Manifold Spectral Clustering Image Segmentation Algorithm Based on Local Geometry Features
ZHANG Rongguo1, YAO Xiaoling1, ZHAO Jian1, HU Jing1, LIU Xiaojun2
1.College of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024 2.School of Mechanical Engineering, Hefei University of Technology, Hefei 230009
Abstract To improve the accuracy and timeliness of spectral clustering image segmentation,an algorithm of manifold spectral clustering image segmentation based on local geometry features is proposed. Firstly, considering the manifold structure of image data, the relationship of data intrinsic dimensions is obtained by performing spectral clustering based on local principal components analysis in the k-nearest neighbor region of data points. Then, the local linear reconstruction technique in manifold learning is introduced, and the similarity of local tangent space between data is obtained via mixed linear analyzers, and the similarity matrix with local geometric features is constructed by merging the intrinsic dimension and the local tangent space. Nyström technique is utilized to approximate eigenvectors of the image to be segmented, and spectral clustering is performed on the constructed k principal eigenvectors. Finally, experiments on Berkeley dataset show the advantages of the proposed algorithm in accuracy and timeliness.
Fund:Supported by National Natural Science Foundation of China(No.51875152), Natural Science Foundation of Shanxi Province(No.201801D121134)
Corresponding Authors:
ZHANG Rongguo , Ph.D., professor. His research interests include image processing, computer vision and pattern recognition.
About author:: YAO Xiaoling, master student. Her research interests include image processing and computer vision.ZHAO Jian, master, lecturer. His resear-ch interests include image processing and computer vision.HU Jing, Ph.D. candidate, associate professor. Her research interests include image processing and pattern recognition.LIU Xiaojun, Ph.D., professor. Her research interests include modern design theory and methodology, pattern recognition.
[1] VON LUXBURG U. A Tutorial on Spectral Clustering. Statistics and Computing, 2007, 17: 395-416. [2] TREMBLAY N, LOUKAS A. Approximating Spectral Clustering via Sampling: A Review[C/OL]. [2020-01-01]. https://arxiv.org/pdf/1901.10204.pdf. [3] LEI T, JIA X H, ZHANG Y N, et al. Significantly Fast and Robust Fuzzy C-means Clustering Algorithm Based on Morphological Reconstruction and Membership Filtering. IEEE Transactions on Fuzzy Systems, 2018, 26(5): 3027-3041. [4] SHI J B, MALIK J. Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905. [5] 张荣国,刘小君,董 磊,等.物体轮廓形状超像素图割快速提取方法.模式识别与人工智能, 2015, 28(4): 344-353. (ZHANG R G, LIU X J, DONG L, et al. Superpixel Graph Cuts Rapid Algorithm for Extracting Object Contour Shapes. Pattern Re-cognition and Artificial Intelligence, 2015, 28(4): 344-353.) [6] SOUVENIR R, PLESS R. Manifold Clustering // Proc of the 10th IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2005, I: 648-653. [7] YAN J Y, POLLEFEYS M. A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate // Proc of the European Conference on Compu-ter Vision. Berlin, Germany: Springer, 2006: 94-106. [8] GOLDBERG A B, ZHU X J, SINGH A, et al. Multi-manifold Semi-supervised Learning. Journal of Machine Learning Research, 2009, 5: 169-176. [9] CHEN G L, LERMAN G. Spectral Curvature Clustering(SCC). International Journal of Computer Vision, 2009, 81(3): 317-330. [10] ZHENG W, CHEN S. Multiple Manifolds Clustering via Local Li-near Analysis. Cybernetics and Information Technologies, 2016, 16(6): 194-206. [11] NIE F P, ZENG Z N, TSANG I W, et al. Spectral Embedded Clustering: A Framework for In-Sample and Out-of-Sample Spectral Clustering. IEEE Transactions on