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The Strange World of the Hausdorff Metric Geometry


XXII. References


[1]        Michael Barnsley, Fractals Everywhere, Academic Press, Inc., San Diego, 1988.


[2]        Christopher Bay, Amber Lembcke, and Steven Schlicker. When Lines go Bad In Hyperspace, Demonstratio Mathematica, Vol. XXXVIII, No. 3, p. 689-701.


[3]        Chantel Blackburn, Kris Lund, Steven Schlicker, Patrick Sigmon, and Alex Zupan, Journal of Geometry , (2009), 92,. Numbers 1-2, 28-59.


[4]        Chantel Blackburn, Steven Schlicker, and Alex Zupan, Graph Theory Applications of the Hausdorff Metric Geometry, in preparation.


[5]        Leonard Blumenthal, Theory and Applications of Distance Geometry, Oxford University Press, 1953.


[6]        Agnieszka Bogdewicz, Some Metric Properties of Hyperspaces, Demonstratio Mathematica, XXXIII: 135-149, 2000.


[7]        Dominic Braun, John Mayberry, Audrey Powers, and Steven Schlicker, A Singular Introduction to the Hausdorff Metric Geometry, Pi Mu Epsilon Journal, Vol. 12, No. 3, p. 129-138, 2005.


[8]        E. R. Dougherty, Application of the Hausdorff metric in gray-scale mathematical morphology via truncated umbrae,JVCIR, Vol. 2 (1991), p. 177-187.


[9]        I. Ginchev and A. Hoffman, The Hausdorff Nearest Circle to a Convex Compact Set in the Plane, Journal for Analysis and its Applications, Vol. 17, No.2 (1998), p. 479-499.


[10]      Paul W. Goldberg, Sally A. Goldman, and Stephen D. Scott, PAC-learning of one-dimensional patterns, Machine Learning, Vol. 25, No. 1 (1996), p. 51-70.


[11]      Katrina Honigs, Missing Edge Coverings of Bipartite Graphs, submitted to the Journal of Graph Theory.


[12]      Thomas Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, Inc., New York, 2001.


[13]      Gabriele Lohmann and D. Yves von Cramon, Automatic labelling of the human cortical surface using sulcal basins, Medical Image Analysis, Vol. 4 (2000), p. 179-188.


[14]      Kristina Lund, Steven Schlicker, and Patrick Sigmon, Fibonacci sequences in the space of compact sets, Involve, Vol. 1 (2008), No. 2, 197-215.


[15]      J. Mayberry, The Hausdorff Metric, Senior Thesis, University of California, Fullerton, Spring, 2002.


[16]      David Montague, Betweenness of Compact Sets, in preparation.


[17]      James R. Munkres, Topology, Second Edition, Prentice Hall, 2000.


[18]      Clark F. Olsen and Daniel P. Huttenlocher, Automatic Target Recognition by Matching Oriented Edge Pixels, IEEE Transactions on Image Processing, Vol. 6, No. 1 (1997), p. 103-113.


[19]      J. Paumard, J. and E. Aubourg, Adjusting astronomical images using a censored Hausdorff distance, Proc. of 4th IEEE Int. Conf. on Image Processing}, Vol. III (1997), p. 232-xxx.


[20]      B. I. Penkov and Bl. Sendov, Hausdorff Metric and its Applications, Numeische Methoden der Approzstheorie, Vol. 1 (1972), p. 127-146.


[21]      Bl. Sendov, Hausdorff Geometry of Polynomials, East Journal on Approximations 7 (2001), p. 123-178


[22]      Steven Schlicker, Lisa Morales, and Daniel Schultheis, Polygonal chain sequences in the space of compact sets, Journal of Integer Sequences, Vol. 12 (2009), Article 09.1.7.


[23]      István Szatmári and Tamás Roska, The CNN Implementation of Wave Type Metric for Image Analysis and Classification, IEEE Int. Workshop on Nonlinear Dynamics of Electronic Systems, Budapest, Hungary, 1998, p. 137-140.


[24]      B. Takacs  H. Wechsler, Face Identification Using the Hausdorff Metric, 3rd Int. Conf. on Automatic Face and Gesture Recognition, Nara, Japan, 1998.


[25]      United States Army Research Office (ARO) Small Business Technology Transfer Proposal, Smooth, Piecewise-Polynomial Terrain Representation Using Nontraditional Metrics, 2004.


[26]      Alexander Zupan, Infinite cardinalities in the Hausdorff metric geometry, in preparation.

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