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An l½ and Graph Regularized Subspace Clustering Method for Robust Image Segmentation

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Published:16 February 2022Publication History
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Abstract

Segmenting meaningful visual structures from an image is a fundamental and most-addressed problem in image analysis algorithms. However, among factors such as diverse visual patterns, noise, complex backgrounds, and similar textures present in foreground and background, image segmentation still stands as a challenging research problem. In this article, the proposed method employs an unsupervised method that addresses image segmentation as subspace clustering of image feature vectors. Initially, an image is partitioned into a set of homogeneous regions called superpixels, from which Local Spectral Histogram features are computed. Subsequently, a feature data matrix is created whereupon subspace clustering methodology is applied. A single-stage optimization model is formulated with enhanced segmentation capabilities by the combined action of l½ and l2 norm minimization. Robustness of l½ regularization toward both the noise and overestimation of sparsity provides simultaneous noise robustness and better subspace selection, respectively. While l2 norm facilitates grouping effect. Hence, the designed optimization model ensures an improved sparse solution and a sparse representation matrix with an accurate block diagonal structure, which thereby favours getting properly segmented images. Then, experimental results of the proposed method are compared with the state-of-art algorithms. Results demonstrate the improved performance of our method over the state-of-art algorithms.

REFERENCES

  1. [1] Zhang Yu Jin. 1996. A survey on evaluation methods for image segmentation. Pattern Recogn. 29, 8 (1996), 13351346.Google ScholarGoogle ScholarCross RefCross Ref
  2. [2] Gonzales Rafael C. and Woods Richard E.. 2002. Digital Image Processing (3rd Edition). Prentice-Hall, Inc..Google ScholarGoogle Scholar
  3. [3] Ghosh Swarnendu, Das Nibaran, Das Ishita, and Maulik Ujjwal. 2019. Understanding deep learning techniques for image segmentation. ACM Comput. Surv. 52, 4, Article 73 (Aug. 2019), 35 pages. DOI: DOI: http://dx.doi.org/10.1145/3329784 Google ScholarGoogle ScholarCross RefCross Ref
  4. [4] Wang Weiwei and Wu Cuiling. 2017. Image segmentation by correlation adaptive weighted regression. Neurocomputing 267 (2017), 426435. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. [5] Li Zhengqin and Chen Jiansheng. 2015. Superpixel segmentation using linear spectral clustering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 13561363.Google ScholarGoogle Scholar
  6. [6] Zohrizadeh Fariba, Kheirandishfard Mohsen, and Kamangar Farhad. 2018. Image segmentation using sparse subset selection. In Proceedings of the IEEE Winter Conference on Applications of Computer Vision (WACV’18). IEEE, 14701479.Google ScholarGoogle ScholarCross RefCross Ref
  7. [7] Lei Tao, Jia Xiaohong, Zhang Yanning, Liu Shigang, Meng Hongying, and Nandi Asoke K.. 2018. Superpixel-based fast fuzzy C-means clustering for color image segmentation. IEEE Trans. Fuzzy Syst. 27, 9 (2018), 17531766.Google ScholarGoogle ScholarCross RefCross Ref
