Vol.5 No.6 (June 2015)
Curvature Estimation Methods and Its Application in Surface Detection
Curvature extraction is required for many applications in image processing and computer vision. Therefore, curvature estimation is a basic task of these applications. This paper gives a classification and summary for existing curvature estimation methods to facilitate further investigations based on describing the original mathematical curvature, Gauss curvature, circle-based discrete curvature, parabola-based curvature, Gauss-Bonnet based curvature, Euler-based curvature etc. Experimental results show that curvature information can improve the robustness to noise in surface detection.
邵晓芳 , 彭志刚 (2015) 曲率估计及其在曲面检测中的应用。 计算机科学与应用， 5， 239-245. doi: 10.12677/CSA.2015.56031
 Zhang, X.P., Li, H.J., Cheng, Z.L. and Zhang, Y.K. Robust curvature estimation and geometry analysis of 3D point cloud surfaces.
 Chanwimaluang, T., Fan, G.L., Yen, G.G. and Fransen, S.R. (2009) 3-D retinal curvature estimation. IEEE Transactions on Information Technology in Biomedicine, 13, 997-1005.
 Koenderink, J.J. (1990) Solid shape. The MIT Press.
 Flynn, P.J. and Jain, A.K. (1989) On reliable curvature estimation. Conference on Computing Vision and Pattern Recognition, 110-116.
 Trucco, E. and Fisher, R.B. (1995) Experiments in curvature-based segmentation of range data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 177-182.
 Bårman, H. (2002) Hierarchical curvature estimation in computer vision. Ph.D. Thesis, Linköpings Universitet, Institutionen för Systemteknik, Bildbehandling.
 Stokely, E.M. and Wu, S.Y. (1992) Surface parameterization and curvature measurement of arbitrary 3d-objects: Five practical methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 833-840.
 Krsek, P., Lukacs, C. and Martin, R.R. (1998) Algorithms for computing curvatures from range data. In: Ball, A., et al., Eds., The Mathematics of Surfaces VIII, Information Geometers, 1-16.
 Sander, P.T. and Zucker, S.W. (1986) Stable Surface Estimation. Proceedings of the International Conference on Pattern Recognition, Vol. 1, 1165-1167.
 Shi, P., Robinson, G. and Duncan, J. (1994) Myocardial motion and function assessment using 4D images. Proceedings of the IEEE Conference on Vision and Biomedical Computing.
 Stewart, C.V. (1995) MINPRAN: A new robust estimator for computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 925-938.
 Werghi, N., Fisher, R.B., Ashbrook, A. and Robertson, C. (1998) Modeling objects having quadric surfaces incorporating geometric constraints. Proceedings of the 5th European Conference on Computer Vision, Freiburg, 2-6 June 1998, 185-201.
 Zhao, H.-K., Osher, S., Merriman, B. and Kang, M. (1999) Implicit and non-parametric shape reconstruction from unorganized data. Using a variational level set method. UCLA Computational and Applied Mathematics Reports 98-7, February 1998, Revised February 1999.
 McIvor, A.M. and Valkenburg, J. (1997) A comparison of local surface geometry estimation methods. Machine Vision and Applications, 10, 17-26.
 Kim, S.J., Kim, C.-H. and Levin, D. (2001) Surface simplification using a discrete curvature norm. Proceedings of the Third Israel-Korea Binational Conference on Geometric Modeling and Computer Graphics, Seoul, 11-12 October 2001.
 Meek, D.S. and Walton, D.J. (2000) On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Computer Aided Geometric Design, 17, 521-543.
 DoCarmo, M. (1976) Differential Geometry of Curves and Surfaces. Prentice-Hall, Upper Saddle River.
 Watanabe, K. and Belyaev, A.G. (2001) Detection of salient curvature features on polygonal surfaces. Eu-rographics, 20.
 Lin, W.-Y., Chiu, Y.-L., Widder, K.R., Hu, Y.H. and Boston, N. (2010) Robust and accurate curvature estimation using adaptive line integrals. EURASIP Journal on Advances in Signal Processing, 2010, Article ID: 240309.
 Campbell, S.R. and Summers, R.M. (2007) Analysis of kernel method for surface curvature estimation. Proceedings of the SPIE, 6511, Article ID: 65112I.
 Mokhtarian, F., Khalili, N. and Yuen, P. (2002) Estimation of error in curvature computation on multi-scale free-form surfaces. IEEE Journal of Computer Vision, 48, 131-149.
 Dudek, G. and Tsotsos, J.K. (1997) Shape representation and recognition from multiscale curvature. Computer Vision and Image Understanding, 68, 170-189.
 Taubin, G. (1995) Estimating the tensor of curvature of a surface from a polyhedral approximation. Proceedings of the Fifth International Conference on Computer Vision, Cambridge, MA, 20-23 June 1995, 902-907.
 Gopi, M., Krishnan, S. and Silva, C.T. (2000) Surface reconstruction based on lower dimensional localized delaunay triangulation. Journal of Eurographics, 19.
 Franken, E.M., Duits, R. and ter Haar Romenij, B.M. (2007) Curvature estimation for enhancement of crossing curves. Proceedings of the 8th MMBIA Workshop, Rio de Janeiro, 14-20 October 2007.
 Page, D.L., Sun, Y., Paik, J. and Abidi, M.A. (2002) Normal vector voting: Crease detection and curvature estimation on large, noisy meshes. Graphical Models, 64, 199-229.
 Tong, W.S. and Tang, C.-K. (2005) Robust estimation of adaptive tensors of curvature by tensor voting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 434-449.
 Lombardi, G., Casiraghi, E. and Campadelli, P. (2008) Curvature estimation and curve inference with tensor voting: A new approach. Lecture Notes in Computer Science, 5259, 613-624.