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• 1. Introduction.- 1.1 Brief Overview of Motion Analysis.- 1.2 Statement of the "Motion from Stereo" Problem.- 1.3 Organization of The Book.-
• 2. Uncertainty Manipulation and Parameter Estimation.- 2.1 Probability Theory and Geometric Probability.- 2.2 Parameter Estimation.- 2.2.1 Standard Kalman filter.- 2.2.2 Extended Kalman filter.- 2.2.3 Discussion.- 2.2.4 Iterated ExtendKalman Filter.- 2.2.5 Robustness and Confidence Procedure.- 2.3 Summary.- 2.4 Appendix: Least-Squares Techniques.-
• 3. Reconstruction of 3D Line Segments.- 3.1 Why 3D Line Segments.- 3.2 Stereo Calibration.- 3.2.1 Camera Calibration.- 3.2.2 Epipolar Constraint.- 3.3 Algorithm of the Trinocular Stereovision.- 3.4 Reconstruction of 3D Segments.- 3.5 Summary.-
• 4. Representations of Geometric Objects.- 4.1 Rigid Motion.- 4.1.1 Definition.- 4.1.2 Representations.- 4.2 3D Line Segments.- 4.2.1 Previous Representations and Deficiencies.- 4.2.2 A New Representation.- 4.3 Summary.- 4.4 Appendix: Visualizing Uncertainty.-
• 5. A Comparative Study of 3D Motion Estimation.- 5.1 Problem Statement.- 5.1.1 Line Segment Representations.- 5.1.2 3D Line Segment Transformation.- 5.2 Extended Kalman Filter Approaches.- 5.2.1 Linearization of the Equations.- 5.2.2 Derivation of Rotation Matrix.- 5.3 Minimization Techniques.- 5.4 Analytical Solution.- 5.4.1 Determining the Rotation.- 5.4.2 Determining the Translation.- 5.5 Kim and Aggarwal's method.- 5.5.1 Determining the Rotation.- 5.5.2 Determining the Translation.- 5.6 Experimental Results.- 5.6.1 Results with Synthetic Data.- 5.6.2 Results with Real Data.- 5.7 Summary.- 5.8 Appendix: Motion putation Using the New Line Segment Representation.-
• 6. Matching and Rigidity Constraints.- 6.1 Matching as a Search.- 6.2 Rigidity Constraint.- 6.3 Completeness of the Rigidity Constraints.- 6.4 Error Measurements inn the Constraints.- 6.4.1 Norm Constraint.- 6.4.2 Dot-Product Constraint.- 6.4.3 Triple-Product Constraint.- 6.5 Other Formalisms Rigidity Constraints.- 6.6 Summary.-
• 7. Hypothesize-and-Verify Method for Two 3D View Motion Analysis.- 7.1 General Presentation.- 7.1.1 Search in the Transformation Space.- 7.1.2 Hypothesize-and-Verify Method.- 7.2 Generating Hypotheses.- 7.2.1 Definition and Primary Algorithm.- 7.2.2 Control Strates in Hypothesis Generation.- 7.2.3 Additional Constraints.- 7.2.4 Algorithm of Hypothesis Generation.- 7.3 Verifying Hypothesis.- 7.3.1 Estimating the Initial Rigid Motion.- 7.3.2 Propagating Hyphoteses.- 7.3.3 Choosing the Best Hypothesis.- 7.3.4 Algorithm of Hypothesis Verification.- 7.4 Matching Noisy Segments.- 7.4.1 Version 1.- 7.4.2 Version 2.- 7.4.3 Version 3.- 7.5 Experimental Results.- 7.5.1 Indoor Scenes with a Large Common Part.- 7.5.2 Indoor Scenes with a Small Common Part.- 7.5.3 Rock Scenes.- 7.6 Summary.- 7.7 Appendix: Transforming a 3D Line Segment.-
• 8. Further Considerations on Reducing Complexity.- 8.1 Sorting Data Features.- 8.2 "Good-Enough" Problem.- 1.3 Organization of The Book.-
• 2. Uncertainty Manipulation and Parameter Estimation.- 2.1 Probability Theory and Geometric Probability.- 2.2 Parameter Estimation.- 2.2.1 Standard Kalman filter.- 2.2.2 Extended Kalman filter.- 2.2.3 Discussion.- 2.2.4 Iterated ExtendKalman Filter.- 2.2.5 Robustness and Confidence Procedure.- 2.3 Summary.- 2.4 Appendix: Least-Squares Techniques.-
• 3. Reconstruction of 3D Line Segments.- 3.1 Why 3D Line Segments.- 3.2 Stereo Calibration.- 3.2.1 Camera Calibration.- 3.2.2 Epipolar Constraint.- 3.3 Algorithm of the Trinocular Stereovision.- 3.4 Reconstruction of 3D Segments.- 3.5 Summary.-
• 4. Representations of Geometric Objects.- 4.1 Rigid Motion.- 4.1.1 Definition.- 4.1.2 Representations.- 4.2 3D Line Segments.- 4.2.1 Previous Representations and Deficiencies.- 4.2.2 A New Representation.- 4.3 Summary.- 4.4 Appendix: Visualizing Uncertainty.-
• 5. A Comparative Study of 3D Motion Estimation.- 5.1 Problem Statement.- 5.1.1 Line Segment Representations.- 5.1.2 3D Line Segment Transformation.- 5.2 Extended Kalman Filter Approaches.- 5.2.1 Linearization of the Equations.- 5.2.2 Derivation of Rotation Matrix.- 5.3 Minimization Techniques.- 5.4 Analytical Solution.- 5.4.1 Determining the Rotation.- 5.4.2 Determining the Translation.- 5.5 Kim and Aggarwal's method.- 5.5.1 Determining the Rotation.- 5.5.2 Determining the Translation.- 5.6 Experimental Results.- 5.6.1 Results with Synthetic Data.- 5.6.2 Results with Real Data.- 5.7 Summary.- 5.8 Appendix: Motion putation Using the New Line Segment Representation.-
