Abstract
Superpixel segmentation methods are generally used as a pre-processing step to speed up image processing tasks. They group the pixels of an image into homogeneous regions while trying to respect existing contours. In this paper, we propose a fast Superpixels segmentation algorithm with Contour Adherence using spectral clustering, combined with normalized cuts in an iterative k-means clustering framework. It produces compact and uniform superpixels with low computational costs. Normalized cut is adapted to measure the color similarity and space proximity between image pixels. We have used a kernel function to estimate the similarity metric. Kernel function maps the pixel values and coordinates into a high dimensional feature space. The objective functions of weighted K-means and normalized cuts share the same optimum point in this feature space. So it is possible to optimize the cost function of normalized cuts by iteratively applying simple K-means clustering algorithm. The proposed framework produces regular and compact superpixels that adhere to the image contours. On segmentation comparison benchmarks it proves to be equally well or better than the state-of-the-art super pixel segmentation algorithms in terms of several commonly used evaluation metrics in image segmentation. In addition, our method is computationally very efficient and its computational complexity is linear.
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References
G. Mori, “Guiding model search using segmentation,” in Proc. IEEE Int. Conf. on Computer Vision (ICCV) (Beijing, 2005).
S. Gould, J. Rodgers, D. Cohen, G. Elidan, and D. Koller, “Multi-class segmentation with relative location prior,” Int. J. Comput. Vision 80 (3), 300–316 (2008).
C. L. Zitnick and S. B. Kang, “Stereo for image-based rendering using image over-segmentation,” Int. J. Comput. Vision 75, 49–65 (2007).
B. Fulkerson, A. Vedaldi, and S. Soatto, “Class segmentation and object localization with superpixel neighborhoods,” in Proc. Int. Conf. on Computer Vision (ICCV) (Kyoto, 2009).
M. Menze and A. Geiger, “Object scene flow for autonomous vehicles,” in Proc. Conf. on Computer Vision and Pattern Recognition (CVPR) (Boston, MA, 2015).
S. Wang, H. Lu, F. Yang, and M.-H. Yang, “Superpixel tracking,” in Proc. IEEE Int. Conf. on Computer Vision (ICCV) (Barcelona, Nov. 2011).
D. Comaniciu and P. Meer, “Mean shift: a robust approach toward feature space analysis,” IEEE Trans. Pattern Anal. Mach. Intellig. 24 (5), 603–619 (2002).
P. Felzenszwalb and D. Huttenlocher, “Efficient graph-based image segmentation,” Int. J. Comput. Vision 59 (2), 167–181 (2004).
X. Ren and J. Malik, Learning a classification model for segmentation, in Proc. ICCV (Madison, 2003), Vol. 1, pp. 10–17.
D. Comaniciu and P. Meer, “Mean shift: a robust approach towards feature space analysis,” IEEE Trans. PAMI 24 (5), 603–619 (2002).
A. Veldadi and S. Soatto, “Quick shift and kernel methods for mode seeking,” in Proc. ECCV (Marseille, 2008), pp. 705–718. φ
A. Levinshtein, A. Stere, K. Kutulakos, D. Fleet, S. Dickinson, and K. Siddiqi, “Turbopixel: fast supepixels using geometric flow,” IEEE Trans. PAMI 31 (12), 2209–2297 (2009).
D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluate segmentation algorithms and measuring ecological statistics,” in Proc. ICCV (Vancouver, 2001), Vol. 2, pp. 416–423.
J. Shi and J. Malik, “Normalized cuts and image segmentation,” IEEE Trans. PAMI 22 (8), 888–905 (2000).
A. Moore, S. Prince, and J. Warrell, “Lattice cut constructing superpixels using layer constraints,” in Proc. CVPR (San Francisco, 2010), pp. 2117–2124.
A. Moore, S. Prince, J. Warrell, U. Mohammed, and G. Jones, “Superpixel lattices,” in Proc. CVPR (Anchorage, 2008), pp. 1–8.
