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Minimum Reliable Scale Selection in 3D
March 2006 (vol. 28 no. 3)
pp. 481-487
Multiscale analysis is often required in image processing applications because image features are optimally detected at different levels of resolution. With the advance of high-resolution 3D imaging, the extension of multiscale analysis to higher dimensions is necessary. This paper extends an existing 2D scale selection method, known as the minimum reliable scale, to 3D volumetric images. The method is applied to 3D boundary detection and is illustrated in examples from biomedical imaging. The experimental results show that the 3D scale selection improves the detection of edges over single scale operators using as few as three different scales.

[1] R. Haralick, “Digital Step Edges from Zero Crossing of Second Directional Derivative,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 1, pp. 58-68, Jan. 1984.
[2] T. Lindeberg, “Edge Detection and Ridge Detection with Automatic Scale Selection,” Int'l J. Computer Vision, vol. 30, no. 2, pp. 117-154, Nov. 1998.
[3] J. Weickert, “A Review of Nonlinear Diffusion Filtering,” Proc. Scale-Space Theory in Computer Vision, pp. 3-28, 1997.
[4] A.P. Witkin, “Scale Space Filtering,” Proc. Int'l Joint Conf. Artificial Intelligence, pp. 1019-1022, 1983.
[5] Gaussian Scale Space Theory, J. Sporring, M. Nielson, L. Florack, and P. Johansen, eds., Dordrecht: The Netherlands, Kluwer Academic, 1997.
[6] F. Bergholm, “Edge Focusing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 6, pp. 726-741, 1987.
[7] Y. Lu and R.C. Jain, “Behavior of Edges in Scale Space,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 4, pp. 337-356, Apr. 1989.
[8] Geometry-Driven Diffusion in Computer Vision, B.M. ter Haar Romeny, ed., Dordrecht: The Netherlands, Kluwer Academic, 1994.
[9] H. Jeong and C. Kim, “Adaptive Determination of Filter Scales for Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 5, pp. 579-585, May 1992.
[10] J.H. Elder and S.W. Zucker, “Local Scale Control for Edge Detection and Blur Estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 7, pp. 699-716, July 1998.
[11] S.W. Zucker and R.A. Hummel, “A Three-Dimensional Edge Operator,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 3, no. 3, pp. 324-331, May 1981.
[12] H.K. Liu, “2-Dimensional and 3-Dimensional Boundary Detection,” Computer Graphics and Image Processing, vol. 6, pp. 123-134, 1977.
[13] D.G. Morgenthaler and A. Rosenfeld, “Multidimensional Edge-Detection by Hypersurface Fitting,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 3, pp. 482-486, 1981.
[14] L.M. Luo, C. Hamitouche, J.L. Dillenseger, and J.L. Coatrieux, “A Moment-Based 3-Dimensional Edge Operator,” IEEE Trans. Biomedical Eng., vol. 40, pp. 693-703, 1993.
[15] S.M. Zhan and R. Mehrotra, “A Zero-Crossing-Based Optimal 3-Dimensional Edge Detector,” CVGIP-Image Understanding, vol. 59, pp. 242-253, 1994.
[16] P. Bhattacharya and D. Wild, “A New Edge Detector for Gray Volumetric Data,” Computers in Biology and Medicine, vol. 26, pp. 315-328, 1996.
[17] I. Bricault and O. Monga, “From Volume Medical Images to Quadratic Surface Patches,” Computer Vision and Image Understanding, vol. 67, pp. 24-38, 1997.
[18] P.E. Danielsson, Q.F. Lin, and Q.Z. Ye, “Efficient Detection of Second-Degree Variations in 2D and 3D Images,” J. Visual Comm. Image Representation, vol. 12, pp. 255-305, 2001.
[19] O. Monga and S. Benayoun, “Using Partial Derivatives of 3D Images to Extract Typical Surface-Features,” Computer Vision and Image Understanding, vol. 61, pp. 171-189, 1995.
[20] M.J. Bentum, B.A. Lichtenbelt, and T. Malzbender, “Frequency Analysis of Gradient Estimators in Volume Rendering,” IEEE Trans. Visualization and Computer Graphics, vol. 2, pp. 242-254, 1996.
[21] M. Bomans, K.H. Hohne, U. Tiede, and M. Riemer, “3-D Segmentation of MR Images of the Head for 3-D Display,” IEEE Trans. Medical Imaging, vol. 9, pp. 177-183, 1990.
[22] J. Blom, B.M. ter Haar Romeny, A. Bel, and J.J. Koenderink, “Spatial Derivatives and the Propagation of Noise in Gaussian Scale Space,” J. Visual Comm. Image Representation, vol. 4, no. 1, pp. 1-13, 1993.
[23] R.T. Whitaker and S.M. Pizer, “A Multiscale Approach to Nonuniform Diffusion,” CVGIP-Image Understanding, vol. 57, no. 1, pp. 99-110, 1993.
[24] W.J. Niessen, K.L. Vincken, J. Weickert, B.M.T. Romeny, and M.A. Viergever, “Multiscale Segmentation of Three-Dimensional MR Brain Images,” Int'l J. Computer Vision, vol. 31, pp. 185-202, 1999.
[25] J.H. Elder, “Are Edges Incomplete?” Int'l J. Computer Vision, vol. 34, no. 2, pp. 97-122, Aug. 1999.
[26] W. Freeman and E. Adelson, “The Design and Use of Steerable Filters,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 9, pp. 891-906, Sept. 1991.
[27] A. Papoulis, Probability, Random Variables and Stochastic Processes. New York: McGraw Hill, 1965.
[28] Y. Viniotis, Probability and Random Processes for Electrical Engineers. Boston: McGraw Hill, 1998.
[29] J.J. Koenderink, “The Structure of Images,” Biological Cybernetics, vol. 50, pp. 363-370, 1984.
[30] D.L. Collins, A.P. Zijdenbos, V. Kollokian, J.G. Sled, N.J. Kabani, C.J. Holmes, and A.C. Evans, “Design and Construction of a Realistic Digital Brain Phantom,” IEEE Trans. Medical Imaging, vol. 17, no. 3, pp. 463-468, June 1998.
[31] J. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 679-698, 1986.
[32] J.M. Rocchisani, O. Monga, and R. Deriche, “3D Edge-Detection Using Recursive Filtering-Application to Scanner Images,” CVGIP-Image Understanding, vol. 53, no. 1, pp. 76-87, Jan. 1991.

Index Terms:
Edge and feature detection, filtering, scale selection, image models.
Citation:
Christopher Wyatt, Ersin Bayram, Yaorong Ge, "Minimum Reliable Scale Selection in 3D," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 3, pp. 481-487, March 2006, doi:10.1109/TPAMI.2006.58
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