Geometric modeling and computer vision

Geometric matching algorithms and geometric representations are examined for point sets, curves, surfaces, volumes, and their space-time trajectories. The author focuses mainly on general-purpose techniques. Geometric matching benefits greatly from taking advantage of symmetries and special features, e.g. dihedral edges and circles or any three reliably identifiable feature points. Volume matching and representation techniques are also presented. Texture and fractal representations are briefly described. >

[1]  W. J. Gordon Blending-Function Methods of Bivariate and Multivariate Interpolation and Approximation , 1971 .

[2]  John W. Woods,et al.  Two-dimensional discrete Markovian fields , 1972, IEEE Trans. Inf. Theory.

[3]  Martin A. Fischler,et al.  The Representation and Matching of Pictorial Structures , 1973, IEEE Transactions on Computers.

[4]  A. K. Cline Scalar- and planar-valued curve fitting using splines under tension , 1974, Commun. ACM.

[5]  E. Catmull,et al.  A CLASS OF LOCAL INTERPOLATING SPLINES , 1974 .

[6]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[7]  Jayaram K. Udupa,et al.  New Concepts for Three-Dimensional Shape Analysis , 1977, IEEE Transactions on Computers.

[8]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[9]  Berthold K. P. Horn Understanding Image Intensities , 1977, Artif. Intell..

[10]  Ramakant Nevatia,et al.  Description and Recognition of Curved Objects , 1977, Artif. Intell..

[11]  Robert B. McGhee,et al.  Aircraft Identification by Moment Invariants , 1977, IEEE Transactions on Computers.

[12]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[13]  W. A. Perkins,et al.  A Model-Based Vision System for Industrial Parts , 1978, IEEE Transactions on Computers.

[14]  John W. Boyse,et al.  Interference detection among solids and surfaces , 1979, CACM.

[15]  R.M. Haralick,et al.  Statistical and structural approaches to texture , 1979, Proceedings of the IEEE.

[16]  Larry S. Davis,et al.  Shape Matching Using Relaxation Techniques , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[18]  Norman I. Badler,et al.  Decomposition of Three-Dimensional Objects into Spheres , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Aristides A. G. Requicha,et al.  Closure of Boolean operations on geometric entities , 1980 .

[20]  Linda G. Shapiro,et al.  A Structural Model of Shape , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Richard W. Conners,et al.  A Theoretical Comparison of Texture Algorithms , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  P. Wintz,et al.  An efficient three-dimensional aircraft recognition algorithm using normalized fourier descriptors , 1980 .

[23]  ARISTIDES A. G. REQUICHA,et al.  Representations for Rigid Solids: Theory, Methods, and Systems , 1980, CSUR.

[24]  Hannan Samet,et al.  Region representation: Quadtrees from binary arrays , 1980 .

[25]  Robert C. Bolles,et al.  Locating Partially Visible Objects: The Local Feature Focus Method , 1980, AAAI.

[26]  Barr,et al.  Superquadrics and Angle-Preserving Transformations , 1981, IEEE Computer Graphics and Applications.

[27]  Robert M. Haralick,et al.  Structural Descriptions and Inexact Matching , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  H. Keith Nishihara,et al.  Intensity, Visible-Surface, and Volumetric Representations , 1981, Artif. Intell..

[29]  Allen R. Hanson,et al.  3D Object Representation and Matching with B-Splines and Surface Patches , 1981, IJCAI.

[30]  Ernest L. Hall,et al.  Measuring Curved Surfaces for Robot Vision , 1982, Computer.

[31]  Herbert Freeman,et al.  Characteristic Views As A Basis For Three-Dimensional Object Recognition , 1982, Other Conferences.

[32]  Donald Meagher,et al.  Geometric modeling using octree encoding , 1982, Comput. Graph. Image Process..

[33]  Requicha,et al.  Solid Modeling: A Historical Summary and Contemporary Assessment , 1982, IEEE Computer Graphics and Applications.

[34]  Michael Potmesil,et al.  Synthetic Image Generation with a Lens and Aperture Camera Model , 1982, TOGS.

[35]  Michael Brady,et al.  Computational Approaches to Image Understanding , 1982, CSUR.

[36]  Robert Tilove,et al.  Extending Solid Modeling Systems for Mechanism Design and Kinematic Simulation , 1983, IEEE Computer Graphics and Applications.

