Abstract
We develop a higher dimensional version of the Canny edge detection algorithm. The Canny operation detects the zero-crossing of the gradient of the Gaussian-convolved image. The segment edge curve detected by the Canny operation is an approximation of zero-crossing of bilinear form defined by second order derivative of an image. This definition of edge points of segment is dimension independent. This definition also allows us to extend the filtering operation from the Gaussian convolution to general linear and non-linear ones.
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References
Iijima, T.: Pattern Recognition, Corona-sha, Tokyo (1974) (in Japanese)
Witkin, A.P.: Scale space filtering. In: Proc. of 8th IJCAI, pp. 1019–1022 (1993)
Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer, Boston (1994)
ter Haar Romeny, B.M.: Front-End Vision and Multi-Scale Image Analysis Multi-scale Computer Vision Theory and Applications, written in Mathematica. Springer, Berlin (2003)
Yuille, A.L., Poggio, T.: Scale space theory for zero crossings. PAMI 8, 15–25 (1986)
Enomoto, H., Yonezaki, N., Watanabe, Y.: Application of structure lines to surface construction and 3-dimensional analysis. In: Fu, K.-S., Kunii, T.L. (eds.) Picture Engineering, pp. 106–137. Springer, Berlin (1982)
Krueger, W.M., Phillips, K.: The geometry of differential operator with application to image processing. PAMI 11, 1252–1264 (1989)
Canny, J.: A computational approach to edge detection. PAMI 8, 679–698 (1986)
Najman, L., Schmitt, M.: Watershed of a continuous function. Signal Processing 38, 99–112 (1994)
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. RAMI 12, 629–639 (1990)
Weickert, J.: Anisotropic Diffusion in Image Processing, Teubner, Stuttgart (1998)
Weickert, J.: Applications of nonlinear diffusion in image processing and computer vision. Acta Mathematica Universitatis Comenianae 70, 33–50 (2001)
Pizarro, L., Mrázek, P., Didas, S., Grewenig, S., Weickert, J.: Genealised nonlocal image smoothing. IJCV 90, 62–87 (2010)
Tomasi, C., Manduchi, R.: Bilateral filtering dor gray colour images. In: Proc., ICCV 1998, pp. 839–846 (1998)
Burt, P.J., Andelson, E.H.: The Laplacian pyramid as a compact image coding. IEEE Trans. Communications 31, 532–540 (1983)
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Narita, M., Imiya, A., Itoh, H. (2012). Edge Detection and Smoothing-Filter of Volumetric Data. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2012. Lecture Notes in Computer Science, vol 7432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33191-6_48
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DOI: https://doi.org/10.1007/978-3-642-33191-6_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33190-9
Online ISBN: 978-3-642-33191-6
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