Skip to main content Accessibility help
×
  • Cited by 18
Publisher:
Cambridge University Press
Online publication date:
July 2015
Print publication year:
2015
Online ISBN:
9781139523967

Book description

This comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical engineering, and computer graphics.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents

References
[1] A., Oppenheim and A., Willsky, Signals and Systems. Prentice Hall, 1996.
[2] R., Gonzalez and R., Woods, Digital Image Processing. Prentice Hall, 2007.
[3] M., do Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, 1976.
[4] V., Guillemin and A., Pollack, Differential Topology. Prentice Hall, 1974.
[5] R., Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications. Springer, 2003.
[6] A., Zomorodian, Topology for Computing. Cambridge University Press, 2009.
[7] H., Edelsbrunner and J., Harer, Computational Topology: An Introduction. American Mathematical Society, 2010.
[8] D., Ziou and S., Tabbone, Edge detection techniques – an overview, International Journal of Pattern Recognition and Image Analysis, vol. 8, pp. 537–59, 1998.
[9] S., Mallat and S., Zhong, Characterization of signals from multiscale edges, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp. 710–32, 1992.
[10] L., Zhang and P., Bao, A wavelet-based edge detection method by scale multiplication, in Proc. Int. Conf. Pattern Recognition, pp. 501–4, 2002.
[11] S., Yi, D., Labate, G., Easley, and H., Krim, A shearlet approach to edge analysis and detection, IEEE Trans. Image Processing, vol. 18, no. 5, pp. 929–41, 2009.
[12] J., Parker, Algorithms for Image Processing and Computer Vision. Wiley, 2010.
[13] T., Chan and L., Vese, Active contours without edges, IEEE Trans. Image Processing, vol. 10, no. 2, pp. 266–77, 2001.
[14] A., Yezzi Jr., A., Tsai, and A., Willsky, A fully global approach to image segmentation via coupled curve evolution equations, Journal of Visual Communication and Image Representation, vol. 13, no. 1–2, pp. 195–216, 2002.
[15] M., Giaquinta and S., Hildebrandt, Calculus of variations I. Springer-Verlag, 2004.
[16] B., Lee, A., Ben Hamza, and H., Krim, An active contour model for image segmentation: A variational perspective, in Proc. IEEE ICASSP, pp. 1585–8, 2002.
[17] P., Basser, J., Mattiello, and D. L., Bihan, MR diffusion tensor spectroscopy and imaging, Biophysical Journal, vol. 66, no. 1, pp. 259–67, 1994.
[18] M., Khader and A., Ben Hamza, Nonrigid image registration using an entropic similarity, IEEE Trans. Information Technology in BioMedicine, vol. 15, no. 5, pp. 681–90, 2011.
[19] G., Taubin, A signal processing approach to fair surface design, in Proc. ACM SIGGRAPH, pp. 351–8, 1995.
[20] Y., Zhang and A., Ben Hamza, Vertex-based diffusion for 3D mesh denoising, IEEE Trans. Image Processing, vol. 16, no. 4, pp. 1036–45, 2007.
[21] Z., Karni and C., Gotsman, Spectral compression of mesh geometry, in Proc. ACM SIGGRAPH, pp. 279–86, 2000.
[22] K., Siddiqi and S., Pizer (eds), Medial Representations: Mathematics, Algorithms and Applications. Springer, 2008.
[23] S., Baloch and H., Krim, Object recognition through topo-geometric shape models using error-tolerant subgraph isomorphisms, IEEE Trans. Image Processing, vol. 19, no. 5, pp. 1191–200, 2010.
[24] D., Aouada and H., Krim, Squigraphs for fine and compact modeling of 3D shapes, IEEE Trans. Image Processing, vol. 19, no. 2, pp. 306–21, 2010.
[25] W., Mohamed and A., Ben Hamza, Reeb graph path dissimilarity for 3D object matching and retrieval, The Visual Computer, vol. 28, no. 3, pp. 305–18, 2012.
[26] A., Fomenko and T., Kunii, Topological Modeling for Visualization. Springer-Verlag, 1997.
[27] A., Ben Hamza and H., Krim, Geodesic matching of triangulated surfaces, IEEE Trans. Image Processing, vol. 15, no. 8, pp. 2249–58, 2006.
