Three-dimensional voxel models are widely applied in various fields such as 3D imaging, industrial design, and medical imaging. The advancement of 3D modeling techniques and measurement devices has made the generation of three-dimensional models more convenient. The exponential increase in the number of 3D models presents a significant challenge for model retrieval. Currently, these models are numerous and typically represented as point clouds or meshes, resulting in sparse data and high feature dimensions within the retrieval database. Traditional methods for 3D model retrieval suffer from high computational complexity and slow retrieval speeds. To address this issue, this paper combines spatial-filling curves with octree structures and proposes a novel approach for representing three-dimensional voxel model sequence data features, along with a similarity measurement method based on symbolic operators. This approach enables efficient similarity calculations and rapid dimensionality reduction for the three-dimensional model database, facilitating efficient similarity calculations and expedited retrieval.

中文翻译：

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基于符号算子的三维体素模型相似度测量与检索

三维体素模型广泛应用于3D成像、工业设计、医学成像等各个领域。3D建模技术和测量设备的进步使得三维模型的生成更加方便。3D 模型数量的指数级增长对模型检索提出了重大挑战。目前，这些模型数量众多，通常表示为点云或网格，导致检索数据库中数据稀疏且特征维度较高。传统的 3D 模型检索方法存在计算复杂度高、检索速度慢的问题。为了解决这个问题，本文将空间填充曲线与八叉树结构相结合，提出了一种表示三维体素模型序列数据特征的新方法，以及基于符号算子的相似性测量方法。该方法能够对三维模型数据库进行高效的相似度计算和快速降维，有利于高效的相似度计算和快速检索。