  8. [8] Kim W., Kanezaki A., and Tanaka M.. 2020. Unsupervised learning of image segmentation based on differentiable feature clustering. IEEE Trans. Image Process. 29 (2020), 80558068. DOI: DOI: http://dx.doi.org/10.1109/TIP.2020.3011269Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. [9] Li Zhenguo, Wu Xiao-Ming, and Chang Shih-Fu. 2012. Segmentation using superpixels: A bipartite graph partitioning approach. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 789796. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. [10] Zhu Pengfei, Zhu Wencheng, Hu Qinghua, Zhang Changqing, and Zuo Wangmeng. 2017. Subspace clustering guided unsupervised feature selection. Pattern Recogn. 66 (2017), 364374. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. [11] Jiao Xue, Chen Yonggang, and Dong Rui. 2020. An unsupervised image segmentation method combining graph clustering and high-level feature representation. Neurocomputing 409 (2020), 8392.Google ScholarGoogle ScholarCross RefCross Ref
  12. [12] Choy Siu Kai, Ng Tsz Ching, and Yu Carisa. 2020. Unsupervised fuzzy model-based image segmentation. Signal Process. 171 (2020), 107483.Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. [13] Saxena Amit, Prasad Mukesh, Gupta Akshansh, Bharill Neha, Patel Om Prakash, Tiwari Aruna, Er Meng Joo, Ding Weiping, and Lin Chin-Teng. 2017. A review of clustering techniques and developments. Neurocomputing 267 (2017), 664681. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. [14] Zhao F., Zeng Z., Liu H., Lan R., and Fan J.. 2020. Semisupervised approach to surrogate-assisted multiobjective kernel intuitionistic fuzzy clustering algorithm for color image segmentation. IEEE Trans. Fuzzy Syst. 28, 6 (2020), 10231034. DOI: DOI: http://dx.doi.org/10.1109/TFUZZ.2020.2973121Google ScholarGoogle ScholarCross RefCross Ref
  15. [15] Xu Jinhuan, Fowler James E., and Xiao Liang. 2020. Hypergraph-regularized low-rank subspace clustering using superpixels for unsupervised spatial-spectral hyperspectral classification. IEEE Geosci. Remote Sens. Lett. 18, 5 (2020), 871875.Google ScholarGoogle Scholar
  16. [16] Francis Jobin and George Sudhish N.. 2020. A unified tensor framework for clustering and simultaneous reconstruction of incomplete imaging data. ACM Trans. Multimedia Comput. Commun. Appl. 16, 3 (2020), 124.Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. [17] Li Teng, Cheng Bin, Ni Bingbing, Liu Guangchan, and Yan Shuicheng. 2016. Multitask low-rank affinity graph for image segmentation and image annotation. ACM Trans. Intell. Syst. Technol. 7, 4, Article 65 (Mar. 2016), 18 pages. DOI: DOI: http://dx.doi.org/10.1145/2856058 Google ScholarGoogle ScholarCross RefCross Ref
  18. [18] Zhang Hongyan, Zhai Han, Zhang Liangpei, and Li Pingxiang. 2016. Spectral–spatial sparse subspace clustering for hyperspectral remote sensing images. IEEE Trans. Geosci. Remote Sens. 54, 6 (2016), 36723684.Google ScholarGoogle ScholarCross RefCross Ref
  19. [19] Liu Junmin, Chen Yijun, Zhang Jiangshe, and Xu Zongben. 2014. Enhancing low-rank subspace clustering by manifold regularization. IEEE Trans. Image Process. 23, 9 (2014), 40224030.Google ScholarGoogle ScholarCross RefCross Ref
  20. [20] Zhai Han, Zhang Hongyan, Zhang Liangpei, and Li Pingxiang. 2018. Laplacian-regularized low-rank subspace clustering for hyperspectral image band selection. IEEE Trans. Geosci. Remote Sens. 57, 3 (2018), 17231740.Google ScholarGoogle Scholar
  21. [21] Yang Shangming, Zhang Lei, He Xiaofei, and Yi Zhang. 2019. Learning manifold structures with subspace segmentations. IEEE Trans. Cybernet. 51, 4 (2019), 19811992.Google ScholarGoogle ScholarCross RefCross Ref
  22. [22] Bouwmans Thierry, Javed Sajid, Zhang Hongyang, Lin Zhouchen, and Otazo Ricardo. 2018. On the applications of robust PCA in image and video processing. Proc. IEEE 106, 8 (2018), 14271457.Google ScholarGoogle ScholarCross RefCross Ref
  23. [23] Seo Junghoon, Koo Jamyoung, and Jeon Taegyun. 2019. Deep closed-form subspace clustering. In Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops. 00.Google ScholarGoogle ScholarCross RefCross Ref