[28] C., Li and A., Ben Hamza, A multiresolution descriptor for deformable 3D shape retrieval, The Visual Computer, vol. 29, pp. 513–24, 2013.
[29] D., Lowe, Distinctive image features from scale-invariant keypoints, Int. Journal of Computer Vision, vol. 60, no. 2, pp. 91–110, 2004.
[30] C., Li and A., Ben Hamza, Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: A comparative survey, Multimedia Systems, vol. 20, no. 3, pp. 253–81, 2014.
[31] M., Armstrong, Groups and Symmetry. Springer, 1988.
[32] D., Saracino, Abstract Algebra: A First Course. Waveland Press Inc, 2008.
[33] A., Baker, Matrix Groups: An Introduction to Lie Group Theory. Springer, 2003.
[34] M., Crossley, Essential Topology. Springer, 2005.
[35] S., Goodman, Beginning Topology. American Mathematical Society, 2009.
[36] W., Tutte, Graph Theory. Cambridge University Press, 2001.
[37] R., Wilson, Introduction to Graph Theory. Pearson, 2012.
[38] C., Li and A., Ben Hamza, Symmetry discovery and retrieval of nonrigid 3D shapes using geodesic skeleton paths, Multimedia Tools and Applications, vol. 72, no. 2, pp. 1027–47, 2014.
[39] M., Kazhdan, B., Chazelle, D., Dobkin, A., Finkelstein, and T., Funkhouser, A reflective symmetry descriptor, Proc. ECCV, pp. 642–56, 2002.
[40] M., Ovsjanikov, J., Sun, and L., Guibas, Global intrinsic symmetries of shapes, Computer Graphics Forum, vol. 27, no. 5, pp. 1341–8, 2008.
[41] N., Mitra, M., Pauly, M., Wand, and D., Ceylan, Symmetry in 3D geometry: Extraction and applications, Computer Graphics Forum, vol. 32, no. 6, pp. 1–23, 2013.
[42] N., Cornea, D., Silver, X., Yuan, and R., Balasubramanian, Computing hierarchical curve-skeletons of 3D objects, The Visual Computer, vol. 21, no. 11, pp. 945–55, 2005.
[43] S., Belongie, J., Malik, and J., Puzicha, Shape matching and object recognition using shape contexts, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 24, pp. 509–22, 2002.
[44] X., Bai and L., Latecki, Path similarity skeleton graph matching, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 7, pp. 1282–92, 2008.
[45] Y., Katznelson and Y., Katznelson, A (Terse) Introduction to Linear Algebra. American Mathematical Society, 2007.
[46] B., Cooperstein, Advanced Linear Algebra. CRC Press, 2010.
[47] L., Debnath and P., Mikusinski, Introduction to Hilbert Spaces with Applications. Academic Press, 2005.
[48] R., Courant and D., Hilbert, Methods of Mathematical Physics, vol. 1. Interscience, 1953.
[49] R., Hartley and A., Zisserman, Multiple View Geometry in Computer Vision. Cambridge University Press, 2004.
[50] D., Marsh, Applied Geometry for Computer Graphics and CAD. Springer, 2005.
[51] G., Sapiro, Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, 2006.
[52] R., Cipolla and P., Giblin, Visual Motion of Curves and Surfaces. Cambridge University Press, 2009.
[53] M., Botsch, L., Kobbelt, M., Pauly, P., Alliez, and B., Levy, Polygon Mesh Processing. A K Peters/CRC Press, 2005.
[54] J., McCleary, Geometry From A Differentiable Viewpoint. Cambridge University Press, 1994.
[55] A., Pressley, Elementary Differential Geometry. Springer-Verlag, 2001.
[56] J., Oprea, Differential Geometry and Its Applications. Prentice Hall, 2003.
[57] A., Gray, E., Abbena, and S., Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica. Chapman and Hall/CRC, 2006.
[58] T., Lindeberg, Scale-space, in Encyclopedia of Computer Science and Engineering, pp. 2495–504, 2009.
[59] E., Kreyszig, Introduction to Differentiable Geometry and Riemannian Geometry. University of Toronto Press, 1969.
