On active contour models and balloons
CVGIP: Image Understanding
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Geometric invariance in computer vision
Geometric invariance in computer vision
Fundamental Limitations on Projective Invariants of Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Differential and Numerically Invariant Signature Curves Applied to Object Recognition
International Journal of Computer Vision
Illumination for computer generated pictures
Communications of the ACM
Numerically Invariant Signature Curves
International Journal of Computer Vision
Shape Analysis and Classification: Theory and Practice
Shape Analysis and Classification: Theory and Practice
Estimating surface normals in noisy point cloud data
Proceedings of the nineteenth annual symposium on Computational geometry
ACM SIGGRAPH 2004 Papers
Arc-Length Based Curvature Estimator
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Projective Splines and Estimators for Planar Curves
Journal of Mathematical Imaging and Vision
Affine-invariant curvature estimators for implicit surfaces
Computer Aided Geometric Design
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Image and geometry processing applications estimate the local geometry of objects using information localized at points. They usually consider information about the tangents as a side product of the points coordinates. This work proposes parabolic polygons as a model for discrete curves, which intrinsically combines points and tangents. This model is naturally affine invariant, which makes it particularly adapted to computer vision applications. As a direct application of this affine invariance, this paper introduces an affine curvature estimator that has a great potential to improve computer vision tasks such as matching and registering. As a proof-of-concept, this work also proposes an affine invariant curve reconstruction from point and tangent data.