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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abu Eid, R., Landini, G.: Morphometrical differences between pseudo-epitheliomatous hyperplasia in granular cell tumours and squamous cell carcinomas. Histopathology 48, 407–416 (2006)
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)
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)
Bing, R.H.: Elementary Point Set Topology. Amer. Math. Monthly 67 (1960)
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)
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic Decomposition Basis Pursuit. SIAM Review 3(1), 129–159 (2001)
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)
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)
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)
Edelsbrunner, H., Kirkpatrick, D.G.: On the shape of set of points in the plane. IEEE Trans. Inform. Theory 29, 551–559 (1983)
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)
Heijmans, H., Nacken, P., Toet, A., Vincent, L.: Graph Morphology. Journal of Visual Communication and Image Representation 3(1), 24–38 (1992)
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)
Loménie, N., Gallo, L., Cambou, N., Stamon, G.: Morphological Operations on Delaunay Triangulations. In: International Conference on Pattern Recognition, pp. 556–559 (2000)
Loménie, N., Stamon, G.: Morphological Mesh filtering and alpha-objects. Pattern Recognition Letters 29(10), 1571–1579 (2008)
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)
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)
Mallat, S.: A Wavelet Tour of Signal Processing, 3rd edn. The Sparse Way. Academic Press (2008)
Meyer, F., Stawiaski, J.: Morphology on Graphs and Minimum Spanning Trees. In: Proceedings of the International Symposium on Mathematical Morphology, pp. 161–170 (2009)
Needell, D., Ward, R.: Stable image reconstruction using total variation minimization (2012), http://arxiv.org/abs/1202.6429
Rusu, R.B., Cousins, S.: 3D is here: Point Cloud Library (PCL). In: IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China (2011)
Sutherland, W.A.: An Introduction to Metric and Topological Spaces. Oxford University Press, New York (1975)
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)
Vaidyanathaswamy, R.: Set Topology. Dover, New York (1999)
Whitehead, J.H.C.: Combinatorial homotopy. Bull. Amer. Math. Soc. 55 (1949)
Zwicker, M., Pauly, M., Knoll, O., Gross, M.: Pointshop 3D: An Interactive System for Point-Based Surface Editing. In: SIGGRAPH 2002 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)