Abstract
Although edge detection is a well investigated topic, 3D edge detectors mostly lack either accuracy or speed. We will show, how to build a highly accurate subvoxel edge detector, which is fast enough for practical applications. In contrast to other approaches we use a spline interpolation in order to have an efficient approximation of the theoretically ideal sinc interpolator. We give theoretical bounds for the accuracy and show experimentally that our approach reaches these bounds while the often-used subpixel-accurate parabola fit leads to much higher edge displacements.
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References
Brent, R.P.: Algorithms for Minimisation Without Derivatives. Prentice-Hall, Englewood Cliffs (1973)
Canny, J.: A computational approach to edge detection. TPAMI 8(6), 679–698 (1986)
Devernay, F.: A non-maxima suppression method for edge detection with sub-pixel accuracy. Technical Report 2724, INRIA Sophia Antipolis (1995)
Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. ACM Trans. Graph. 13(1), 43–72 (1994)
Jonker, P.P.: Skeletons in n dimensions using shape primitives. Pattern Recognition Letters 23, 677–686 (2002)
Köthe, U.: Vigra. Web Resource, http://hci.iwr.uni-heidelberg.de/vigra/ (visited March 1, 2009)
Köthe, U.: Reliable Low-Level Image Analysis. Habilitation thesis, University of Hamburg, Germany (2008)
Luo, L., Hamitouche, C., Dillenseger, J., Coatrieux, J.: A moment-based three-dimensional edge operator. IEEE Trans. Biomed. 40(7), 693–703 (1993)
Mendonça, P.R.S., Padfield, D.R., Miller, J., Turek, M.: Bias in the localization of curved edges. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3022, pp. 554–565. Springer, Heidelberg (2004)
Monga, O., Deriche, R., Rocchisani, J.: 3d edge detection using recursive filtering: application to scanner images. CVGIP: Image Underst. 53(1), 76–87 (1991)
Moré, J.J., Thuente, D.J.: Line search algorithms with guaranteed sufficient decrease. ACM Trans. Math. Software 20, 286–307 (1994)
Udupa, J.K., Hung, H.M., Chuang, K.S.: Surface and volume rendering in three dimensional imaging: A comparison. J. Digital Imaging 4, 159–169 (1991)
Unser, M., Aldroubi, A., Eden, M.: B-Spline signal processing: Part I—Theory. IEEE Trans. Signal Process. 41(2), 821–833 (1993)
Unser, M., Aldroubi, A., Eden, M.: B-Spline signal processing: Part II—Efficient design and applications. IEEE Trans. Signal Process. 41(2), 834–848 (1993)
Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++: The Art of Scientific Computing. Cambridge University Press, Cambridge (2002)
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Bähnisch, C., Stelldinger, P., Köthe, U. (2009). Fast and Accurate 3D Edge Detection for Surface Reconstruction. In: Denzler, J., Notni, G., Süße, H. (eds) Pattern Recognition. DAGM 2009. Lecture Notes in Computer Science, vol 5748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03798-6_12
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DOI: https://doi.org/10.1007/978-3-642-03798-6_12
Publisher Name: Springer, Berlin, Heidelberg
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