[37]  H. Voelcker,et al.  Solid modeling: current status and research directions , 1983, IEEE Computer Graphics and Applications.

[38]  Bradford Smith IGES: A Key to CAD/CAM Systems Integration , 1983, IEEE Computer Graphics and Applications.

[39]  Anil K. Jain,et al.  Markov Random Field Texture Models , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[40]  Klaus Höllig,et al.  Bivariate box splines and smooth pp functions on a three direction mesh , 1983 .

[41]  Ronald A. DeVore,et al.  Approximation by smooth multivariate splines , 1983 .

[42]  Robert Barnhill,et al.  A survey of the representation and design of surfaces , 1983, IEEE Computer Graphics and Applications.

[43]  William Gordon An Operator Calculus for Surface and Volume Modeling , 1983, IEEE Computer Graphics and Applications.

[44]  Demetri Terzopoulos,et al.  Multilevel computational processes for visual surface reconstruction , 1983, Comput. Vis. Graph. Image Process..

[45]  Michael Potmesil,et al.  Generating Models of Solid Objects by Matching 3D Surface Segments , 1983, IJCAI.

[46]  W. Eric L. Grimson,et al.  An implementation of a computational theory of visual surface interpolation , 1983, Comput. Vis. Graph. Image Process..

[47]  Robert C. Bolles,et al.  3DPO: A Three- Dimensional Part Orientation System , 1986, IJCAI.

[48]  Wayne Tiller,et al.  Rational B-Splines for Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.

[49]  Rodney A. Brooks,et al.  Model-Based Three-Dimensional Interpretations of Two-Dimensional Images , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[50]  G. Farin Algorithms for rational Bézier curves , 1983 .

[51]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[52]  Prasanna G. Mulgaonkar,et al.  Matching 'sticks, plates and blobs' objects using geometric and relational constraints , 1984, Image and Vision Computing.

[53]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[54]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[55]  M. Brady,et al.  Smoothed Local Symmetries and Their Implementation , 1984 .

[56]  W. Grimson,et al.  Model-Based Recognition and Localization from Sparse Range or Tactile Data , 1984 .

[57]  J. W. Bruce,et al.  Seeing—the mathematical viewpoint , 1984 .

[58]  Berthold K. P. Horn Extended Gaussian images , 1984, Proceedings of the IEEE.

[59]  John W. Boyse,et al.  Solid Modeling by Computers , 1984, Springer US.

[60]  Alex Pentland,et al.  Fractal-Based Description of Natural Scenes , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[61]  Andrew Blake,et al.  Reconstructing a Visible Surface , 1984, AAAI.

[62]  Glen M. Castore,et al.  Solid Modeling, Aspect Graphs, and Robot Vision , 1984 .

[63]  C. Ian Connolly,et al.  Cumulative generation of octree models from range data , 1984, ICRA.

[64]  Olivier D. Faugeras,et al.  Shape Matching of Two-Dimensional Objects , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[65]  Rida T. Farouki,et al.  A Hierarchy of Geometric Forms , 1985, IEEE Computer Graphics and Applications.

[66]  David Lee,et al.  Optimal algorithms for image understanding: Current status and future plans , 1985, J. Complex..

[67]  Thomas W. Sederberg Piecewise algebraic surface patches , 1985, Comput. Aided Geom. Des..

[68]  Richard A. Volz,et al.  Recognizing Partially Occluded Parts , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[69]  Malcolm S. Casale,et al.  An Overview of Analytic Solid Modeling , 1985, IEEE Computer Graphics and Applications.

[70]  Ramesh C. Jain,et al.  Three-dimensional object recognition , 1985, CSUR.

[71]  Donald D. Hoffman,et al.  Codon constraints on closed 2D shapes , 1985, Comput. Vis. Graph. Image Process..

[72]  Tony DeRose,et al.  The Beta2-spline: A Special Case of the Beta-spline Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.

[73]  Micha Sharir,et al.  Motion Planning in the Presence of Moving Obstacles , 1985, FOCS.

[74]  Jean Ponce,et al.  Describing surfaces , 1985, Comput. Vis. Graph. Image Process..

[75]  Thomas O. Binford,et al.  The Recovery of Three-Dimensional Structure from Image Curves , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[76]  Edith Schonberg,et al.  Object recognition by three‐dimensional curve matching , 1986, Int. J. Intell. Syst..