• 6. Matching and Rigidity Constraints.- 6.1 Matching as a Search.- 6.2 Rigidity Constraint.- 6.3 Completeness of the Rigidity Constraints.- 6.4 Error Measurements inn the Constraints.- 6.4.1 Norm Constraint.- 6.4.2 Dot-Product Constraint.- 6.4.3 Triple-Product Constraint.- 6.5 Other Formalisms Rigidity Constraints.- 6.6 Summary.-
• 7. Hypothesize-and-Verify Method for Two 3D View Motion Analysis.- 7.1 General Presentation.- 7.1.1 Search in the Transformation Space.- 7.1.2 Hypothesize-and-Verify Method.- 7.2 Generating Hypotheses.- 7.2.1 Definition and Primary Algorithm.- 7.2.2 Control Strates in Hypothesis Generation.- 7.2.3 Additional Constraints.- 7.2.4 Algorithm of Hypothesis Generation.- 7.3 Verifying Hypothesis.- 7.3.1 Estimating the Initial Rigid Motion.- 7.3.2 Propagating Hyphoteses.- 7.3.3 Choosing the Best Hypothesis.- 7.3.4 Algorithm of Hypothesis Verification.- 7.4 Matching Noisy Segments.- 7.4.1 Version 1.- 7.4.2 Version 2.- 7.4.3 Version 3.- 7.5 Experimental Results.- 7.5.1 Indoor Scenes with a Large Common Part.- 7.5.2 Indoor Scenes with a Small Common Part.- 7.5.3 Rock Scenes.- 7.6 Summary.- 7.7 Appendix: Transforming a 3D Line Segment.-
• 8. Further Considerations on Reducing Complexity.- 8.1 Sorting Data Features.- 8.2 "Good-Enough" Method.- 8.3 Speeding Up the Hypothesis Generation Process Through Grouping.- 8.4 Finding Clusters Based on Proximity.- 8.5 Finding Planes.- 8.6 Experimental Results.- 8.6.1 Grouping Results.- 8.6.2 Motion Results.- 8.7 Conclusion.-
• 9. Multiple Object Motions.- 9.1 Multiple Object Motions.- 9.2 Influence of Egomotion on Observed Object Motion.- 9.3 Experimental Results.- 9.3.1 Real Scene with Synthetic Moving Objects.- 9.3.2 Real Scene with a Real Moving Object.- 9.4 Summary.-
• 10. Object Recognition and Localization.- 10.1 Model-Based Object Recognition.- 10.2 Adapting the Motion-Determination Algorithm.- 10.3 Experimental Result.- 10.4 Summary.-
• 11. Calibrating a Mobile Robot and Visual Navigation.- 11.1 The INRIA Mobile Robot.- 11.2 Calibration Problem.- 11.3 Navigation Problem.- 11.4 Experimental Results.- 11.5 Integrating Motion Information from Odometry.- 11.6 Summary.-
• 12. Fusing Multiple 3D Frames.- 12.1 System Description.- 12.2 Fusing Segments from Multiple Views.- 12.2.1 Fusing General Primitives.- 12.2.2 Fusing Line Segments.- 12.2.3 Example.- 12.2.4 Summary of the Fusion Algorithm.- 12.3 Experimental Results.- 12.3.1 Example
• 1: Integration of Two Views.- 12.3.2 Example
• 2: Integration of a Long Sequence.- 12.4 Summary.-
• 13. Solving the Motion Tracking Problem: A Framework.- 13.1 Previous Work.- 13.2 Position of the Problem and Primary Ideas.- 13.3 Solving the Motion Tracking Problem: A Framework.- 13.3.1 Outline of the Framework.- 13.3.2 A Pedagogical Example.- 13.4 Splitting or Merging.- 13.5 Handling Abrupt Changes of Motion.- 13.6 Discussion.- 13.7 Summary.-
• 14. Modeling and Estimating Motion Kinematics.- 14.1 The Classical Kinematic Model.- 14.2 Closed-Form Solutions for Some Special Motions.- 14.2.1 Motion with Constant Angular and Translational Velocities.- 14.2.2 Motion with Constant Angular Velocity and Constant Translational Acceleration.- 14.2.3 Motion with Constant Angular Velocity and General Translational Velocity.- 14.2.4 Discussions.- 14.3 Relation with Two-View Motion Analysis.- 14.4 Formulation for the EKF Approach.- 14.4.1 State Transition Equation.- 14.4.2 Measurement Equations.- 14.5 Linearized Kinematic Model.- 14.5.1 Linear Approximation.- 14.5.2 State Transition Equation.- 14.5.3 Measurement Equations.- 14.5.4 Discussions.- 14.6 Summary.-
• 15. Implementation Details and Experimental Results.- 15.1 Matching Segments.- 15.1.1 Prediction of a Token.- 15.1.2 Matching Criterion.- 15.1.3 Reducing the Complexity by Bucketing Techniques.- 15.2 Support of Existence.- 15.3 Algorithm of the Token Tracking Process.- 15.4 Grouping Tokens into Objects.- 15.5 Experimental Results.- 15.5.1 Synthetic Data.- 15.5.2 Real Data with Controlled Motion.- 15.5.3 Real Data with Uncontrolled Motion.- 15.6 Summary.-
