Abstract
Computational geometry and topology are areas which have much potential for the analysis of arbitrarily high-dimensional data sets. In order to apply geometric or topological methods one must first generate a representative point cloud data set from the original data source, or at least a metric or distance function, which defines a distance between the elements of a given data set. Consequently, the first question is: How to get point cloud data sets? Or more precise: What is the optimal way of generating such data sets? The solution to these questions is not trivial. If a natural image is taken as an example, we are concerned more with the content, with the shape of the relevant data represented by this image than its mere matrix of pixels. Once a point cloud has been generated from a data source, it can be used as input for the application of graph theory and computational topology. In this paper we first describe the case for natural point clouds, i.e. where the data already are represented by points; we then provide some fundamentals of medical images, particularly dermoscopy, confocal laser scanning microscopy, and total-body photography; we describe the use of graph theoretic concepts for image analysis, give some medical background on skin cancer and concentrate on the challenges when dealing with lesion images. We discuss some relevant algorithms, including the watershed algorithm, region splitting (graph cuts), region merging (minimum spanning tree) and finally describe some open problems and future challenges.
Keywords
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
Holzinger, A., Dehmer, M., Jurisica, I.: Knowledge discovery and interactive data mining in bioinformatics state-of-the-art, future challenges and research directions. BMC Bioinformatics 15(suppl. 6), S1 (2014)
Edelsbrunner, H., Harer, J.L.: Computational Topology: An Introduction. American Mathematical Society, Providence (2010)
Memoli, F., Sapiro, G.: A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics 5(3), 313–347 (2005)
Holzinger, A.: Topological Data Mining in a Nutshell. Springer, Heidelberg (2014) (in print)
Mmoli, F., Sapiro, G.: A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics 5(3), 313–347 (2005)
Canutescu, A.A., Shelenkov, A.A., Dunbrack, R.L.: A graph-theory algorithm for rapid protein side-chain prediction. Protein Science 12(9), 2001–2014 (2003)
Zomorodian, A.: Topology for computing, vol. 16. Cambridge University Press, Cambridge (2005)
Vegter, G.: Computational topology, pp. 517–536. CRC Press, Inc., Boca Raton (2004)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Cannon, J.W.: The recognition problem: What is a topological manifold? Bulletin of the American Mathematical Society 84(5), 832–866 (1978)
De Berg, M., Van Kreveld, M., Overmars, M., Schwarzkopf, O.C.: Computational geometry, 3rd edn. Springer, Heidelberg (2008)
Aurenhammer, F.: Voronoi diagrams - a survey of a fundamental geometric data structure. Computing Surveys 23(3), 345–405 (1991)
Axelsson, P.E.: Processing of laser scanner data - algorithms and applications. ISPRS Journal of Photogrammetry and Remote Sensing 54(2-3), 138–147 (1999)
Vosselman, G., Gorte, B.G., Sithole, G., Rabbani, T.: Recognising structure in laser scanner point clouds. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 46(8), 33–38 (2004)
Smisek, J., Jancosek, M., Pajdla, T.: 3D with Kinect, pp. 3–25. Springer (2013)
Dal Mutto, C., Zanuttigh, P., Cortelazzo, G.M.: Time-of-Flight Cameras and Microsoft Kinect. Springer, Heidelberg (2012)
Khoshelham, K., Elberink, S.O.: Accuracy and resolution of kinect depth data for indoor mapping applications. Sensors 12(2), 1437–1454 (2012)
Kayama, H., Okamoto, K., Nishiguchi, S., Yamada, M., Kuroda, T., Aoyama, T.: Effect of a kinect-based exercise game on improving executive cognitive performance in community-dwelling elderly: Case control study. Journal of Medical Internet Research 16(2) (2014)
Gonzalez-Ortega, D., Diaz-Pernas, F.J., Martinez-Zarzuela, M., Anton-Rodriguez, M.: A kinect-based system for cognitive rehabilitation exercises monitoring. Computer Methods and Programs in Biomedicine 113(2), 620–631 (2014)
