CURVATURE APPROXIMATION FROM PARABOLIC SECTORS
Keywords:curvature, digital curve, shape analysis, three-point curvature approximation
We propose an invariant three-point curvature approximation for plane curves based on the arc of a parabolic sector, and we analyze how closely this approximation is to the true curvature of the curve. We compare our results with the obtained with other invariant three-point curvature approximations. Finally, an application is discussed.
Archimedes (1952). Quadrature of the parabola, (translated by sir thomas l. heath). In: Hutchins RM, ed., Great Books of the Western World, vol. 11. Encyclopedia Britannica, Inc., 527537.
Belyaev A (1999). A note on invariant three-point curvature approximations. Surikaisekikenkyusho Kokyuroku RIMS Kyoto 1111:157–64.
Calabi E, Olver P, Shakiban C, Tannenbaum A, Haker S (1998). Differential and numerically invariant signature curves applied to object recognition. International Journal of Computer Vision 26:107–
Calabi E, Olver P, Tannenbaum A (1996). Affine geometry, curve flows, and invariant numerical approximations. Advances in Mathematics
Gual-Arnau X, Herold-Garcıa S, Simo A (2015). Erythrocyte shape classification using integralgeometry-based methods. Medical biological
engineering computing 53:623–33.
Hermann S, Klette R (2006). A comparative study on 2d curvature estimators. Tech. rep., CITR, The University of Auckland, New Zealand.
Lai Y, Hu S, Fang T (2009). Robust principal curvatures using feature adapted integral invariants. In: 2009 SIAM/ACM Joint Conference
on Geometric and Physical Modeling. ACM.
Manay S, Hong B, Yezzi A, Soatto S (2004). Integral invariant signatures. Lecture Notes in Computer Science. Springer.
MATLAB (2015). version R2015b. Natick,Massachusetts: The MathWorks Inc.
Pottmann H, Wallner J, Huang Q, Yang Y (2009). Integral invariants for robust geometry processing. Computer Aided Geometric Design 26:37–60.
Pottmann H, Wallner J, Yang Y, Lai Y, Hu S (2007). Principal curvatures from the integral invariant viewpoint. Computer Aided Geometric Design
Rueda S, Udupa J, Bai L (2008). Local curvature scale: a new concept of shape description. In:Medical Imaging. International Society for Optics
Rueda S, Udupa J, Bai L (2010). Shape modeling via local curvature scale. Pattern Recognition Letters 31:324–36.
Serra J (1983). Image analysis and mathematical morphology. Academic Press, Inc.
Sethian JA (1996). Level set methods, Evolving interfaces in geometry, fluid mechanics computer vision, and materials sciences. Cambridge
Monographs on Applied and Computational Mathematics, 3. Cambridge University Press.
Worring M, Smeulders A (1992). The accuracy and precision of curvature estimation methods. In: Pattern Recognition, 1992. Vol. III. Conference C: Image, Speech and Signal Analysis, Proceedings., 11th IAPR International Conference on. IEEE.
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