[60] S., Gallot, D., Hulin, and J., Lafontaine, Riemannian Geometry. Springer-Verlag, 1990.
[61] C., Isham, Modern Differential Geometry for Physicists. World Scientific, 1999.
[62] W., Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, 2002.
[63] S., Lovett, Differential Geometry of Manifolds. A K Peters, Ltd., 2010.
[64] L., Tu, An Introduction to Manifolds. Springer, 2011.
[65] M. W., Hirsh, Differential Topology, vol. 33 of Graduate Texts in Mathematics. NewYork: Springer-Verlag, 1976.
[66] S., Yi and H., Krim, A subspace learning of dynamics on a shape manifold: A generative modeling approach, IEEE Trans. Image Processing, vol. 23, no. 11, pp. 4907–19, 2014.
[67] A., Bronstein, M., Bronstein, and R., Kimmel, Numerical Geometry of Non-rigid Shapes. Springer, 2008.
[68] S., Rosenberg, The Laplacian on a Riemannian Manifold. Cambridge University Press, 1997.
[69] F., Chung, Spectral Graph Theory. American Mathematical Society, 1997.
[70] M., Fiedler, Algebraic connectivity of graphs, Czechoslovak Mathematical Journal, vol. 23, no. 98, pp. 298–305, 1973.
[71] M., Kac, Can one hear the shape of a drum?, The American Mathematical Monthly, vol. 73, no. 4, pp. 1–23, 1966.
[72] C., Gordon and D., Webb, You can't hear the shape of a drum, American Scientist, vol. 84, no. 1, pp. 46–55, 1996.
[73] M., Meyer, M., Desbrun, P., Schroder, and A., Barr, Discrete differential-geometry operators for triangulated 2-manifolds, Visualization and Mathematics III, vol. 3, no. 7, pp. 35–57, 2003.
[74] M., Wardetzky, S., Mathur, F., Kalberer, and E., Grinspun, Discrete Laplace operators: No free lunch, in Proc. Eurographics Symposium on Geometry Processing (SGP'07), pp. 33–7, 2007.
[75] R., Rustamov, Laplace–Beltrami eigenfunctions for deformation invariant shape representation, in Proc. Symposium on Geometry Processing (SGP'07), pp. 225–33, 2007.
[76] J., Milnor, Morse Theory. Princeton University Press, 1963.
[77] B., Horn and M., Brooks, Shape from Shading. MIT Press, 1989.
[78] M., Ghomi, Shadows and convexity of surfaces, Annals of Mathematics, vol. 155, pp. 281–93, 2002.
[79] M., Ghomi, Solution to the shadow problem in 3-space, Adv. Studies in Pure Math., vol. 34, pp. 129–42, 2000.
[80] Y., Shinagawa, T., Kunii, and Y., Kergosien, Surface coding based on Morse theory, IEEE Computer Graphics and Applications, vol. 11, no. 5, pp. 66–78, 1991.
[81] F., Lazarus and A., Verroust, Level set diagrams of polyhedral objects, in Proc. ACM Sympo. Solid Modeling and Applications, pp. 130–40, 1999.
[82] K., Siddiqi, A., Shokoufandeh, S., Dickinson, and S., Zucker, Shock graphs and shape matching, Int. Journal of Computer Vision, vol. 35, no. 1, pp. 13–32, 1999.
[83] M., Hilaga, Y., Shinagawa, T., Kohmura, and T., Kunii, Topology matching for fully automatic similarity estimation of 3D shapes, in Proc. SIGGRAPH, pp. 203–12, 2001.
[84] K., Siddiqi, J., Zhang, D., Macrini, A., Shokoufandeh, S., Bouix, and S., Dickinson, Retrieving articulated 3-D models using medial surfaces, Machine Vision and Applications, vol. 19, no. 4, pp. 261–75, 2008.
[85] J., Damon, Tree structure for contractible regions in ℝ3, Int. Journal of Computer Vision, vol. 74, no. 2, pp. 103–16, 2007.
[86] N., Cornea, M., Demirci, D., Silver, A., Shokoufandeh, S., Dickinson, and P., Kantor, 3D object retrieval using many-to-many matching of curve skeletons, in Proc. Int. Conf. Shape Modeling and Applications, pp. 368–73, 2005.