M. Bergh, X. Boix, G. Roig, B. Capitani, and L. V. Gool, “Seeds: superpixels extracted via energy-driven sampling,” in Proc. ECCV (Firenze, 2012), Vol. 7578, pp. 13–26.
R. Achanta, A. Shaji, K. Smith, A. Lucchi, P. Fua, and S. Süsstrunk, “SLIC superpixels compared to state-ofthe-art superpixel methods,” IEEE Trans. Pattern Anal. Mach. Intell. 34 (11), 2274–2282 (2012).
S. Wang, H. Lu, F. Yang, and M. Yang, “Superpixel tracking,” in Proc. ICCV (Barcelona, 2011), Vol. 1, pp. 1323–1330.
I. Dhillon, Y. Guan, and B. Kulis, “Weighted graph cuts without eigenvectors: a multilevel approach,” IEEE Trans. PAMI 29 (11), 1944–1957 (2007).
S. Yu and J. Shi, “Multiclass spectral clustering,” in Proc. ICCV (Madison, 2003), Vol. 1, pp. 313–319.
A. Ng, M. Jordan, and Y. Weiss, “On spectral clustering: analysis and an algorithm,” in Proc. NIPS (Vancouver, 2001), pp. 849–856.
N. Cristianini and J. Taylor, An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods (Cambridge Univ. Press, New York, 2000).
Y. Zhang, R. Hartley, J. Mashford, and S. Burn, “Superpixels via pseudo-Boolean optimization,” in Proc. IEEE Int. Conf. Computer Vision (Barcelona, Nov. 2011), pp. 1387–1394.
M.-Y. Liu, O. Tuzel, S. Ramalingam, and R. Chellappa, “Entropy rate superpixel segmentation,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition (Colorado Springs, Jun. 2011), pp. 2097–2104.
J. Shen, Y. Du, W. Wang, and X. Li, “Lazy random walks for superpixel segmentation,” IEEE Trans. Image Process. 23 (4), 1451–1462 (2014).
Z. Li and J. Chen, “Superpixel segmentation using linear spectral clustering,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) (Boston, MA, Jun. 2015), pp. 1356–1363.
D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in Proc. IEEE Int. Conf. on Computer Vision (Vancouver, Jul. 2001), Vol. 2, pp. 416–423.
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Partha Ghosh is an Assistant Professor in the Department of Computer Science and Engineering of Govt. College of Engineering and Ceramic Technology under Maulana Abul Kalam Azad University of Technology, Kolkata. He received the B.Sc.(Physics), from University of Calcutta. B.Tech., M. Tech. in Computer Science and Engineering from University of Kalyani and Pursuing Ph.D. degree from University of Kalyani, India. His research interests are in the area of computer vision, pattern recognition and image processing. He is a life member of CSTA, IAENG.
Kalyani Mali is a Professor in the Department of Computer Science and Engineering of University of Kalyani. She received the B.Sc.(Math), B. Tech. in Computer Science, M. Tech. in Computer Science from University of Calcutta and Ph.D. degree from Jadavpur University, Kolkata, India. His research interests are in the area of Digital image processing, pattern recognition, neural network. She is a life member of CSI from 2011. IEEE member.
Sitansu Kumar Das is an Assistant Professor in the Department of Computer Science of Chittaranjan College under University of Calcutta. He received the B. E. Degree in Mechanical Engineering from Bengal Engineering College (Deemed University), Shibpur, India, M.Tech. degree in Computer Science from Indian Statistical Institute, Kolkata, India and Ph.D. degree from Jadavpur University, Kolkata, India. His research interests are in the area of computer vision, pattern recognition and image processing.
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Ghosh, P., Mali, K. & Das, S.K. Use of Spectral Clustering Combined with Normalized Cuts (N-Cuts) in an Iterative k-Means Clustering Framework (NKSC) for Superpixel Segmentation with Contour Adherence. Pattern Recognit. Image Anal. 28, 400–409 (2018). https://doi.org/10.1134/S1054661818030161
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DOI: https://doi.org/10.1134/S1054661818030161