• 16. Conclusions and Perspectives.- 16.1 Summary.- 16.2 Perspectives.- Appendix: Vector Manipulation and Differentiation.- A.1 Manipulation of Vectors.- A.2 Differentiation of Vectors.- References.
• (source: Nielsen Book Data)

he problem of analyzing sequences of images to extract three-dimensional T motion and structure has been at the heart of the research in computer vi- sion for many years. It is very important since its success or failure will determine whether or not vision can be used as a sensory process in reactive systems. The considerable research interest in this field has been motivated at least by the following two points: 1. The redundancy of information contained in time-varying images can over- come several difficulties encountered in interpreting a single image. 2. There are a lot of important applications including automatic vehicle driv- ing, traffic control, aerial surveillance, medical inspection and global model construction. However, there are many new problems which should be solved: how to effi- ciently process the abundant information contained in time-varying images, how to model the change between images, how to model the uncertainty inherently associated with the imaging system and how to solve inverse problems which are generally ill-posed. There are of course many possibilities for attacking these problems and many more remain to be explored. We discuss a few of them in this book based on work carried out during the last five years in the Computer Vision and Robotics Group at INRIA (Institut National de Recherche en Informatique et en Automatique).
(source: Nielsen Book Data)

Provides full-text access to journals published and distributed by the American Institute of Physics, American Physical Society, American Society of Civil Engineers, American Society of Mechanical Engineers International, International Society for Optical Engineering, and other science and engineering societies. Covers physics, astronomy, electronics, engineering, materials science, mathematics and associated disciplines.

• A high performance matrix multiplication algorithm for MPPs.- Iterative moment method for electromagnetic transients in grounding systems on CRAY T3D.- Analysis of crystalline solids by means of a parallel FEM method.- Parallelization strategies for Tree N-body codes.- Numerical solution of stochastic differential equations on transputer network.- Development of a stencil compiler for one-dimensional convolution operators on the CM-5.- Automatic parallelization of the AVL FIRE benchmark for a distributed-memory system.- 2-D cellular automata and short range molecular dynamics programs for simulations on networked workstations and parallel computers.- Pablo-based performance monitoring tool for PVM applications.- Linear algebra computation on parallel machines.- A neural classifier for radar images.- ScaLAPACK: A portable linear algebra library for distributed memory computers - Design issues and performance.- A proposal for a set of parallel basic linear algebra subprograms.- Parallel implementation of a Lagrangian stochastic particle model of turbulent dispersion in fluids.- Reduction of a regular matrix pair (A, B) to block Hessenberg-triangular form.- Parallelization of algorithms for neural networks.- Paradigms for the parallelization of Branch&Bound algorithms.- Three-dimensional version of the Danish Eulerian Model.- A proposal for a Fortran 90 interface for LAPACK.- ScaLAPACK tutorial.- Highly parallel concentrated heterogeneous computing.- Adaptive polynomial preconditioning for the conjugate gradient algorithm.- The IBM parallel engineering and scientific subroutine library.- Some preliminary experiences with sparse BLAS in parallel iterative solvers.- Load balancing in a Network Flow Optimization code.- User-level VSM optimization and its application.- Benchmarking the cache memory effect.- Efficient Jacobi algorithms on multicomputers.- Front tracking: A parallelized approach for internal boundaries and interfaces.- Program generation techniques for the development and maintenance of numerical weather forecast Grid models.- High performance computational chemistry: NWChem and fully distributed parallel applications.