[87] M., Hassouna and A., Farag, Variational curve skeletons using gradient vector flow, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 12, pp. 2257–74, 2009.
[88] A., Tagliasacchi, H., Zhang, and D., Cohen-Or, Curve skeleton extraction from incomplete point cloud, ACM Trans. Graphics, vol. 28, no. 3, 2009.
[89] M., Ankerst, G., Kastenmüller, H., Kriegel, and T., Seidl, 3D shape histograms for similarity search and classification in spatial databases, in Proc. Int. Sympo. Advances in Spatial Databases, pp. 207–26, 1999.
[90] R., Osada, T., Funkhouser, B., Chazelle, and D., Dobkin, Shape distributions, ACM Trans. Graphics, vol. 21, no. 4, pp. 807–32, 2002.
[91] M., Kazhdan, T., Funkhouser, and S., Rusinkiewicz, Rotation invariant spherical harmonic representation of 3D shape descriptors, in Proc. Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (SGP'03), pp. 156–64, 2003.
[92] D.-Y., Chen, X.-P., Tian, Y.-T., Shen, and M., Ouhyoun, On visual similarity based 3D model retrieval, Computer Graphics Forum, vol. 22, no. 3, pp. 223–32, 2003.
[93] P., Shilane, P., Min, M., Kazhdan, and T., Funkhouser, The Princeton shape benchmark, in Proc. Shape Modeling International (SMI'04), pp. 167–78, 2004.
[94] X., Ni, M., Garland, and J., Hart, Fair Morse functions for extracting the topological structure of a surface mesh, in Proc. Int. Conf. Computer Graphics and Interactive Techniques, pp. 613–22, 2004.
[95] J., Tierny, J.-P., Vandeborre, and M., Daoudi, Partial 3D shape retrieval by Reeb pattern unfolding, Computer Graphics Forum, vol. 28, no. 1, pp. 41–55, 2008.
[96] S., Biasotti, D., Giorgi, M., Spagnuolo, and B., Falcidieno, Reeb graphs for shape analysis and applications, Theoretical Computer Science, vol. 392, no. 1-3, pp. 5–22, 2007.
[97] V., Pascucci, G., Scorzelli, P., Bremer, and A., Mascarenhas, Robust on-line computation of Reeb graphs: Simplicity and speed, ACM Trans. Graphics, vol. 26, no. 3, 2007.
[98] G., Patane, M., Spagnuolo, and B., Falcidieno, A minimal contouring approach to the computation of the Reeb graph, IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 4, pp. 583–95, 2009.
[99] M., Reuter, Hierarchical shape segmentation and registration via topological features of Laplace–Beltrami eigenfunctions, Int. Journal of Computer Vision, vol. 89, no. 2, pp. 287–308, 2010.
[100] K., Uhlenbeck, Generic properties of eigenfunctions, American Journal of Mathematics, vol. 98, no. 4, pp. 1059–78, 1976.
[101] D. G., Kendall, D., Barden, T. K., Carne, and H., Le, Shape and Shape Theory. Wiley, 1999.
[102] S. H., Baloch, H., Krim, W., Mio, and A., Srivastava, 3D curve interpolation and object reconstruction, in Proc. IEEE Int. Conf. Image Processing, vol. 2, pp. 982–5, 2005.
[103] S. H., Baloch, H., Krim, I., Kogan, and D. V., Zenkov, Rotation invariant topology coding of 2D and 3D objects using Morse theory, in Proc. Int. Conf. Image Processing, pp. 796–9, 2005.
[104] S., Yi, H., Krim, and L. K., Norris, Human activity as a manifold-valued random process, IEEE Trans. Image Processing, vol. 21, no. 8, pp. 3416–28, 2012.
[105] E., Klassen, A., Srivastava, W., Mio, and S. H., Joshi, Analysis of planar shapes using geodesic paths on shape spaces, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 3, pp. 372–83, 2003.
[106] D., Mumford, Elastica and computer vision, Algebraic Geometry and its Applications, pp. 491–506, 1994.
[107] D. S., Broomhead and M., Kirby, A new approach for dimensionality reduction: Theory and algorithms, SIAM Journal of Applied Mathematics, vol. 60, no. 6, pp. 2114–42, 2000.
