摘要： 针对于目前已有的复杂网络图像形状分类算法中复杂网络构建的稳定性不足，在复杂情形下提取的形状特征分类性能较差等问题，提出一种基于持续同调与复杂网络的图像形状分类算法。该算法将复杂网络与Vietoris-Rips复形过滤相结合，在图像轮廓点云上构建持续性复杂网络，利用持续同调计算持续性复杂网络中不同维度的全局拓扑特征；选择从度分布提取的度特征和相关度特征作为局部形状特征，分别融合全局拓扑特征得到两组特征PHCND和PHCNJD，使得图像具有更为丰富的形状特征表示。将融合后的特征向量通过LDA进行分类，在9个公共图像数据集上，与其他传统算法以及ResNet-50进行对比实验，同时设计消融实验验证了全局拓扑特征的有效性，以及在持续性复杂网络下局部形状特征与全局拓扑特征的互补性。实验结果表明，该算法在其中5个公共数据集上，取得了最高的准确率和F1值。相较于其他7种传统图像形状分类算法分类准确率提高了2.2%~30.3%，F1值提高了2.2%~30.9%。最后表明该算法在图像形状数据集上的分类上是有效的，且提取出的形状特征具有一定的鲁棒性。

Abstract: To address the limitations of stability in complex network construction and poor classification performance of shape features extracted in complex situations in existing complex network image shape classification algorithms, this paper proposes a shape classification algorithm based on continuous homology and complex networks. The algorithm combines complex networks with Vietoris-Rips filtration to build a persistent complex network on the image contour point cloud. Persistent homology is used to compute global topological features at different dimensions. Local shape features are extracted from the degree distribution, and these are fused with global topological features to form two feature sets: PHCND and PHCNJD, enhancing the image’s shape representation. The fused feature vectors are classified using Linear Discriminant Analysis (LDA). Experiments on nine benchmark datasets show that our algorithm outperforms traditional methods and ResNet-50. Ablation studies confirm the effectiveness of global topological features and the complementarity between local and global features in the persistent complex network. Results demonstrate that our algorithm achieves the highest accuracy and F1 score on five datasets, with accuracy improvements of 2.2%–30.3% and F1 score improvements of 2.2%–30.9% compared to seven traditional algorithms. These findings validate the effectiveness and robustness of the algorithm for image shape classification.