Holzinger, A., Dorner, S., Födinger, M., Valdez, A.C., Ziefle, M.: Chances of Increasing Youth Health Awareness through Mobile Wellness Applications. In: Leitner, G., Hitz, M., Holzinger, A. (eds.) USAB 2010. LNCS, vol. 6389, pp. 71–81. Springer, Heidelberg (2010)
Sitek, A., Huesman, R.H., GuIlberg, G.T.: Tomographic reconstruction using an adaptive tetrahedral mesh defined by a point cloud. IEEE Transactions on Medical Imaging 25(9), 1172–1179 (2006)
Caramella, D., Bartolozzi, C.: 3D image processing: techniques and clinical applications (Medical Radiology / Diagnostic Imaging). Springer, London (2002)
Salton, G., Wong, A., Yang, C.S.: A vector space model for automatic indexing. Commun. ACM 18(11), 613–620 (1975)
Holzinger, A.: On Knowledge Discovery and Interactive Intelligent Visualization of Biomedical Data - Challenges in Human Computer Interaction & Biomedical Informatics. INSTICC, Rome, pp. 9–20 (2012)
Wagner, H., Dlotko, P., Mrozek, M.: Computational topology in text mining, pp. 68–78 (2012)
Argenziano, G., Soyer, H.P.: Dermoscopy of pigmented skin lesions–a valuable tool for early diagnosis of melanoma. The Lancet Oncology 2(7) (2001)
Eisemann, N., Waldmann, A., Katalinic, A.: Incidence of melanoma and changes in stage-specific incidence after implementation of skin cancer screening in Schleswig-Holstein. Bundesgesundheitsblatt, Gesundheitsforschung, Gesundheitsschutz 57, 77–83 (2014)
Argenziano, G., Giacomel, J., Zalaudek, I., Blum, A., Braun, R.P., Cabo, H., Halpern, A., Hofmann-Wellenhof, R., Malvehy, J., Marghoob, A.A., Menzies, S., Moscarella, E., Pellacani, G., Puig, S., Rabinovitz, H., Saida, T., Seidenari, S., Soyer, H.P., Stolz, W., Thomas, L., Kittler, H.: A Clinico-Dermoscopic Approach for Skin Cancer Screening. Recommendations Involving a Survey of the International Dermoscopy Society (2013)
Australia, M.I.: Dermoscopy (November 2013)
Ahlgrimm-Siess, V., Hofmann-Wellenhof, R., Cao, T., Oliviero, M., Scope, A., Rabinovitz, H.S.: Reflectance confocal microscopy in the daily practice. Semin. Cutan. Med. Surg. 28(3), 180–189 (2009)
Meijering, E., van Cappellen, G.: Biological image analysis primer (2006), booklet online available via www.imagescience.org
Risser, J., Pressley, Z., Veledar, E., Washington, C., Chen, S.C.: The impact of total body photography on biopsy rate in patients from a pigmented lesion clinic. Journal of the American Academy of Dermatology 57(3), 428–434
Mikailov, A., Blechman, A.: Gigapixel photography for skin cancer surveillance: A novel alternative to total-body photography. Cutis 92(5), 241–243 (2013)
dos Santos, S., Brodlie, K.: Gaining understanding of multivariate and multidimensional data through visualization. Computers & Graphics 28(3), 311–325 (2004)
Emmert-Streib, F., de Matos Simoes, R., Glazko, G., McDade, S., Haibe-Kains, B., Holzinger, A., Dehmer, M., Campbell, F.: Functional and genetic analysis of the colon cancer network. BMC Bioinformatics 15(suppl. 6), S6 (2014)
Bramer, M.: Principles of data mining, 2nd edn. Springer, Heidelberg (2013)
Kropatsch, W., Burge, M., Glantz, R.: Graphs in Image Analysis, pp. 179–197. Springer, New York (2001)
Palmieri, G., Sarantopoulos, P., Barnhill, R., Cochran, A.: 4. Current Clinical Pathology. In: Molecular Pathology of Melanocytic Skin Cancer, pp. 59–74. Springer, New York (2014)
Xu, L., Jackowski, M., Goshtasby, A., Roseman, D., Bines, S., Yu, C., Dhawan, A., Huntley, A.: Segmentation of skin cancer images. Image and Vision Computing 17(1), 65–74 (1999)
Argenziano, G., Soyer, H.P., Chimenti, S., Talamini, R., Corona, R., Sera, F., Binder, M., Cerroni, L., De Rosa, G., Ferrara, G., Hofmann-Wellenhof, R., Landthaler, M., Menzies, S.W., Pehamberger, H., Piccolo, D., Rabinovitz, H.S., Schiffner, R., Staibano, S., Stolz, W., Bartenjev, I., Blum, A., Braun, R., Cabo, H., Carli, P., De Giorgi, V., Fleming, M.G., Grichnik, J.M., Grin, C.M., Halpern, A.C., Johr, R., Katz, B., Kenet, R.O., Kittler, H., Kreusch, J., Malvehy, J., Mazzocchetti, G., Oliviero, M., Özdemir, F., Peris, K., Perotti, R., Perusquia, A., Pizzichetta, M.A., Puig, S., Rao, B., Rubegni, P., Saida, T., Scalvenzi, M., Seidenari, S., Stanganelli, I., Tanaka, M., Westerhoff, K., Wolf, I.H., Braun-Falco, O., Kerl, H., Nishikawa, T., Wolff, K., Kopf, A.W.: Dermoscopy of pigmented skin lesions: Results of a consensus meeting via the internet. Journal of the American Academy of Dermatology 48, 679–693 (2003)