[108] D., Broomhead and M. J., Kirby, The Whitney reduction network: A method for computing autoassociative graphs, Neural Computation, vol. 13, pp. 2595–616, 2001.
[109] Y., Yang, H., Lin, and Y., Zhang, Content-based 3-D model retrieval: A survey, IEEE Trans. Systems, Man, and Cybernetics, Part C, vol. 37, no. 6, pp. 1081–98, 2007.
[110] A., DelBimbo and P., Pala, Content-based retrieval of 3D models, ACM Trans. Multimedia Computing, Communications, and Applications, vol. 2, no. 1, pp. 20–43, 2006.
[111] J., Tangelder and R., Veltkamp, A survey of content based 3D shape retrieval methods, Multimedia Tools and Applications, vol. 39, no. 3, pp. 441–71, 2008.
[112] B., Bustos, D., Keim, D., Saupe, T., Schreck, and D., Vranic, Feature-based similarity search in 3D object databases, ACM Computing Surveys, vol. 37, no. 4, pp. 345–87, 2005.
[113] Z., Lian, A., Godil, B., Bustos, M., Daoudi, J., Hermans, S., Kawamura, Y., Kurita, G., Lavoue, H., Nguyen, R., Ohbuchi, Y., Ohkita, Y., Ohishi, F., Porikli, M., Reuter, I., Sipiran, D., Smeets, P., Suetens, H., Tabia, and D., Vandermeulen, SHREC'11 track: Shape retrieval on non-rigid 3D watertight meshes, in Proc. Eurographics/ACM SIGGRAPH Symposium on 3D Object Retrieval (EG 3DOR'11), pp. 79–88, 2011.
[114] B., Li, A., Godil, M., Aono, X., Bai, T., Furuya, L., Li, R., López-Sastre, H., Johan, R., Ohbuchi, C., Redondo-Cabrera, A., Tatsuma, T., Yanagimachi, and S., Zhang, SHREC'12 track: Generic 3D shape retrieval, in Proc. Eurographics Conference on 3D Object Retrieval (EG 3DOR'12), pp. 119–26, 2012.
[115] M., Belkin, P., Niyogi, and V., Sindhwani, Manifold regularization: A geometric framework for learning from labeled and unlabeled examples, Journal of Machine Learning Research, vol. 7, pp. 2399–434, 2006.
[116] B., Lévy, Laplace–Beltrami eigenfunctions: Towards an algorithm that “understands” geometry, in Proc. IEEE Int. Conf. Shape Modeling and Applications, p. 13, 2006.
[117] M., Reuter, F., Wolter, and N., Peinecke, Laplace–Beltrami spectra as “Shape-DNA” of surfaces and solids, Computer-Aided Design, vol. 38, no. 4, pp. 342–66, 2006.
[118] A., Bronstein, M., Bronstein, L., Guibas, and M., Ovsjanikov, Shape Google: Geometric words and expressions for invariant shape retrieval, ACM Trans. Graphics, vol. 30, no. 1, 2011.
[119] J., Sun, M., Ovsjanikov, and L., Guibas, A concise and provably informative multi-scale signature based on heat diffusion, Computer Graphics Forum, vol. 28, no. 5, pp. 1383–92, 2009.
[120] K., Gębal, J. A., Bcerentzen, H., Aances, and R., Larsen, Shape analysis using the auto diffusion function, Computer Graphics Forum, vol. 28, no. 5, pp. 1405–513, 2009.
[121] I., Kokkinos, M., Bronstein, and A., Yuille, Dense scale invariant descriptors for images and surfaces, 2012.
[122] M., Aubry, U., Schlickewei, and D., Cremers, The wave kernel signature: A quantum mechanical approach to shape analysis, in Proc. Computational Methods for the Innovative Design of Electrical Devices, pp. 1626–33, 2011.
[123] R., Litman and A., Bronstein, Learning spectral descriptors for deformable shape correspondence, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 36, no. 1, pp. 171–80, 2014.
[124] S., Mallat, A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press, 2008.
[125] R., Coifman and S., Lafon, Diffusion maps, Applied and Computational Harmonic Analysis, vol. 21, no. 1, pp. 5–30, 2006.
