A fast algorithm for active contours and curvature estimation
CVGIP: Image Understanding
Circle fitting by linear and nonlinear least squares
Journal of Optimization Theory and Applications
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Discrete Curvature Based on Osculating Circle Estimation
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
2D Image Analysis by Generalized Hilbert Transforms in Conformal Space
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Accurate curvature estimation along digital contours with maximal digital circular arcs
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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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.