Using weighted Alpha Complexes in Subsurface Modelling: Reconstructing the shape of observed natural objects

[1]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[2]  H. Cramér Mathematical methods of statistics , 1947 .

[3]  Wolfgang Böhm,et al.  Geometric concepts for geometric design , 1993 .

[4]  U. Rembold,et al.  Computer Integrated Manufacturing And Engineering , 1993 .

[5]  H. V. Craig Vector and tensor analysis , 1943 .

[6]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[7]  Alistair R. Brown Interpretation of three-dimensional seismic data , 1986 .

[8]  A. Bossavit Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements , 1997 .

[9]  Karl Sigman Stationary marked point processes , 1995 .

[10]  M. N. Shanmukha Swamy,et al.  Graphs: Theory and Algorithms , 1992 .

[11]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[12]  Robert F. Woodbury,et al.  Variations in solids: A declarative treatment , 1990, Comput. Graph..

[13]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[14]  Robert L. Ogniewicz,et al.  Skeleton-space: a multiscale shape description combining region and boundary information , 1994, 1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Carlo Cattani,et al.  Dimension-independent modeling with simplicial complexes , 1993, TOGS.

[16]  G. Lieberman,et al.  Statistical Theory with Engineering Applications , 1952 .

[17]  C. Read,et al.  Handbook of the normal distribution , 1982 .

[18]  Michael T. Goodrich,et al.  Finding the Convex Hull of a Sorted Point Set in Parallel , 1987, Inf. Process. Lett..

[20]  Prem K. Kythe,et al.  Computational Conformal Mapping , 1998 .

[21]  S. Mardešić Shape Theory: The Inverse System Approach , 1982 .

[22]  Unny Menon,et al.  Concurrent engineering : concepts, implementation and practice , 1994 .

[23]  Ivar Aavatsmark,et al.  Discretization on Non-Orthogonal, Quadrilateral Grids for Inhomogeneous, Anisotropic Media , 1996 .

[24]  M LieshoutvanM.N.,et al.  Stochastic geometry : likelihood and computation , 2000 .

[25]  Pedro Meseguer,et al.  Constraint Satisfaction Problems: An Overview , 1989, AI Commun..

[26]  Joseph N. Wilson,et al.  Handbook of computer vision algorithms in image algebra , 1996 .

[27]  R. R. Martin,et al.  Differential geometry applied to curve and surface design , 1988 .

[28]  J. Ed Akin Computer-assisted mechanical design , 1990 .

[29]  Christopher J. Taylor,et al.  A Method of Automated Landmark Generation for Automated 3D PDM Construction , 1998, BMVC.

[30]  Clement T. Yu,et al.  Segmentation of skin cancer images , 1999, Image Vis. Comput..

[31]  H. Reineck,et al.  Depositional sedimentary environments , 1973 .

[32]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[33]  J. R. Allen,et al.  Principles of physical sedimentology , 1985 .

[34]  Christoph M. Hoffmann,et al.  A graph-constructive approach to solving systems of geometric constraints , 1997, TOGS.

[35]  Remco C. Veltkamp,et al.  Modelling natural objects with -complexes , 2002, Comput. Aided Des..

[36]  R. Veltkamp,et al.  Geometric Modelling with a-Complexes , 2001 .

[37]  Andreas Hartwig Algebraic 3-D Modeling , 1996 .

[38]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[39]  Eliseo Clementini,et al.  A Small Set of Formal Topological Relationships Suitable for End-User Interaction , 1993, SSD.

[40]  Remco C. Veltkamp,et al.  Closed Object Boundaries from Scattered Points , 1994, Lecture Notes in Computer Science.

[41]  David Eppstein,et al.  Dihedral bounds for mesh generation in high dimensions , 1995, SODA '95.

[42]  Herbert Edelsbrunner,et al.  On the Definition and the Construction of Pockets in Macromolecules , 1998, Discret. Appl. Math..

[43]  G. Ranalli Rheology of the Earth : Deformation and Flow Processes in Geophysics and Geodynamics , 1987 .

[44]  Y. Takeda FLOW IN ROCKS MODELLED AS MULTIPHASE CONTINUA : APPLICATION TO POLYMINERALIC ROCKS , 1998 .

[45]  T.P.H. Steeghs Local Power Spectra and Seismic Interpretation , 1997 .

