If the class labels of the two points are identical, their feature representations are encouraged to be similar; otherwise, they are encouraged to be dissimilar.


Class	PTv3 [ 28 ] (%)		Ours (%)
Ground	$95.59$ $\pm$	$0.13$	95.97 $\pm$	0.08
Vegetation	$92.14$ $\pm$	$0.17$	92.37 $\pm$	0.14
Cars	$83.77$ $\pm$	0.06	84.28 $\pm$	$0.38$
Trucks	$24.64$ $\pm$	$2.56$	31.83 $\pm$	2.24
Power lines	$92.08$ $\pm$	0.15	93.18 $\pm$	$0.61$

Table 1: Evaluation of the proposed method on DALES.


Class	PTv3 [ 28 ] (%)		Ours (%)
Ceiling	$91.35$ $\pm$	$0.65$	93.69 $\pm$	0.50
Floor	$98.22$ $\pm$	$0.06$	98.40 $\pm$	0.04
Wall	$83.66$ $\pm$	$0.79$	84.12 $\pm$	0.26
Beam	$0.00$ $\pm$	$0.00$	$0.00$ $\pm$	$0.00$
Column	34.21 $\pm$	1.40	$32.25$ $\pm$	$2.23$

Table 2: Evaluation of the proposed method on S3DIS.


Class	PTv3 [ 28 ] (%)		Ours (%)
Wall	$87.38$ $\pm$	0.32	87.61 $\pm$	$0.55$
Floor	$95.64$ $\pm$	0.05	95.88 $\pm$	$0.16$
Cabinet	$72.39$ $\pm$	0.79	73.12 $\pm$	$1.20$
Bed	$84.30$ $\pm$	0.82	87.09 $\pm$	$1.69$
Chair	$91.73$ $\pm$	$0.56$	92.97 $\pm$	0.44

Table 3: Evaluation of the proposed method on ScanNet V2.


Method	ScanNet V2 [ 7 ] (%)	S3DIS [ 1 ] (%)	Latency	VRAM

BAAF-Net [ 21 ]	-	65.4	-	-
MinkUNet [ 6 ]	72.2	65.4	126ms	4.7G
OctFormer [ 27 ]	75.7	-	112ms	12.5G
PointNeXt [ 20 ]	71.5	70.5	-	-

Table 4: Performance comparison between existing methods and the proposed method on S3DIS and ScanNet V2. Bold numbers indicate the best performance among the compared methods, and underlined numbers indicate the second-best performance. Latency and memory are measured during inference on ScanNet V2. Results for PT and PTv2 are averaged over three independent runs conducted by us.

Figure 4: Qualitative evaluation of the proposed method on S3DIS. The input point cloud is visualized with original colors in the 1st column. The areas where improvements were observed compared to the conventional model are highlighted with yellow boxes in the figure.


Dataset	$\mathcal{L}_{same}$ (%)	$\mathcal{L}_{diff}$ (%)	$\mathcal{L}_{DAS}$ (%)
DALES [ 25 ]	77.16	77.77	77.53
S3DIS [ 1 ]	71.20	70.50	71.42
ScanNet V2 [ 7 ]	76.63	76.80	77.26

Table 5: Evaluation experiments for each component of DAS Loss. For

\mathcal{L}_{same}

and

\mathcal{L}_{diff}

, the averaging operation in Eq. 5 is not applied. Instead, each loss is directly introduced into Point Transformer V3 as the final loss function.


Threshold	DALES [ 25 ] (%)	S3DIS [ 1 ] (%)	ScanNet V2 [ 7 ] (%)
$D_{i}>0.0$	76.20	70.41	76.45
$D_{i}<D_{\mathrm{mean}}-D_{\mathrm{std}}$	76.48	70.07	76.79
$D_{i}>D_{\mathrm{mean}}+D_{\mathrm{std}}$	77.53	71.42	77.26

Table 6: Evaluation of the DAS Loss threshold. DAS Loss is applied to all point pairs when the threshold is 0.0, and only to spatially distant point pairs when the threshold is

D_{mean}+D_{std}

. Changing the threshold and inequality condition enables DAS Loss to target either spatially close or distant point pairs.


Loss Application	DALES [ 25 ] (%)	S3DIS [ 1 ] (%)	ScanNet V2 [ 7 ] (%)
Close- $\mathcal{L}_{diff}$ & Distant- $\mathcal{L}_{same}$	77.35	69.43	77.16
Close- $\mathcal{L}_{same}$ & Distant- $\mathcal{L}_{diff}$	77.13	71.36	77.44
Distant- $\mathcal{L}_{same}$ & Distant- $\mathcal{L}_{diff}$	77.53	71.42	77.26

Table 7: Evaluation of different loss application conditions. "Close-

\mathcal{L}

" applies

\mathcal{L}

to SFC-based neighboring point pairs that are spatially close, whereas "Distant-

\mathcal{L}

" applies

\mathcal{L}

to SFC-based neighboring point pairs that are spatially distant. In the "Close" setting, we use the threshold

D_{i}<D_{\mathrm{mean}}-D_{\mathrm{std}}

, whereas in the "Distant" setting, we use

D_{i}>D_{\mathrm{mean}}+D_{\mathrm{std}}

3D Point Cloud Segmentation

3D point cloud segmentation assigns semantic, instance, or part labels to points for scene understanding, mapping, robotics, and scientific measurement.

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Loss Landscape Topology Reveals Why Simple Baselines are Competitive at 3D Point Cloud Segmentation Under Class Imbalance

Antonis Savva, Christos Kyrkou, Theocharis Theocharides

KIOS Research and Innovation Center of Excellence, University of Cyprus, 1 Panepistimiou Avenue, 2109 Aglantzia, Nicosia · Department of Electrical and Computer Engineering, University of Cyprus, 1 Panepistimiou Avenue, 2109 Aglantzia, Nicosia

Class-Imbalanced Learning Loss Landscape 3D Semantic Segmentation

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Semantic segmentation of 3D point clouds faces severe class imbalance, yet the effectiveness of specialized imbalance-aware methods from 2D computer vision remains unclear in 3D contexts. We systematically evaluate 11 imbalance mitigation approaches across datasets with extreme (641:1) and moderate (56:1) imbalance ratios, revealing a surprising finding: standard cross-entropy with uniform weighting achieves competitive performance, typically within 0.8-3.3% mIoU of specialized methods across architectures and datasets. Through multifaceted mechanistic analysis of error patterns, decision boundaries, and the geometry of the optimization landscape, our analyses suggest that imbalance severity shapes the topology, creating narrow solution basins under extreme imbalance and flat plateaus under moderate imbalance. This appears to constrain the effectiveness of loss-level modifications, as all methods must navigate these geometric constraints. Our findings offer practical guidance; standard cross-entropy provides a robust baseline, with specialized methods offering modest improvements (0.8-3.3% mIoU) that vary by architecture and dataset but risk substantial degradation if poorly tuned. This work provides the first mechanistic explanation for why techniques proven effective in 2D do not readily transfer to point-based 3D point cloud segmentation, validated across two representative architectures.

Abstract

3D Point Cloud Segmentation

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