Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVGIP: Image Understanding
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Shape Analysis and Classification: Theory and Practice
Shape Analysis and Classification: Theory and Practice
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Efficient Edgebreaker for Surfaces of Arbitrary Topology
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Hierarchical Isocontours Extraction and Compression
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Estimation of curvature along curves with application to fibres in 3D images of paper
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Curvature and Torsion Estimators for 3D Curves
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Comparison and improvement of tangent estimators on digital curves
Pattern Recognition
Estimation of end curvatures from planar point data
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Experimental comparison of continuous and discrete tangent estimators along digital curves
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
An algorithmic framework for segmenting trajectories based on spatio-temporal criteria
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Toward an automatic hole characterization for surface correction
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
An error bounded tangent estimator for digitized elliptic curves
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Affine-invariant curvature estimators for implicit surfaces
Computer Aided Geometric Design
Constructing 3D motions from curvature and torsion profiles
Computer-Aided Design
Technical note: Modeling piecewise helix curves from 2D sketches
Computer-Aided Design
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Many applications of geometry processing and computer vision rely on geometric properties of curves, particularly, their curvature. Several methods have already been proposed to estimate the curvature of a planar curve, most of them for curves in digital spaces. This work proposes a new scheme for estimating curvature and torsion of planar and spatial curves, based on weighted least-squares fitting and local arc-length approximation. The method is simple enough to admit a convergence analysis that takes into account the effect of noise in the samples. The implementation of the method is compared to other curvature estimation methods showing a good performance. Applications to prediction in geometry compression are presented both as a practical application and as a validation of this new scheme.