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A k-max Geodesic Distance and Its Application in Image Segmentation

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9256))

Abstract

The geodesic distance is commonly used when solving image processing problems. In noisy images, unfortunately, it often gives unsatisfactory results. In this paper, we propose a new k-max geodesic distance. The length of path is defined as the sum of the k maximum edge weights along the path. The distance is defined as the length of the path that is the shortest one in this sense. With an appropriate choice of the value of k, the influence of noise can be reduced substantially. The positive properties are demonstrated on the problem of seeded image segmentation. The results are compared with the results of geodesic distance and with the results of the random walker segmentation algorithm. The influence of k value is also discussed.

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References

  1. Bai, X., Sapiro, G.: Geodesic matting: A framework for fast interactive image and video segmentation and matting. Int. J. Comput. Vision 82(2), 113–132 (2009)

    Article  Google Scholar 

  2. Berclaz, J., Turetken, E., Fleuret, F., Fua, P.: Multiple object tracking using k-shortest paths optimization. IEEE Trans. Pattern Anal. Mach. Intell. (2011)

    Google Scholar 

  3. Borgefors, G.: Distance transformations in arbitrary dimensions. Computer Vision, Graphics, and Image Processing 27(3), 321–345 (1984)

    Article  Google Scholar 

  4. Criminisi, A., Sharp, T., Blake, A.: GeoS: geodesic image segmentation. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 99–112. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Eppstein, D.: Finding the \(k\) shortest paths. SIAM J. Comp. 28(2), 652–673 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Grady, L.: Random walks for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 28(11), 1768–1783 (2006)

    Article  Google Scholar 

  7. Kormos, A., Kormos, J., Nagy, B., Zrg, Z.: Choosing appropriate distance measurement in digital image segmentation. Annales Univ. Sci. Budapest. Sect. Comp. 24, 193–208 (2004)

    MATH  Google Scholar 

  8. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proc. 8th Int’l Conf. Computer Vision, vol. 2, pp. 416–423 (2001)

    Google Scholar 

  9. Price, B.L., Morse, B.S., Cohen, S.: Geodesic graph cut for interactive image segmentation. In: CVPR, pp. 3161–3168. IEEE (2010)

    Google Scholar 

  10. Toivanen, P.J.: New geodesic distance transforms for gray-scale images. Pattern Recogn. Lett. 17(5), 437–450 (1996)

    Article  Google Scholar 

  11. Wang, J., Yagi, Y.: Shape priors extraction and application for geodesic distance transforms in images and videos. Pattern Recogn. Lett. 34(12), 1386–1393 (2013)

    Article  Google Scholar 

  12. Zhou, L., Qiao, Y., Yang, J., He, X.: Learning geodesic CRF model for image segmentation. In: 2012 19th IEEE International Conference on Image Processing (ICIP) (2012)

    Google Scholar 

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Correspondence to Michael Holuša .

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Holuša, M., Sojka, E. (2015). A k-max Geodesic Distance and Its Application in Image Segmentation. In: Azzopardi, G., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2015. Lecture Notes in Computer Science(), vol 9256. Springer, Cham. https://doi.org/10.1007/978-3-319-23192-1_52

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  • DOI: https://doi.org/10.1007/978-3-319-23192-1_52

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23191-4

  • Online ISBN: 978-3-319-23192-1

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