A Novel Curvature Estimator for Digital Curves and Images
We propose a novel curvature estimation algorithm which is capable of estimating the curvature of digital curves and two-dimensional curved image structures. The algorithm is based on the conformal projection of the curve or image signal to the two-sphere. Due to the geometric structure of the embedded signal the curvature may be estimated in terms of first order partial derivatives in ℝ3. This structure allows us to obtain the curvature by just convolving the projected signal with the appropriate kernels. We show that the method performs an implicit plane fitting by convolving the projected signals with the derivative kernels. Since the algorithm is based on convolutions its implementation is straightforward for digital curves as well as images. We compare the proposed method with differential geometric curvature estimators. It turns out that the novel estimator is as accurate as the standard differential geometric methods in synthetic as well as real and noise perturbed environments.
KeywordsCurvature Estimator Ground Truth Image Projected Signal Inverse Radon Conformal Method
Unable to display preview. Download preview PDF.
- 1.Hermann, S., Klette, R.: Global Curvature Estimation for Corner Detection. Technical report, The University of Auckland, New Zealand (2005)Google Scholar
- 3.Morse, B., Schwartzwald, D.: Isophote-based Interpolation. In: International Conference on Image Processing, vol. 3, p. 227 (1998)Google Scholar
- 6.Hermann, S., Klette, R.: Multigrid Analysis of Curvature Estimators. In: Proc. Image Vision Computing, New Zealand, pp. 108–112 (2003)Google Scholar
- 10.Needham, T.: Visual Complex Analysis. Oxford University Press, USA (1999)Google Scholar
- 15.Gander, W., Golub, G.H., Strebel, R.: Least-Squares Fitting of Circles and Ellipses. BIT (4), 558–578 (1994)Google Scholar