结合隐式几何编码与Lipschitz线性约束的保守包围盒构造方法

doi:10.11996/JG.j.2095-302X.2026010152

图学学报 ›› 2026, Vol. 47 ›› Issue (1): 152-161.DOI: 10.11996/JG.j.2095-302X.2026010152

• 计算机图形学与虚拟现实 • 上一篇下一篇

结合隐式几何编码与Lipschitz线性约束的保守包围盒构造方法

张冰钰¹^,²^,³, 况立群¹^,²^,³(), 熊风光¹^,²^,³, 孙凡淑¹^,²^,³, 焦世超¹^,²^,³

¹ 中北大学计算机科学与技术学院，山西太原 030051
² 机器视觉与虚拟现实山西省重点实验室，山西太原 030051
³ 山西省视觉信息处理及智能机器人工程研究中心，山西太原 030051

收稿日期:2025-05-08 接受日期:2025-09-17 出版日期:2026-02-28 发布日期:2026-03-16
通讯作者:况立群，E-mail：kuang@nuc.edu.cn
基金资助:
国家自然科学基金(62272426);山西省科技重大专项计划“揭榜挂帅”项目(202201150401021);山西省基础研究项目(202303021212189)

Conservative enclosing box construction algorithm based on implicit geometric coding with Lipschitz linear constraints

ZHANG Bingyu¹^,²^,³, KUANG Liqun¹^,²^,³(), XIONG Fengguang¹^,²^,³, SUN Fanshu¹^,²^,³, JIAO Shichao¹^,²^,³

¹ School of Computer Science and Technology, North University of China, Taiyuan Shanxi 030051, China
² Shanxi Provincial Key Laboratory of Machine Vision and Virtual Reality, Taiyuan Shanxi 030051, China
³ Shanxi Province’s Vision Information Processing and Intelligent Robot Engineering Research Center, Taiyuan Shanxi 030051, China

Received:2025-05-08 Accepted:2025-09-17 Published:2026-02-28 Online:2026-03-16
Supported by:
National Natural Science Foundation of China(62272426);Shanxi Provincial Science and Technology Major Special Programs “Listed and Commanded” Project(202201150401021);Basic Research Program of Shanxi Province(202303021212189)

摘要/Abstract

摘要：

目前主流的包围盒方法在三维场景渲染、光线追踪和碰撞检测等任务中广泛应用，但在拟合复杂几何形状时存在空间利用率低、拟合精度不足等问题，难以确保严格的保守性，并在降低误检率方面仍有改进空间。为解决上述问题，提出一种结合隐式几何编码与Lipschitz约束的保守包围盒构造方法，隐式几何编码通过位置编码将输入坐标映射至高维空间，从而捕捉局部及全局的几何信息，提升包围盒的适应性；随后，引入可训练的Lipschitz线性约束层，动态调整Lipschitz常数以控制梯度变化，并结合Lipschitz正则化损失与动态加权交叉熵损失，在优化边界拟合的同时降低假阳率。实验结果表明，该方法在多个三维模型上均能实现假阴率为0，且相比基准方法，误检率最高降低3.1%，单条光线查询方法提高1.7 ms，为高精度保守包围盒拟合提供了一种高效、稳健的解决方案。

关键词: 保守包围盒, Lipschitz约束, 隐式几何编码, 光线追踪, 碰撞检测

Abstract:

Currently the mainstream enveloping box methods are widely used in 3D scene rendering, ray tracing, and collision detection tasks; however, these methods suffer from the problems of low space utilization and insufficient fitting accuracy in fitting complex geometries, which are difficult to ensure strict conservatism and still have room for improvement in reducing false detection rates. To address these issues, a conservative bounding-box construction method combining implicit geometric coding and Lipschitz constraints was proposed. Implicit geometric coding mapped the input coordinates to a high-dimensional space via position coding, thus capturing local and global geometric information and improving bounding-box adaptability. A trainable Lipschitz-constrained linear layer was introduced to dynamically adjust Lipschitz constants control gradient changes, and Lipschitz regularization loss was combined with dynamically weighted cross-entropy loss to reduce the FP rate while optimizing the boundary fitting. The experimental results demonstrated that the method can achieve a false-negative rate of 0 on multiple 3D models and reduce the false-detection rate by up to 3.1% compared to the benchmark method, and improve the single-ray query method by 1.7 ms, providing a highly efficient and robust solution for high-precision conservative bounding box fitting.

