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Title of Journal: Int J Comput Vis

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Abbravation: International Journal of Computer Vision

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Springer US

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DOI

10.1016/0006-8993(86)91341-7

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ISSN

1573-1405

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Fast and Stable Polynomial Equation Solving and It

Authors: Martin Byröd Klas Josephson Kalle Åström
Publish Date: 2009/04/11
Volume: 84, Issue: 3, Pages: 237-256
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Abstract

This paper presents several new results on techniques for solving systems of polynomial equations in computer vision Gröbner basis techniques for equation solving have been applied successfully to several geometric computer vision problems However in many cases these methods are plagued by numerical problems In this paper we derive a generalization of the Gröbner basis method for polynomial equation solving which improves overall numerical stability We show how the action matrix can be computed in the general setting of an arbitrary linear basis for ℂx/I In particular two improvements on the stability of the computations are made by studying how the linear basis for ℂx/I should be selected The first of these strategies utilizes QR factorization with column pivoting and the second is based on singular value decomposition SVD Moreover it is shown how to improve stability further by an adaptive scheme for truncation of the Gröbner basis These new techniques are studied on some of the latest reported uses of Gröbner basis methods in computer vision and we demonstrate dramatically improved numerical stability making it possible to solve a larger class of problems than previously possible

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  2. Objects, Actions, Places
  3. Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions
  4. Geometric Image Parsing in Man-Made Environments
  5. On Taxonomies for Multi-class Image Categorization
  6. Full and Partial Symmetries of Non-rigid Shapes
  7. A Two-Layer Framework for Piecewise Linear Manifold-Based Head Pose Estimation
  8. Learning Discriminative Space–Time Action Parts from Weakly Labelled Videos
  9. Recognizing Fine-Grained and Composite Activities Using Hand-Centric Features and Script Data
  10. 3D Human Pose Tracking Priors using Geodesic Mixture Models
  11. Exemplar-Guided Similarity Learning on Polynomial Kernel Feature Map for Person Re-identification
  12. Ethnicity- and Gender-based Subject Retrieval Using 3-D Face-Recognition Techniques
  13. A Variational Approach to Video Registration with Subspace Constraints
  14. The Fisher-Rao Metric for Projective Transformations of the Line
  15. Planar Motion Estimation and Linear Ground Plane Rectification using an Uncalibrated Generic Camera
  16. Guest Editorial: Human Activity Understanding from 2D and 3D Data
  17. Robust Pose Recognition of the Obscured Human Body
  18. Teichmüller Shape Descriptor and Its Application to Alzheimer’s Disease Study
  19. Parsing Images into Regions, Curves, and Curve Groups
  20. Using Biologically Inspired Features for Face Processing
  21. Two-View Motion Segmentation with Model Selection and Outlier Removal by RANSAC-Enhanced Dirichlet Process Mixture Models
  22. Information-Theoretic Active Polygons for Unsupervised Texture Segmentation
  23. Virtual Volumetric Graphics on Commodity Displays Using 3D Viewer Tracking
  24. 3-D Symmetry Detection and Analysis Using the Pseudo-polar Fourier Transform
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