摘要：

针对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线性判别分析(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深度学习算法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的分类准确率提高了2.2~30.3百分点, F1值提高了2.2~30.9百分点。上述结果验证了该算法在图像形状数据集上的分类是有效的, 且提取出的形状特征具有一定的鲁棒性。

关键词: 图像分类, 形状特征提取, 复杂网络, 持续同调, 持续性复形

Abstract:

To address the problems of insufficient stability in complex network construction and poor classification performance of shape features extracted in complex situations in existing complex network-based image shape classification algorithms, this paper proposes an image shape classification algorithm based on persistent homology and complex networks. The algorithm combines complex networks with Vietoris-Rips filtration to construct a persistent complex network on the image contour point cloud. Persistent homology is used to compute global topological features of different dimensions within the persistent complex network. Degree features and correlation degree features extracted from the degree distribution are selected as local shape features, and are fused with global topological features respectively to obtain two feature sets, PHCND and PHCNJD, enabling a richer shape representation of the images. The fused feature vectors are classified using Linear Discriminant Analysis (LDA). Comparative experiments are conducted with other traditional algorithms as well as a deep learning algorithm ResNet-50 on nine public image datasets. Meanwhile, ablation studies are designed to validate the effectiveness of the global topological features and the complementarity between local shape features and global topological features within the persistent complex network. Experimental results show that the proposed algorithm achieves the highest accuracy and F1-score on five public datasets, with improvements of 2.2%—30.3% in classification accuracy and 2.2%—30.9% in F1-score compared to seven traditional image shape classification algorithms. These results validate the effectiveness of the proposed algorithm for image shape classification, and demonstrate that the extracted shape features exhibit certain robustness.

Key words: image classification, shape feature extraction, complex network, persistent homology, persistence complex