Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
A comparison of normal estimation schemes
VIS '97 Proceedings of the 8th conference on Visualization '97
Computer Vision: A Modern Approach
Computer Vision: A Modern Approach
Affine Differential Signatures for Gray Level Images of Planar Shapes
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Affine-Invariant Skeleton of 3D Shapes
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
A Performance Evaluation of Local Descriptors
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Comparison of Affine Region Detectors
International Journal of Computer Vision
International Journal of Computer Vision
Salient geometric features for partial shape matching and similarity
ACM Transactions on Graphics (TOG)
Affine-Invariant Geometric Shape Priors for Region-Based Active Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface reconstruction using local shape priors
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Drums, curve descriptors and affine invariant region matching
Image and Vision Computing
Combining Points and Tangents into Parabolic Polygons
Journal of Mathematical Imaging and Vision
Curvature formulas for implicit curves and surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Curvature and torsion estimators based on parametric curve fitting
Computers and Graphics
Short Communication to SMI 2011: Affine-invariant geodesic geometry of deformable 3D shapes
Computers and Graphics
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Affine Differential Geometry provides a set of measures invariant under a larger set of transformations compared to rigid motions. This leads to several applications using robust shape descriptors. Although affine-invariant operations are already used for surfaces, they do not intend to approximate the definitions of Affine Differential Geometry, which are the basis for further differential invariants. In this work we propose estimators for the local affine structure of an implicit surface, i.e. the affine metric, the co-normal and normal vectors, and the affine Gaussian and mean curvatures. The direct derivation of the formulae from the implicit function theorem lead to very intensive computations and numerical instabilities. This work further proposes a geometrical reduction allowing a much simpler and more stable formulae, and compares the results by incorporating the proposed estimators in Marching Cubes based algorithms.