  24. [24] Wang Weiwei, Zhang Binbin, and Feng Xiangchu. 2017. Subspace segmentation by correlation adaptive regression. IEEE Trans. Circ. Syst. Video Technol. 28, 10 (2017), 26122621. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. [25] Ji Qiang, Sun Yanfeng, Gao Junbin, Hu Yongli, and Yin Baocai. 2019. Nonlinear subspace clustering via adaptive graph regularized autoencoder. IEEE Access 7 (2019), 7412274133.Google ScholarGoogle ScholarCross RefCross Ref
  26. [26] Elhamifar Ehsan and Vidal Rene. 2013. Sparse subspace clustering: Algorithm, theory, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 35, 11 (2013), 27652781. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. [27] Liu Guangcan, Lin Zhouchen, Yan Shuicheng, Sun Ju, Yu Yong, and Ma Yi. 2012. Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35, 1 (2012), 171184. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. [28] Liu Guangcan, Lin Zhouchen, and Yu Yong. 2010. Robust subspace segmentation by low-rank representation. In Proceedings of the 27th International Conference on Machine Learning (ICML’10). 663670. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. [29] Lu Can-Yi, Min Hai, Zhao Zhong-Qiu, Zhu Lin, Huang De-Shuang, and Yan Shuicheng. 2012. Robust and efficient subspace segmentation via least squares regression. In Proceedings of the European Conference on Computer Vision. Springer, 347360. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. [30] Cheng Bin, Liu Guangcan, Wang Jingdong, Huang Zhongyang, and Yan Shuicheng. 2011. Multi-task low-rank affinity pursuit for image segmentation. In Proceedings of the International Conference on Computer Vision. IEEE, 24392446. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. [31] Lu Canyi, Feng Jiashi, Lin Zhouchen, and Yan Shuicheng. 2013. Correlation adaptive subspace segmentation by trace lasso. In Proceedings of the IEEE International Conference on Computer Vision. 13451352. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. [32] Yin Ming, Gao Junbin, and Lin Zhouchen. 2015. Laplacian regularized low-rank representation and its applications. IEEE Trans. Pattern Anal. Mach. Intell. 38, 3 (2015), 504517. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. [33] Shi Jianbo and Malik Jitendra. 2000. Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22, 8 (2000), 888905. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. [34] Lu Xiaoqiang, Wang Yulong, and Yuan Yuan. 2013. Graph-regularized low-rank representation for destriping of hyperspectral images. IEEE Trans. Geosci. Remote Sens. 51, 7 (2013), 40094018.Google ScholarGoogle ScholarCross RefCross Ref
  35. [35] Zheng Miao, Bu Jiajun, Chen Chun, Wang Can, Zhang Lijun, Qiu Guang, and Cai Deng. 2010. Graph regularized sparse coding for image representation. IEEE Trans. Image Process. 20, 5 (2010), 13271336. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. [36] Xie Yuan, Zhang Wensheng, Qu Yanyun, Dai Longquan, and Tao Dacheng. 2018. Hyper-Laplacian regularized multilinear multiview self-representations for clustering and semisupervised learning. IEEE Trans. Cybernet. 50, 2 (2018), 572586.Google ScholarGoogle ScholarCross RefCross Ref
  37. [37] Xu Zongben, Chang Xiangyu, Xu Fengmin, and Zhang Hai. 2012. \(L\_\){\(1/2\)} regularization: A thresholding representation theory and a fast solver. IEEE Trans. Neural Netw. Learn. Syst. 23, 7 (2012), 10131027.Google ScholarGoogle ScholarCross RefCross Ref
  38. [38] Zeng Jinshan, Lin Shaobo, Wang Yao, and Xu Zongben. 2014. \(L\_\){\(1/2\)} regularization: Convergence of iterative half thresholding algorithm. IEEE Trans. Signal Process. 62, 9 (2014), 23172329. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. [39] Xu Chen, Peng ZhiMing, and Jing WenFeng. 2013. Sparse kernel logistic regression based on L 1/2 regularization. Sci. China Info. Sci. 56, 4 (2013), 116.Google ScholarGoogle ScholarCross RefCross Ref