[126] D., Hammond, P., Vandergheynst, and R., Gribonval, Wavelets on graphs via spectral graph theory, Applied and Computational Harmonic Analysis, vol. 30, no. 2, pp. 129–50, 2011.
[127] W., Kim, D., Pachauri, C., Hatt, M., Chung, S., Johnson, and V., Singh, Wavelet based multiscale shape features on arbitrary surfaces for cortical thickness discrimination, in Proc. NIPS, pp. 1135–43, 2012.
[128] Z., Lian, A., Godil, T., Fabry, T., Furuya, J., Hermans, R., Ohbuchi, C., Shu, D., Smeets, P., Suetens, D., Vandermeulen, and S., Wuhrer, SHREC'10 track: Non-rigid 3D shape retrieval, in Proc. Eurographics/ACM SIGGRAPH Sympo. 3D Object Retrieval, pp. 101–8, 2010.
[129] S., Lazebnik, C., Schmid, and J., Ponce, Beyond bags of features: Spatial pyramid matching for recognizing natural scene categories, in Proc. IEEE Computer Vision and Pattern Recognition (CVPR'06), vol. 2, pp. 2169–78, 2006.
[130] K., Järvelin and J., Kekalainen, IR evaluation methods for retrieving highly relevant documents, in Proc. International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR'00), pp. 41–8, 2000.
[131] A., Hatcher, Algebraic Topology. Cambridge University Press, 2002.
[132] J. R., Munkres, Topology: A First Course. Prentice Hall, 1988.
[133] J., May, A Concise Course in Algebraic Topology. Chicago Lectures in Mathematics, University of Chicago Press, 1999.
[134] J. F., Davis and P., Kirk, Lecture Notes in Algebraic Topology, vol. 35 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society, 2001.
[135] H., Edelsbrunner and J. L., Harer, Computational Topology. American Mathematical Society, 2010.
[136] D., Forman, Combinatorial differential topology and geometry: New perspectives in geometric combinatorics, MSRI Publications, vol. 38, 1999.
[137] R., Forman, A user's guide to discrete Morse theory, in Proc. of the 2001 Internat. Conf. on Formal Power Series and Algebraic Combinatorics, A Special Volume of Advances in Applied Mathematics, p. 48, 2001.
[138] P., Hersh, On optimizing discrete Morse functions, Advances in Applied Mathematics, vol. 35, no. 3, pp. 294–322, 2005.
[139] G., Carlsson, Topology and data, Bull. of the Amer. Math. Soc., vol. 46, no. 2, pp. 255–308, 2009.
[140] H., Chintakunta and H., Krim, Divide and conquer: Localizing coverage holes in sensor networks, in SECON, pp. 359–66, IEEE, 2010.
[141] H., Chintakunta and H., Krim, Distributed localization of coverage holes using topological persistence, IEEE Transactions on Signal Processing, vol. 62, pp. 2531–41, May 2014.
[142] V., de Silva and R., Ghrist, Coordinate-free coverage in sensor networks with controlled boundaries via homology, I. J. Robotic Res., vol. 25, no. 12, pp. 1205–22, 2006.
[143] J. W., Vick, Homology Theory: An Introduction to Algebraic Topology. Springer, 1994.
[144] A., Muhammad and M., Egerstedt, Control using higher order Laplacians in network topologies, in Proc. of 17th International Symposium on Mathematical Theory of Networks and Systems, pp. 1024–38, 2006.
[145] R., Ghrist and A., Muhammad, Coverage and hole-detection in sensor networks via homology, in Proceedings ofthe 4th international symposium on information processing in sensor networks, p. 34, IEEE Press, 2005.
[146] Y., Wang, J., Gao, and J. S., Mitchell, Boundary recognition in sensor networks by topological methods, ACM Special Interest Group on Mobility of Systems, Users, Data and Computing, pp. 122–33, 2006.
[147] E., Čech, Theorie generale de l'homologie dans un espace quelconque, Fundamenta Mathematicae, vol. 19, pp. 149–83, 1932.
[148] M., Kahle, Random geometric complexes, Discrete & Computational Geometry, vol. 45, no. 3, pp. 553–73, 2011.