[77]  Ramesh C. Jain,et al.  Recognizing partially visible objects using feature indexed hypotheses , 1986, IEEE J. Robotics Autom..

[78]  M. Hebert,et al.  The Representation, Recognition, and Locating of 3-D Objects , 1986 .

[79]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[80]  Eric A. Bier,et al.  Two-Part Texture Mappings , 1986, IEEE Computer Graphics and Applications.

[81]  Jake K. Aggarwal,et al.  Curvature-based representation of objects from range data , 1986, Image Vis. Comput..

[82]  Alex Pentland,et al.  Shading into Texture , 1984, Artif. Intell..

[83]  Su-Shing Chen,et al.  Shape and motion of nonrigid bodies , 1986, Comput. Vis. Graph. Image Process..

[84]  Gerald Farin,et al.  Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[85]  Charles R. Dyer,et al.  Model-based recognition in robot vision , 1986, CSUR.

[86]  S. Rippa,et al.  Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions , 1986 .

[87]  Peter Cheeseman,et al.  On the Representation and Estimation of Spatial Uncertainty , 1986 .

[88]  R. Y. Tsai,et al.  An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision , 1986, CVPR 1986.

[89]  Jake K. Aggarwal,et al.  Identification of 3D objects from multiple silhouettes using quadtrees/octrees , 1985, Comput. Vis. Graph. Image Process..

[90]  Olivier D. Faugeras,et al.  HYPER: A New Approach for the Recognition and Positioning of Two-Dimensional Objects , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[91]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[92]  Gregory M. Nielson,et al.  Rectangular v-Splines , 1986, IEEE Computer Graphics and Applications.

[93]  Alex Pentland,et al.  Perceptual Organization and the Representation of Natural Form , 1986, Artif. Intell..

[94]  Thomas A. Foley,et al.  Local control of interval tension using weighted splines , 1986, Comput. Aided Geom. Des..

[95]  Richard S. Weiss,et al.  Reconstruction of Surfaces from Profiles , 1987, ICCV 1987.

[96]  George C. Stockman,et al.  Object recognition and localization via pose clustering , 1987, Comput. Vis. Graph. Image Process..

[97]  Demetri Psaltis,et al.  Optical Neural Computers , 1987, Topical Meeting on Optical Computing.

[98]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[99]  John Knapman,et al.  Dupin's cyclide and the cyclide patch , 1987, Image Vis. Comput..

[100]  Michael Brady,et al.  Generating and Generalizing Models of Visual Objects , 1987, Artif. Intell..

[101]  K. S. Arun,et al.  Least-Squares Fitting of Two 3-D Point Sets , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[102]  David G. Lowe,et al.  Three-Dimensional Object Recognition from Single Two-Dimensional Images , 1987, Artif. Intell..

[103]  Bir Bhanu,et al.  CAD-Based 3D Object Representation for Robot Vision , 1987, Computer.

[104]  Olivier D. Faugeras,et al.  An object centered hierarchical representation for 3D objects: The prism tree , 1987, Comput. Vis. Graph. Image Process..

[105]  John W. Roach,et al.  A CAD System Based on Spherical Dual Representations , 1987, Computer.

[106]  Juyang Weng,et al.  Octree of objects in arbitrary motion: representation and efficiency , 1987 .

[107]  Michael Potmesil Generating octree models of 3D objects from their silhouettes in a sequence of images , 1987, Comput. Vis. Graph. Image Process..

[108]  R. Bajcsy,et al.  Three dimensional object representation revisited , 1987 .

[109]  D. W. Murray Model-based recognition using 3D shape alone , 1987, Comput. Vis. Graph. Image Process..

[110]  Charles R. Dyer,et al.  3-D multiview object representations for model-based object recognition , 1987, Pattern Recognit..

[111]  Micha Sharir,et al.  Identification of Partially Obscured Objects in Two and Three Dimensions by Matching Noisy Characteristic Curves , 1987 .

[112]  Joachim H. Rieger,et al.  On the classification of views of piecewise smooth objects , 1987, Image Vis. Comput..

[113]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

[114]  David Lee,et al.  One-Dimensional Regularization with Discontinuities , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[115]  E. D. Dickmanns,et al.  4 D-dynamic scene analysis with integral spatio-temporal models , 1988 .