On Recognizing and Positioning Curved 3-D Objects from Image Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Descriptors for 3D Object Recognition and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Geometric Distance Fits for 3-D Object Modeling and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Graphics (TOG)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Programming Fitting of Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Symbolic Computation to Find Algebraic Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topologically Faithful Fitting of Simple Closed Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Aided Geometric Design
Determination of the Method of Construction of 1650 B.C. Wall Paintings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stable Algebraic Surfaces for 3D Object Representation
Journal of Mathematical Imaging and Vision
Computer Aided Geometric Design
Automated freehand sketch segmentation using radial basis functions
Computer-Aided Design
Image based visual servoing using algebraic curves applied to shape alignment
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Modeling and Estimation of the Dynamics of Planar Algebraic Curves via Riccati Equations
Journal of Mathematical Imaging and Vision
2D shape tracking using algebraic curve spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
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A problem which often arises while fitting implicit polynomials to 2D and 3D data sets is the following: Although the data set is simple, the fit exhibits undesired phenomena, such as loops, holes, extraneous components, etc. Previous work tackled these problems by optimizing heuristic cost functions, which penalize some of these topological problems in the fit. This paper suggests a different approach驴to design parameterized families of polynomials whose zero-sets are guaranteed to satisfy certain topological properties. Namely, we construct families of polynomials with star-shaped zero-sets, as well as polynomials whose zero-sets are guaranteed not to intersect an ellipse circumscribing the data or to be entirely contained in such an ellipse. This is more rigorous than using heuristics which may fail and result in pathological zero-sets. The ability to parameterize these families depends heavily on the ability to parameterize positive polynomials. To achieve this, we use some powerful recent results from real algebraic geometry.