[149] D., Kempe and F., McSherry, A decentralized algorithm for spectral analysis, in Proceedings of the thirty-sixth annual ACM symposium on Theory of computing, pp. 561–8, 2004.
[150] S., Boyd, A., Ghosh, B., Prabhakar, and D., Shah, Mixing times for random walks on geometric random graphs, in Proc. SIAM Workshop on Analytic Algorithmics and Combinatorics, 2005.
[151] S., Boyd, A., Ghosh, B., Prabhakar, and D., Shah, Analysis and optimization of randomized gossip algorithms, in Proc. IEEE Conf. Decision and Control, vol. 43, pp. 5310–15, 2004.
[152] J. M., Kleinberg, An impossibility theorem for clustering, Proc. Conf. Advances in Neural Information Processing Systems, vol. 15, pp. 446–53, 2002.
[153] G., Carlsson and F., Memoli, Characterization, stability and convergence of hierarchical clustering methods, Journal of Machine Learning Research, vol. 11, pp. 1425–70, 2010.
[154] H., Edelsbrunner and J., Harer, Persistent homology – a survey, Contemporary mathematics, vol. 453, pp. 257–82, 2008.
[155] G., Carlsson and A., Zomorodian, The theory of multidimensional persistence, Discrete Comput. Geom., vol. 42, pp. 71–93, May 2009.
[156] A., Vergne, L., Decreusefond, and P., Martins, Reduction algorithm for simplicial complexes, preprint: http://hal.archives-ouvertes.fr/hal-00688919, pp. 1–8, 2012.
[157] A. C., Wilkerson, T. J., Moore, A., Swami, and H., Krim, Simplifying the homology of networks via strong collapses., in ICASSP, pp. 5258–62, IEEE, 2013.
[158] J. A., Barmak and E. G., Minian, Strong homotopy types, nerves, and collapses, Discrete & Computational Geometry, vol. 47, pp. 301–28, 2012.
[159] C. H., Dowker, Homology groups of relations, The Annals of Mathematics, vol. 56, pp. 84–95, 1952.
[160] R. H., Atkin, From cohomology in physics to q-connectivity in social sciences, International Journal of Man-Machine Studies, vol. 4, no. 2, pp. 139–67, 1972.
[161] J. H., Johnson, Some structures and notation of Q-analysis, Environment and Planning B, vol. 8, no. 1,pp. 73–86, 1981.
[162] S., Maletić, M., Rajković, and D., Vasiljević, Simplicial complexes of networks and their statistical properties, in: M., Bubak, G. D., van Albada, J., Dongarra, P. M. A., Sloot (eds), ICCS 2008, Part II, LNCS, vol. 5102, pp. 568–75, 2008.
[163] T. J., Moore, R. J., Drost, P., Basu, R., Ramanathan, and A., Swami, Analyzing collaboration networks using simplicial complexes: A case study, Proceedings of the IEEE INFOCOM 2012 Workshop (NetSciCom), pp. 238–43, March 2012.
[164] N. H., Packard, J. P., Crutchfield, J. D., Farmer, and R. S., Shaw, Geometry from a Time Series, Physical Review Letters, vol. 45, no. 9, p. 712, 1980.
[165] F., Takens, Detecting strange attractors in turbulence, in Dynamical Systems and Turbulence, vol. 898 of Lecture Notes in Mathematics, pp. 366–81, 1981.
[166] S., Emrani, T., Gentimis, and H., Krim, Persistent homology of delay embeddings and its application to wheeze detection, IEEE Signal Processing Letters, vol. 21, no. 4, pp. 459–63, 2014.
[167] L. J., Hadjileontiadis, Lung Sounds: An Advanced Signal Processing Perspective. Morgan and Claypool Publishers, 2009.
[168] W., Lippincott and E., Wilkins, Auscultation Skills: Breath and Heart Sounds. Princeton University Press, 2009.
[169] D., Wrigley, Heart and Lung Sounds Reference Library. PESI HealthCare, 2011.
[170] R., Wilkins, J., Hodgkin, and B., Lopez, Fundamentals of Lung and Heart Sounds. Mosby, 2004.
[171] V., De Silva and G., Carlsson, Topological estimation using witness complexes, in The First Eurographics Conference on Point-Based Graphics, pp. 157–66, 2004.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.