Key words: conservative bounding box, Lipschitz constraint, implicit geometric encoding, ray tracing, collision detection

中图分类号:

TP391.41

张冰钰, 况立群, 熊风光, 孙凡淑, 焦世超. 结合隐式几何编码与Lipschitz线性约束的保守包围盒构造方法[J]. 图学学报, 2026, 47(1): 152-161.

ZHANG Bingyu, KUANG Liqun, XIONG Fengguang, SUN Fanshu, JIAO Shichao. Conservative enclosing box construction algorithm based on implicit geometric coding with Lipschitz linear constraints[J]. Journal of Graphics, 2026, 47(1): 152-161.

图/表 13

图1 经典包围盒类型((a) 包围球；(b) AABB包围盒；(c) OBB包围盒；(d) k-DOP包围盒)

Fig. 1 Classic bounding box types ((a) Bounding Sphere; (b) AABB bounding box; (c) OBB bounding box; (d) k-DOP bounding box)

图2 模型总体网络架构图

Fig. 2 Model general network architecture diagram

图3 隐式几何编码模块

Fig. 3 ImplicitNet module

图4 Lipschitz约束模块

Fig. 4 Lipschitz constraints module

图5 数据集模型图片((a) ShapeNet数据集部分模型; (b) 斯坦福大学三维扫描存储库)

Fig. 5 Dataset model images ((a) ShapeNet partial models; (b) The Stanford 3D scanning repository)

表1 不同包围盒方法的FPR对比

Table 1 Comparison of FPR for different methods of bounding boxes

方法	ShapeNet数据集				斯坦福大学三维扫描存储库
方法	Point	Box	Plane	Ray	Point	Box	Plane	Ray
AABB	49.3	45.4	55.2	69.2	66.6	51.2	49.6	70.2
OBB	42.1	49.2	58.4	63.3	51.2	41.9	45.3	65.6
Sphere	54.2	56.7	64.9	70.3	77.4	56.3	59.3	71.9
k-DOP	34.5	40.9	41.6	62.3	45.2	51.8	42.3	68.3
NN	4.2	6.1	7.6	6.9	5.9	7.5	8.2	8.7
NBE	3.9	5.5	6.2	7.5	5.5	7.5	8.4	8.3
SCNI	4.2	4.6	6.4	7.9	5.6	7.8	9.6	9.3
DRFC	11.6	12.4	23.1	29.9	10.4	16.6	26.7	32.8
Ours	3.5	4.1	4.3	5.5	3.2	4.4	5.9	6.9

图6 各种包围盒方法的FPR对比图((a) ShapeNet数据集；(b) 斯坦福大学三维扫描存储库)

Fig. 6 Comparison of FPR for each bracketed box methodology ((a) ShapeNet dataset; (b) Stanford 3D scanning repository)

图7 基准模型与本文方法FNR对比

Fig. 7 Comparison of FNR between the benchmark model and the method in this paper ((a) Point; (b) Plane; (c) Box; (d) Ray)

表2 单条光线查询时间对比/ms

Table 2 Comparison of single ray query time/ms

方法	时间
AABB	2.83
OBox	2.85
Sphere	2.49
k-DOP	43.26
NN	71.38
NBE	47.52
SCNI	55.85
DRFC	65.44
Ours	45.82

图8 模型包围盒可视化对比

Fig. 8 Visual comparison of model bounding boxes ((a) Ours; (b) SCNI; (c) NN; (d) NBE)

表3 消融实验结果对比

Table 3 Comparison of ablation experiment results

方法	FPR/%	时间/ms
Baseline	7.6	46.3
ImplicitNet	6.4	43.2
Lipschitz	5.9	43.6
ImplicitNet+Lipschitz	4.9	45.1

图9 参数λ在Airplane模型上的性能比较

Fig. 9 Performance comparison of parameter λ on airplane model

图10 参数c在Airplane模型上的性能比较

Fig. 10 Performance comparison of parameter c on airplane model

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结合隐式几何编码与Lipschitz线性约束的保守包围盒构造方法

Conservative enclosing box construction algorithm based on implicit geometric coding with Lipschitz linear constraints

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