Abstract
In this paper we show how geometry-driven diffusion can be used to develop a system of curve-evolution that is able to preserve salient features of closed curves (such as corners and straight line segments), while simultaneously suppressing noise and irrelevant details. The idea is to characterise the curve by means of its angle function (i.e. the angle between the tangent and a fixed axis) and to apply geometry-driven diffusion to this one-dimensional representation.
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P. Fiddelaers, E.J. Pauwels, M. Proesmans, L.J. Van Gool and T. Moons: Geometry-Driven Curve Evolution. Technical Report KUL/ESAT/MI2/9309, 1993.
M. Gage: Curve shortening makes convex curves circular. Invent. Math. 76, pp. 357–364, 1984.
M. Gage and R.S. Hamilton: The heat equation shrinking convex plane curves. J. Differential Geometry 23, pp. 69–96, 1986.
M. Grayson: The heat equation shrinks embedded plane curves to round points. J. Differential Geometry 26, pp. 285–314, 1987.
M. Grayson: Shortening embedded curves. Annals of Mathematics 129, pp.71–111, 198
B.B. Kimia, A. Tannenbaum and S.W. Zucker: Shapes, Shocks, and Deformations I: The Components of Shape and the Recation-Diffusion Space Technical Report LEMS-105, Division of Engineering Brown University, June 1992.
N. Nordström: Biased Anisotropic Diffusion: A Unified Regularization and Diffusion Approach to Edge Detection. Image and Vision Computing, Vol.8, No.4. 1990.
P. Perona and J. Malik: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12, pp. 629–639, 1990.
G. Sapiro and A. Tannenbaum: Affine Invariant Scale-Space. International Journal of Computer Vision, 11:1, 25–44, 1993.
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© 1994 Springer-Verlag Berlin Heidelberg
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Fiddelaers, P., Pauwels, E.J., Van Gool, L.J. (1994). Geometry-driven curve evolution. In: Eklundh, JO. (eds) Computer Vision — ECCV '94. ECCV 1994. Lecture Notes in Computer Science, vol 800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57956-7_46
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DOI: https://doi.org/10.1007/3-540-57956-7_46
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