B-Spline Embedded Structure Learning for 3D Tooth Segmentation

Xianghan Wei; Jianwen Lou; Zhiguo Lu; Hairong Jin; Haihua Zhu

cs.CVAug 18, 2026

B-Spline Embedded Structure Learning for 3D Tooth Segmentation

Authors: Xianghan Wei, Jianwen Lou, Zhiguo Lu, Hairong Jin, Haihua Zhu

Organizations: School of Software Technology, Zhejiang University · School of Computer and Computing Science, Hangzhou City University · The Affiliated Stomatology Hospital, Zhejiang University School of Medicine

Abstract

Accurate 3D tooth segmentation forms the cornerstone of digital dentistry, yet it remains a formidable challenge due to the inherent intricacy of real-world dentitions, such as crowding, misaligned teeth and high morphological similarity between adjacent teeth. To resolve this, we present B-Spline Embedded Structure Learning, a novel framework that distills the inherent sequential arrangement of teeth into a continuous structural constraint to regularize representation space. Our approach parameterizes the global dental topology by fitting a parametric B-spline trajectory to tooth centers, assigning each point a continuous structural embedding that forces the shared backbone to capture global arch organization. To fully exploit these embedded priors, we introduce a Structure-Aware Dynamic Classifier (SADC) to substitute rigid static templates with adaptive, case-calibrated decision boundaries. SADC regularizes dynamic prototype pooling via a localized Gaussian proximity gate and contextually co-evolves them through an attention block modeling spatial relations and bilateral symmetries across teeth. Extensive evaluations on the 3DTeethSeg22 benchmark demonstrate that our method establishes a new state-of-the-art accuracy with exceptional structural robustness and efficiency in computational overhead, markedly enhancing the model's capacity to handle complex dental configurations.

Figures & tables

Figure 1: Overview of the proposed framework. A PTv3 backbone first extracts multi-scale geometric features from each dental arch. The B-spline embedded structural representation assigns each point a continuous structural coordinate $t$ , while SADC uses these embeddings to construct and refine sample-specific tooth prototypes as dynamic classifier weights for final segmentation.

Method	OA $\uparrow$	T-mIoU $\uparrow$	Dice $\uparrow$	B-IoU $\uparrow$	TIR $\uparrow$	TIR =1 $\uparrow$
TSegAgent ( Zhuang et al. 2026 )	62.16	31.45	32.52	64.38	34.38	14.67
TeethGNN ( Zheng et al. 2023 )	90.96	83.89	88.46	48.49	93.78	73.33
ISBNet ( Ngo et al. 2023 )	91.53	81.01	87.65	39.61	96.49	89.00
CBANet ( Jin et al. 2025a )	92.72	86.63	91.03	50.73	96.44	86.67
TSRNet ( Jin et al. 2025b )	92.87	86.56	90.91	51.11	96.09	87.17
DilatedToothSegNet ( Krenmayr et al. 2024 )	93.40	86.55	91.26	51.57	96.80	89.33

Table 1: Quantitative results on the test set (%).

Rank	Count	Binary Vector	Missing Tooth
1	334	0111111111111110	1, 16
2	104	0011111111111100	1, 2, 15, 16
3	29	0011111111111110	1, 2, 16
4	22	1111111111111111	None
5	21	0111111111111100	1, 15, 16
Others	$\leq 8$ each, 90 in total	-	-

Table 2: Tooth-presence configurations in the test set.

Method	Top-1 Pattern (334)			Rank 2–5 Patterns (176)			Rare Patterns (90)
	T-mIoU $\uparrow$	TIR $\uparrow$	TIR =1 $\uparrow$	T-mIoU $\uparrow$	TIR $\uparrow$	TIR =1 $\uparrow$	T-mIoU $\uparrow$	TIR $\uparrow$	TIR =1 $\uparrow$
TeethGNN ( Zheng et al. 2023 )	88.73	98.99	94.01	80.48	90.61	53.41	72.60	80.64	35.56
ISBNet ( Ngo et al. 2023 )	83.84	99.30	97.60	82.33	98.95	93.18	67.95	81.23	48.89
CBANet ( Jin et al. 2025a )	89.55	99.57	97.31	88.38	98.33	91.48	72.39	81.13	37.78
TSRNet ( Jin et al. 2025b )	89.81	99.45	97.31	88.19	98.37	90.91	71.30	79.13	42.22
DilatedToothSegNet ( Krenmayr et al. 2024 )	89.45	99.68	98.50	87.47	98.12	89.20	74.01	83.55	55.56

Table 3: Comparison across frequency-stratified tooth-presence pattern groups (%). Our pronounced advantage on rare patterns demonstrates superior robustness and generalization.

Figure 2: Visual comparison on challenging test samples. Our method demonstrates superior boundary delineation and tooth identification in cases with missing teeth, severe crowding, and malalignment.

Method	Training Time	Total Inference Time	Avg. / Scan
3DTeethSAM	20 h 36 m	34 m 29 s	3.45 s
ToothGroupNet	22 h 9 m	29 m 6 s	2.91 s
Ours	2 h 15 m	8 m 21s	0.84 s

Table 4: Computational efficiency comparison.

Setting	OA $\uparrow$	T-mIoU $\uparrow$	Dice $\uparrow$	B-IoU $\uparrow$	TIR $\uparrow$	TIR =1 $\uparrow$
Full model	96.01	92.62	94.90	71.36	97.50	92.67
w/o BSS	95.82	92.28	94.59	71.16	97.18	91.83
w/o SADC	95.73	92.10	94.46	70.81	97.17	91.33
w/o BSS & SADC	94.76	89.59	92.49	67.85	96.77	88.50
w/o SADC’s GSS	95.83	92.30	94.57	71.35	97.15	91.61
w/o SADC’s RAL	95.89	92.37	94.68	71.22	97.36	92.00

Table 5: Ablation study of core components (%). “BSS” denotes continuous B-spline structural supervision; “GSS” and “RAL” denote SADC’s Gaussian structural gate and relation attention layer, respectively.

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