A 3D random particle modeling method integrating KL expansion and frequency perturbation

doi:10.11996/JG.j.2095-302X.2026040736

Abstract

Abstract:

Efficiently establishing a random particle-model dataset with realistic geometric and shape characteristics is a critical issue for applications such as 3D particle recognition and particle simulation. To address the problems of insufficient morphological realism and low generation efficiency in traditional random modeling methods, a 3D random particle modeling method based on KL (Karhunen-Loeve) expansion integrated with frequency perturbation was proposed. First, three-dimensional reconstruction and spectral analysis were performed on real mineral particle surfaces to extract surface spectral features and construct particle-surface perturbation functions. Then, KL expansion was introduced to perform feature decomposition and correlation analysis on discretized particle-surface sampling data. By retaining the principal feature modes, the random generation of the primary structural morphology was achieved. Furthermore, the frequency perturbation information from real particles was incorporated into the primary structure, generating 3D random particle models with both primary structural characteristics and local perturbation features, thereby effectively improving the realism and diversity of random particle modeling. Finally, to verify the effectiveness of the proposed method, comparisons were conducted with two improved spherical harmonic analysis methods. The evaluation was performed from the perspectives of geometric characteristic parameters (length, width, and height), shape characteristic parameters (aspect ratio, sphericity, and normal perturbation angle), as well as comprehensive metrics including Wasserstein distance and model-generation efficiency. The results demonstrated that the generated particle models exhibited geometric and shape characteristic parameters that were closest to those of real particles. Moreover, the Wasserstein distance between the generated models and real particles was only 0.397 3, which was lower than 0.569 4 for the improved spherical harmonic analysis method based on fractal characteristics and 1.066 7 for the improved spherical harmonic analysis method based on genetic variation. In addition, the proposed method required less time (15.3 s) to generate the same number of particle models, achieving a favorable balance between accuracy and efficiency. The proposed method provided a new and efficient approach for generating 3D random particle models with realistic particle characteristics for applications such as 3D particle recognition and simulation.

Key words: 3D particle models, KL expansion, frequency perturbation, stochastic modeling, real particles

CLC Number:

TP391

ZHAO Lala, YANG Yizhuo, DUAN Chenlong, GUO Chenhao, WANG Qinglong, WANG Hongdu. A 3D random particle modeling method integrating KL expansion and frequency perturbation[J]. Journal of Graphics, 2026, 47(4): 736-745.

Figures/Tables 12

Fig. 1 Proposed method core process

Fig. 2 Mineral particle sample 3d scanning experiment configuration ((a) Experimental system composition; (b) Recognition error)

Fig. 3 Particle 3d point cloud alignment process ((a) Process 1; (b) Process 2)

Fig. 4 Real particle sample model

Fig. 5 3D Gaussian vector normalization ((a) Original standard 3D gaussian; (b) Normalized direction distribution)

Fig. 6 Irregular particle model

Fig. 7 3D Gaussian-correlated ellipsoid (3.5σ contour)

Fig. 8 Comparison of three particle model generation methods ((a) Improved spherical harmonic analysis based on fractal characteristics; (b) Improved spherical harmonic analysis based on genetic variation; (c) Ours)

Fig. 9 Schematic diagram of particle characteristic parameters ((a) Principal axes of the particle model; (b) Minimum cuboid bounding box of the particle; (c) Particle surface normal perturbation angle)

Fig. 10 Probability density distribution curve of geometric parameters for a particle model ((a) Length probability density distribution curve; (b) Width probability density distribution curve; (c) Height probability density distribution curve)

Fig. 11 Probability density distribution curve of geometric parameters for a particle model ((a) Probability density distribution curves of the aspect ratios of different particle models; (b) Probability density distribution curves of the sphericity of different particle models; (c) Probability density distribution curves of the normal perturbation angles of different particle models)

Table 1 Comparative analysis of comprehensive evaluation metrics for different particle random modeling methods

方法	Wasserstein距离	颗粒建模用时/s
基于分形特性的改进球谐分析方法	0.569 4	5.79
基于基因变异的改进球谐分析方法	1.066 7	712.56
本文方法	0.397 3	15.30

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