[46]  K. Richards,et al.  River Channels: Environment and Process , 1989 .

[47]  O. Berg,et al.  Seismic stratigraphy II : an integrated approach to hydrocarbon exploration , 1985 .

[48]  J. L. Coolidge,et al.  A Treatise On The Circle And Sphere , 1916 .

[49]  Hans-Hermann Bock,et al.  Classification and Clustering: Problems for the Future , 1994 .

[50]  Exploration and Appraisal Technology: Maximising Rewards by Integration , 1994 .

[51]  Franz Aurenhammer,et al.  Recognising Polytopical Cell Complexes and Constructing Projection Polyhedra , 1987, J. Symb. Comput..

[52]  Aristides A. G. Requicha,et al.  Representaiton of Rigid Solid Objects , 1980, CAD Advanced Course.

[53]  Raimund Seidel,et al.  Exact Upper Bounds for the Number of Faces in d-Dimensional Voronoi Diagrams , 1990, Applied Geometry And Discrete Mathematics.

[54]  J. Lammens A computational model of color perception and color naming , 1995 .

[55]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[56]  Raymond E. Levitt Knowledge-based systems in engineering , 1991 .

[57]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[58]  Duvvuru Sriram,et al.  Artificial intelligence in engineering design (Volume I): design representation and models of routine design , 1992 .

[59]  Robert Bix,et al.  Conics and Cubics: A Concrete Introduction to Algebraic Curves , 1998 .

[60]  Herbert Edelsbrunner,et al.  Weighted alpha shapes , 1992 .

[61]  C. C. Spicer,et al.  Algorithm AS 52: Calculation of Power Sums of Deviations about the Mean , 1972 .

[62]  J. Coolidge The geometry of the complex domain , 1924 .

[63]  Martin Gardner,et al.  Time Travel And Other Mathematical Bewilderments , 1987 .

[64]  A. R. Humphries,et al.  Dynamical Systems And Numerical Analysis , 1996 .

[65]  G. Pinder,et al.  Numerical solution of partial differential equations in science and engineering , 1982 .

[66]  H. Edelsbrunner The union of balls and its dual shape , 1995 .

[67]  I. Aavatsmark,et al.  Discretization on Non-Orthogonal, Curvilinear Grids for Multi-Phase Flow , 1994 .

[68]  J. Hammersley,et al.  Markov fields, correlated percolation, and the Ising model , 1983 .

[69]  Bjørn N. Freeman-Benson,et al.  An incremental constraint solver , 1990, CACM.

[70]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[71]  Klaus Helbig,et al.  Modeling the earth for oil exploration : final report of the CEC's Geoscience I Program, 1990-1993 , 1994 .

[72]  P. D. Newendorp,et al.  Decision analysis for petroleum exploration , 1975 .

[73]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[74]  Ernst P. Mücke,et al.  Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations , 1999, Comput. Geom..

[75]  R. E. Megill,et al.  introduction to risk analysis , 1971 .

[76]  Franz Aurenhammer,et al.  Power Diagrams: Properties, Algorithms and Applications , 1987, SIAM J. Comput..

[77]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[78]  Hanan Samet,et al.  Applications of spatial data structures , 1989 .

[79]  Franz Aurenhammer,et al.  Geometric Relations Among Voronoi Diagrams , 1987, STACS.

[80]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[81]  B. Rust,et al.  The Sedimentology of a Braided River , 1969 .

[82]  Kevin Weiler Topological Structures for Geometric Modeling , 1986 .

[83]  Olaf Kübler,et al.  Medial manifolds and hierarchical description of 2D and 3D objects with applications to MRI data of , 1993 .

[84]  Eliseo Clementini,et al.  Composite Regions in Topological Queries , 1995, Inf. Syst..

[85]  Kurt Mehlhorn,et al.  A computational basis for higher-dimensional computational geometry and applications , 1998, Comput. Geom..

[86]  Martin Breunig,et al.  Space-time modelling of the Lower Rhine Basin supported by an object-oriented database , 1998 .

[87]  B. Moss,et al.  The partitioning of petrophysical data: a review , 1997, Geological Society, London, Special Publications.

[88]  Reid G. Simmons,et al.  The Roles of Associational and Causal Reasoning in Problem Solving , 1992, Artif. Intell..

[89]  Mahmoud Melkemi,et al.  Computing the shape of a planar points set , 2000, Pattern Recognit..