Ferri, M., Stanganelli, I.: Size functions for the morphological analysis of melanocytic lesions. International Journal of Biomedical Imaging 2010, 621357 (2010)
Pizzichetta, M.A., Stanganelli, I., Bono, R., Soyer, H.P., Magi, S., Canzonieri, V., Lanzanova, G., Annessi, G., Massone, C., Cerroni, L., Talamini, R.: Dermoscopic features of difficult melanoma. Dermatologic Surgery: Official Publication for American Society for Dermatologic Surgery 33, 91–99 (2007)
Ballard, D.H.: Generalizing the hough transform to detect arbitrary shapes. Pattern Recognition 13(2), 111–122 (1981)
Ruppertshofen, H., Lorenz, C., Rose, G., Schramm, H.: Discriminative generalized hough transform for object localization in medical images. International Journal of Computer Assisted Radiology and Surgery 8(4), 593–606 (2013)
Tsai, A., Yezzi Jr., A., Willsky, A.S.: Curve evolution implementation of the mumford-shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Transactions on Image Processing 10(8), 1169–1186 (2001)
de Mauro, C., Diligenti, M., Gori, M., Maggini, M.: Similarity learning for graph-based image representations. Pattern Recognition Letters 24(8), 1115–1122 (2003)
Bianchini, M., Gori, M., Mazzoni, P., Sarti, L., Scarselli, F.: Face Localization with Recursive Neural Networks. In: Apolloni, B., Marinaro, M., Tagliaferri, R. (eds.) WIRN 2003. LNCS, vol. 2859, pp. 99–105. Springer, Heidelberg (2003)
Chen, C., Freedman, D.: Topology noise removal for curve and surface evolution. In: Menze, B., Langs, G., Tu, Z., Criminisi, A. (eds.) MICCAI 2010. LNCS, vol. 6533, pp. 31–42. Springer, Heidelberg (2011)
Vincent, L., Soille, P.: Watersheds in digital spaces: An efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(6), 583–598 (1991)
Meyer, F.: The steepest watershed: from graphs to images. arXiv preprint arXiv:1204.2134 (2012)
Sonka, M., Hlavac, V., Boyle, R.: Image processing, analysis, and machine vision, 3rd edn. Cengage Learning (2007)
Rogowska, J.: Overview and fundamentals of medical image segmentation, pp. 69–85. Academic Press, Inc. (2000)
Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient Graph-Based Image Segmentation. International Journal of Computer Vision 59(2), 167–181 (2004)
Lee, Y.J., Grauman, K.: Object-graphs for context-aware visual category discovery. IEEE Transactions on Pattern Analysis and Machine Intelligence 34(2), 346–358 (2012)
Wiltgen, M., Gerger, A.: Automatic identification of diagnostic significant regions in confocal laser scanning microscopy of melanocytic skin tumors. Methods of Information in Medicine, 14–25 (2008)
Oesterling, P., Heine, C., Janicke, H., Scheuermann, G.: Visual analysis of high dimensional point clouds using topological landscapes. In: North, S., Shen, H.W., Vanwijk, J.J. (eds.) IEEE Pacific Visualization Symposium 2010, pp. 113–120. IEEE (2010)
Oesterling, P., Heine, C., Janicke, H., Scheuermann, G., Heyer, G.: Visualization of high-dimensional point clouds using their density distribution’s topology. IEEE Transactions on Visualization and Computer Graphics 17(11), 1547–1559 (2011)
Oesterling, P., Heine, C., Weber, G.H., Scheuermann, G.: Visualizing nd point clouds as topological landscape profiles to guide local data analysis. IEEE Transactions on Visualization and Computer Graphics 19(3), 514–526 (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Holzinger, A. et al. (2014). On the Generation of Point Cloud Data Sets: Step One in the Knowledge Discovery Process. In: Holzinger, A., Jurisica, I. (eds) Interactive Knowledge Discovery and Data Mining in Biomedical Informatics. Lecture Notes in Computer Science, vol 8401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43968-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-43968-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43967-8
Online ISBN: 978-3-662-43968-5
eBook Packages: Computer ScienceComputer Science (R0)