Neural Networks, 2011, 22(11): 1796-1808. [12] COUR T, BENEZIT F, SHI J B. Spectral Segmentation with Multiscale Graph Decomposition // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2005: 1124-1131. [13] GITTENS A, MAHONEY M W. Revisiting the Nyström Method for Improved Large-Scale Machine Learning. Journal of Machine Learning Research, 2016, 17: 3977-4041. [14] HE L, ZHANG H. Kernel K-means Sampling for Nyström Approximation. IEEE Transactions on Image Processing, 2018, 27(5): 2108-2120. [15] LI Z Q, CHEN J S. Superpixel Segmentation Using Linear Spectral Clustering // Proc of the IEEE Conference Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2015: 1356-1363. [16] CHEN J S, LI Z Q, HUANG B. Linear Spectral Clustering Superpixel. IEEE Transactions on Image Processing, 2017, 26(7): 3317-3330. [17] HE L, RAY N, GUAN Y S, et al. Fast Large-Scale Spectral Clustering via Explicit Feature Mapping. IEEE Transactions on Cybernetics, 2019, 49(3): 1058-1071. [18] WANG Y, JIANG Y, WU Y, et al. Spectral Clustering on Multiple Manifolds. IEEE Transactions on Neural Networks, 2011, 22(7): 1149-1161. [19] ARIAS-CASTRO E, LERMAN G, ZHANG T. Spectral Clustering Based on Local PCA. Journal of Machine Learning Research, 2017, 18: 253-309. [20] HUANG S N, ZHANG L, LI F Z. Spectral Embedded Clustering on Multi-manifold // Proc of the IEEE International Conference on Pattern Recognition. Washington, USA: IEEE, 2018: 391-396. [21] SONG W B, WEN L, GAO L, et al. Unsupervised Fault Diagnosis Method Based on Iterative Multi-manifold Spectral Clustering. IET Collaborative Intelligent Manufacturing, 2019, 1(2): 48-55. [22] ELHAMIFAR E,VIDAL R. Sparse Subspace Clustering: Algorithm, Theory,and Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(11): 2765-2781. [23] JAVED S, MAHMOOD A, BOUWMANS T, et al. Background Foreground Modeling Based on Spatiotemporal Sparse Subspace Clustering. IEEE Transactions on Image Processing, 2017, 26(12): 5840-5854. [24] 李建元,周脚根,关佶红,等.谱图聚类算法研究进展.智能系统学报, 2011, 6(5): 405-414. (LI J Y, ZHOU J G, GUAN J H, et al. A Survey of Clustering Algorithm Based on Spectra of Graphs. CAAI Transactions on Intelligent Systems, 2011, 6(5): 405-414.) [25] 王瑞霞,彭国华.基于黎曼流形稀疏编码的图像检索算法.自动化学报, 2017, 43(5): 778-788. (WANG R X, PENG G H. An Image Retrieval Method with Sparse Coding Based on Riemannian Manifold. Acta Automatica Sinica, 2017, 43(5): 778-788.) [26] MA X J, LI B, WANG Y S, et al. Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality[C/OL]. [2020-01-01]. https://arxiv.org/pdf/1801.02613.pdf. [27] HALIMI A, HONEINE P, KHAROUF M, et al. Estimating the Intrinsic Dimension of Hyperspectral Images Using a Noise-Whitened Eigengap Approach. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(7): 3811-3821. [28] GILBERT A C, SONTHALIA R. Unrolling Swiss Cheese: Metric Repair on Manifolds with Holes[C/OL]. [2020-01-01]. https://arxiv.org/pdf/1807.07610v1.pdf [29] HOU C P, NIE F P, YI D Y, et al. Discriminative Embedded Clustering: A Framework for Grouping High Dimensional Data. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(6): 1287-1299. [30] TIPPING M E, BISHOP C M. Mixtures of Probabilistic Principal Component Analyzers. Neural Computation, 1999, 11(2): 443-482. [31] VAN DEN BERGH M, BOIX X, ROIG G, et al. SEEDS: Superpixels Extracted via Energy-Driven Sampling // Proc of the European Conference on Computer Vision. Berlin, Germany: Springer, 2012: 13-26. [32] ARBELÁEZ P, MAIRE M, FOWLKES C, et al. Contour Detection and Hierarchical Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(5): 898-916. [33] UNNIKRISHNAN R, PANTOFARU C, HEBERT M. Toward Objective Evaluation of Image Segmentation Algorithms. IEEE Tran-sactions on Pattern Analysis and Machine Intelligence, 2007, 29(6): 929-944.
2020, Vol. 33 