- Parallel ab-initio molecular dynamics.- Dynamic domain decomposition and load balancing for parallel simulations of long-chained molecules.- Concurrency in feature analysis.- A parallel iterative solver for almost block-diagonal linear systems.- Distributed general matrix multiply and add for a 2D mesh processor network.- Distributed and parallel computing of short-range molecular dynamics.- Lattice field theory in a parallel environment.- Parallel time independent quantum calculations of atom diatom reactivity.- Parallel oil reservoir simulation.- Formal specification of multicomputers.- Multi-million particle molecular dynamics on MPPs.- Wave propagation in urban microcells: a massively parallel approach using the TLM method.- The NAG Numerical PVM Library.- Cellular automata modeling of snow transport by wind.- Parallel algorithm for mapping of parallel programs into pyramidal multiprocessor.- Data-parallel molecular dynamics with neighbor-lists.- Visualizing astrophysical 3D MHD turbulence.- A parallel sparse QR-factorization algorithm.- Decomposing linear programs for parallel solution.- A parallel computation of the Navier-Stokes equation for the simulation of free surface flows with the volume of fluid method.- Improving the performance of parallel triangularization of a sparse matrix using a reconfigurable multicomputer.- Comparison of two image-space subdivision algorithms for Direct Volume Rendering on distributed-memory multicomputers.- Communication harnesses for transputer systems with tree structure and cube structure.- A thorough investigation of the projector quantum Monte Carlo method using MPP technologies.- Distributed simulation of a set of elastic macro objects.- Parallelization of ab initio molecular dynamics method.- Parallel computations with large atmospheric models.
• (source: Nielsen Book Data)

This book presents the refereed proceedings of the Second International Workshop on Applied Parallel Computing in Physics, Chemistry and Engineering Science, PARA'95, held in Lyngby, Denmark, in August 1995. The 60 revised full papers included have been contributed by physicists, chemists, and engineers, as well as by computer scientists and mathematicians, and document the successful cooperation of different scientific communities in the booming area of computational science and high performance computing. Many widely-used numerical algorithms and their applications on parallel computers are treated in detail.
(source: Nielsen Book Data)

• 1. Triangular Operations and Negations (Allegro).- 1
• .1. Triangular Norms and Conorms.- 1
• .2. Negations.- 1
• .3. Associated Triangular Operations.- 1
• .4. Archimedean Triangular Operations.- 1
• .5. Induced Negations and Complementary Triangular Operations.- 1
• .6. Implications Induced by Triangular Norms.-
• 2. Fuzzy Sets (Andante spianato).- 2
• .1. The Concept of a Fuzzy Set.- 2
• .2. Operations on Fuzzy Sets.- 2
• .3. Generalized Operations.- 2
• .4. Other Elements of the Language of Fuzzy Sets.- 2
• .5. Towards Cardinalities of Fuzzy Sets.-
• 3. Scalar Cardinalities of Fuzzy Sets (Scherzo).- 3
• .1. An Axiomatic Viewpoint.- 3
• .2. Cardinality Patterns.- 3
• .3. Valuation Property and Subadditivity.- 3
• .4. Cartesian Product Rule and Complementarity.- 3
• .5. On the Fulfilment of a Group of the Properties.- 3.5
• .1. VAL and CART.- 3.5
• .2. CART and COMP.- 3.5
• .3. VAL and COMP.- 3.5
• .4. VAL, CART and COMP.-
• 4. Generalized Cardinals with Triangular Norms (Rondeau a la polonaise).- 4
• .1. Generalized FGCounts.- 4.1
• .1. The Corresponding Equipotency Relation.- 4.1
• .2. Inequalities.- 4.1
• .3. Arithmetical Operations.- 4.1.3
• .1. Addition.- 4.1.3
• .2. Subtraction.- 4.1.3
• .3. Multiplication.- 4.1.3
• .4. Division.- 4.1.3
• .5. Exponentiation.- 4.1
• .4. Some Derivative Concepts of Cardinality.- 4
• .2. Generalized FLCounts.- 4.2
• .1. Equipotencies and Inequalities.- 4.2
• .2. Addition and Other Arithmetical Operations.- 4
• .3. Generalized FECounts.- 4.3
• .1. The Height of a Generalized FECount.- 4.3
• .2. Singular Fuzzy Sets.- 4.3
• .3. Equipotencies, Inequalities and Arithmetical Questions.- List of Symbols.
• (source: Nielsen Book Data)

Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.
(source: Nielsen Book Data)