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Visual Point Set Processing with Lattice Structures: Application to Parsimonious Representations of Digital Histopathology Images

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Geometric Science of Information (GSI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8085))

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Abstract

Digital tissue images are too big to be processed with traditional image processing pipelines. We resort to the nuclear architecture within the tissue to explore such big images with geometrical and topological representations based on Delaunay triangulations of seed points. Then, we relate this representation to the parsimonious paradigm. Finally, we develop specific mathematical morphology operators to analyze any point set and contribute to the exploration of these huge medical images.

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References

  1. Abu Eid, R., Landini, G.: Morphometrical differences between pseudo-epitheliomatous hyperplasia in granular cell tumours and squamous cell carcinomas. Histopathology 48, 407–416 (2006)

    Article  Google Scholar 

  2. Basavanhally, A.N., Ganesan, S., Agner, S., Monaco, J.P., Feldman, M.D., Tomaszewski, J.E.: Computerized image-based detection and grading of lymphocytic infiltration in HER2+ breast cancer histopathology. IEEE Trans. Biomed. Eng. 57, 642–653 (2010)

    Article  Google Scholar 

  3. Benoît, L., Mairal, J., Bach, F., Ponce, J.: Sparse Image Representation with Epitomes. In: IEEE Conference on Computer Vision and Pattern Recognition, Colorado Springs, United States, pp. 2913–2920 (2011)

    Google Scholar 

  4. Bing, R.H.: Elementary Point Set Topology. Amer. Math. Monthly 67 (1960)

    Google Scholar 

  5. Brostow, G.J., Shotton, J., Fauqueur, J., Cipolla, R.: Segmentation and Recognition Using Structure from Motion Point Clouds. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 44–57. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic Decomposition Basis Pursuit. SIAM Review 3(1), 129–159 (2001)

    Article  MathSciNet  Google Scholar 

  7. Cousty, J., Najman, L., Serra, J.: Some morphological operators in graph spaces. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 149–160. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Doyle, S., Agner, S., Madabhushi, A., Feldman, M., Tomaszewski, J.: Automated Grading of Breast Cancer Histopathology Using Spectral Clustering with Textural and Architectural Image Features. In: 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI, vol. 29, pp. 496–499 (2008)

    Google Scholar 

  9. Doyle, S., Hwang, M., Shah, K., Madabhushi, A., Feldman, M., Tomaszeweski, J.: Automated grading of prostate cancer using architectural and textural image features. In: Proceedings of the 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 1284–1287 (2008)

    Google Scholar 

  10. Edelsbrunner, H., Kirkpatrick, D.G.: On the shape of set of points in the plane. IEEE Trans. Inform. Theory 29, 551–559 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pathology Innovation Centre of Excellence (PICOE). Digital Histopathology: A New Frontier in Canadian Healthcare. White Paper. GE Healthcare (January 2012), http://www.gehealthcare.com/canada/it/downloads/digitalpathology/GE_PICOE_Digital_Pathology_A_New_Frontier_in_Canadian_Healthcare.pdf (accessed December 2012)

  12. Heijmans, H., Nacken, P., Toet, A., Vincent, L.: Graph Morphology. Journal of Visual Communication and Image Representation 3(1), 24–38 (1992)

    Article  Google Scholar 

  13. Levillain, R., Géraud, T., Najman, L.: Milena: Write Generic Morphological Algorithms Once, Run on Many Kinds of Images. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) ISMM 2009. LNCS, vol. 5720, pp. 295–306. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Loménie, N., Gallo, L., Cambou, N., Stamon, G.: Morphological Operations on Delaunay Triangulations. In: International Conference on Pattern Recognition, pp. 556–559 (2000)

    Google Scholar 

  15. Loménie, N., Stamon, G.: Morphological Mesh filtering and alpha-objects. Pattern Recognition Letters 29(10), 1571–1579 (2008)

    Article  Google Scholar 

  16. Loménie, N., Stamon, G.: Point Set Analysis. In: Hawkes, P.W. (ed.) Advances in Imaging and Electron Physics, vol. 167, pp. 255–294. Academic Press, San Diego (2011)

    Google Scholar 

  17. Loménie, N., Racoceanu, D.: Point set morphological filtering and semantic spatial configuration modeling: application to microscopic image and bio-structure analysis. Pattern Recognition 45(8), 2894–2911 (2012)

    Article  Google Scholar 

  18. Mallat, S.: A Wavelet Tour of Signal Processing, 3rd edn. The Sparse Way. Academic Press (2008)

    Google Scholar 

  19. Meyer, F., Stawiaski, J.: Morphology on Graphs and Minimum Spanning Trees. In: Proceedings of the International Symposium on Mathematical Morphology, pp. 161–170 (2009)

    Google Scholar 

  20. Needell, D., Ward, R.: Stable image reconstruction using total variation minimization (2012), http://arxiv.org/abs/1202.6429

  21. Rusu, R.B., Cousins, S.: 3D is here: Point Cloud Library (PCL). In: IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China (2011)

    Google Scholar 

  22. Sutherland, W.A.: An Introduction to Metric and Topological Spaces. Oxford University Press, New York (1975)

    Google Scholar 

  23. Ta, V.T., Lezoray, O., Elmoataz, A., Schupp, S.: Graph-based Tools for Microscopic Cellular Image Segmentation. Pattern Recognition, Special Issue on Digital Image Processing and Pattern Recognition Techniques for the Detection of Cancer 42(6), 1113–1125 (2009)

    Google Scholar 

  24. Vaidyanathaswamy, R.: Set Topology. Dover, New York (1999)

    MATH  Google Scholar 

  25. Whitehead, J.H.C.: Combinatorial homotopy. Bull. Amer. Math. Soc. 55 (1949)

    Google Scholar 

  26. Zwicker, M., Pauly, M., Knoll, O., Gross, M.: Pointshop 3D: An Interactive System for Point-Based Surface Editing. In: SIGGRAPH 2002 (2002)

    Google Scholar 

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Loménie, N. (2013). Visual Point Set Processing with Lattice Structures: Application to Parsimonious Representations of Digital Histopathology Images. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_94

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  • DOI: https://doi.org/10.1007/978-3-642-40020-9_94

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40019-3

  • Online ISBN: 978-3-642-40020-9

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