  40. [40] Qian Yuntao, Jia Sen, Zhou Jun, and Robles-Kelly Antonio. 2011. Hyperspectral unmixing via \(L\_\){\(1/2\)} sparsity-constrained nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sens. 49, 11 (2011), 42824297.Google ScholarGoogle ScholarCross RefCross Ref
  41. [41] Tom Anju Jose and George Sudhish N.. 2019. A three-way optimization technique for noise robust moving object detection using tensor low-rank approximation, l1/2, and TTV regularizations. IEEE Trans. Cybernet. 51, 2 (2019), 1004–1014.Google ScholarGoogle ScholarCross RefCross Ref
  42. [42] Tang Zhenyu, Ahmad Sahar, Yap Pew-Thian, and Shen Dinggang. 2018. Multi-atlas segmentation of MR tumor brain images using low-rank based image recovery. IEEE Trans. Med. Imag. 37, 10 (2018), 22242235.Google ScholarGoogle ScholarCross RefCross Ref
  43. [43] Belkin Mikhail and Niyogi Partha. 2002. Laplacian eigenmaps and spectral techniques for embedding and clustering. In Advances in Neural Information Processing Systems. MIT Press, 585591. Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. [44] Yang Congyuan, Robinson Daniel, and Vidal Rene. 2015. Sparse subspace clustering with missing entries. In Proceedings of the International Conference on Machine Learning. PMLR, 24632472. Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. [45] Grave Edouard, Obozinski Guillaume R., and Bach Francis R.. 2011. Trace Lasso: A trace norm regularization for correlated designs. In Advances in Neural Information Processing Systems. MIT Press, 21872195. Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. [46] Vidal René. 2011. Subspace clustering. IEEE Signal Processing Magazine 28, 2 (2011), 5268.Google ScholarGoogle ScholarCross RefCross Ref
  47. [47] Wang Wenhong and Qian Yuntao. 2015. Adaptive \(L_{\frac{1}{2}}\) Sparsity-constrained NMF with half-thresholding algorithm for hyperspectral unmixing. IEEE J. Select. Top. Appl. Earth Observ. Remote Sens. 8, 6 (2015), 26182631.Google ScholarGoogle ScholarCross RefCross Ref
  48. [48] Pedroche Francisco, Rebollo Miguel, Carrascosa Carlos, and Palomares Alberto. 2016. On some properties of the Laplacian matrix revealed by the RCM algorithm. Czech. Math. J. 66, 3 (2016), 603620.Google ScholarGoogle ScholarCross RefCross Ref
  49. [49] Wu Tong. 2020. Graph regularized low-rank representation for submodule clustering. Pattern Recogn. 100 (2020), 107145.Google ScholarGoogle ScholarCross RefCross Ref
  50. [50] Madathil Baburaj and George Sudhish N. 2020. Noise robust image clustering based on reweighted low rank tensor approximation and \(l_{\frac{1}{2}}\) regularization. Signal, Image Video Process. 15, 2 (2020), 341349.Google ScholarGoogle ScholarCross RefCross Ref
  51. [51] Zhu Xiaofeng, Zhang Shichao, Zhang Jilian, Li Yonggang, Lu Guangquan, and Yang Yang. 2020. Sparse graph connectivity for image segmentation. ACM Trans. Knowl. Discov. Data 14, 4 (2020), 119. Google ScholarGoogle ScholarDigital LibraryDigital Library
  52. [52] Wang Zhaobin, Wang E., and Zhu Ying. 2020. Image segmentation evaluation: a survey of methods. Artific. Intell. Rev. 53, 8 (2020), 56375674.Google ScholarGoogle ScholarDigital LibraryDigital Library

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      • Published in

        cover image ACM Transactions on Multimedia Computing, Communications, and Applications
        ACM Transactions on Multimedia Computing, Communications, and Applications  Volume 18, Issue 2
        May 2022
        494 pages
        ISSN:1551-6857
        EISSN:1551-6865
        DOI:10.1145/3505207
        Issue’s Table of Contents

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        Publication History

        • Published: 16 February 2022
        • Accepted: 1 July 2021
        • Revised: 1 May 2021
        • Received: 1 February 2020
        Published in tomm Volume 18, Issue 2

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