Abstract
The aim of the present paper is to introduce two efficient robust schemes for edge detection and boundary detection. The main idea is based on the odd-order B-spline wavelets. In the first proposed scheme, high-pass filter of an odd-order B-spline wavelet has been rotated in four directions, and then the best directions for each pixel have been selected through computations. The novelty aspect of this scheme is that unlike to other edge detectors based on wavelets which use wavelet transform modulus value for detecting the edges of the images, each direction information is involved in detecting the singularities of the image independently and then those directions where the singularity in those directions has high absolute value are chosen for detecting the edges. The second scheme, which is a modified active contour model, has been designed for image boundary detection. This model not only is applicable in different scales, but also against the previous active contour models, uses more directional information to guide the motion of the initial contour and is more accurate than previous active contour models for boundary detection or in some cases for segmentation. Moreover, this scheme is not sensitive to the location of initial contour. Experimental results show the accuracy of the proposed schemes in comparison with other state-of-the-art edge detectors like curvelets, shearlets, wavelets and Canny method.
Similar content being viewed by others
References
N. Aghazadeh, Y. Gholizade Atani, Edge detection with hessian matrix property based on wavelet transform. J. Sci. Islam. Repub. Iran 26(2), 163–170 (2015)
L. Bin, M.S. yeganeh, Comparison for image edge detection algorithms. IOSR J. Comput. Eng. (IOSRJCE) 2(6), 01–04 (2012)
X. Cai, R. Chan, S. Morigi, F. Sgallari, Vessel segmentation in medical imaging using a tight-frame based algorithm. SIAM J. Imaging Sci. 6(1), 464–486 (2013)
E.J. Cands, D.L. Donoho, New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities. Commun. Pure Appl. Math. 57(2), 219–266 (2004)
E.J. Cands, D.L. Donoho, Ridgelets: a key to higher-dimensional intermittency? Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 357(1760), 24952509 (1999)
J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–697 (1986)
K. Guo, G. Kutyniok, D. Labate, Sparse multidimensional representations using anisotropic dilation and shear operators, in International Conference on the Interaction between Wavelets and Splines, At Athens, GA, Volume: Wavelets and Splines: Athens (2005)
W. Guo, M.-J. Lai, Box spline wavelet frames for image edge analysis. SIAM J. Imaging Sci. 6(3), 1553–1578 (2013)
P.C. Hansen, J.G. Nagy, D.P. O’Leary, Debluring Images, Matrices, Spectra and Filtering (SIAM, Philadelphia, 2006)
G. Kutyniok, J. Lemvig, W.-Q. Lim, Optimally sparse approximations of 3D functions by compactly supported shearlet frames. SIAM J. Math. Anal. 44, 2962–3017 (2012)
C. Li et al., Minimization of region-scalable fitting energy for image segmentation. IEEE Trans. Image Process. 17(10), 1940–1949 (2008)
J. Li, A wavelet approach to edge detection. Masters Thesis. Sam Houston State University (2003)
P. Lin et al., Image detection of rice fissures using biorthogonal B-spline wavelets in multi-resolution spaces. Food Bioprocess Technol. 5, 2017–2024 (2012)
S. Mallat, W.L. Hwang, Singularity detection and processing with wavelets. IEEE Trans. Inf. Theory 38(2), 617–643 (1992)
S. Mallat, S. Zhong, Charactrization of signals from multiscale edges. IEEE Trans. Pattern Anal. Mach. Intell. 14(7), 710–732 (1992)
J.K. Mandal, A. Ghosh, Edge detection by modified Otsu method. Comput. Sci. Inf. Technol. 3(6), 233–240 (2013)
D.-Y. Po, M.N. Do, Directional multiscale modeling of images using the contourlet transform. IEEE Trans. Image Process. 15(6), 16101620 (2006)
P.M.K. Prasad et al., Performance analysis of orthogonal and biorthogonal wavelets for edge detection of x-ray images. Procedia Comput. Sci. 87, 116–121 (2016)
I.W. Selesnick, R.G. Baraniuk, N.C. Kingsbury, The dual-tree complex wavelet transform. IEEE Signal Process. Mag. 22(6), 123151 (2005)
D. Selvathi, N. Balagopal, Detection of retinal blood vessels using curvelet transform, in International Conference of Devices, Circuits and Systems (ICDCS). pp. 325–329 (2012)
K.P. Soman, K.I. Ramachandran, N.G. Resmi, Insight into Wavelets: From Theory to Practice, 3rd edn. (PHI Learning, New Delhi, 2010)
J.L. Starck, E.J. Candes, D.L. Donoho, The curvelet transform for image denoising. IEEE Trans. Image Process. 11(6), 670–684 (2002)
R. Szeliski, Computer Vision: Algorithms and Applications (Springer, New York, 2011)
C.L. Tu, W.L. Hwang, J. Ho, Analysis of singularities from modulus complex wavelets. IEEE Trans. Inf. Theory 51(3), 10491062 (2005)
S. Yi, D. Labate, G.R. Easley, H. Karim, A shearlet approach to edge detection. IEEE Trans. Image Process. 18(5), 929–941 (2009)
L. Zhang, P. Bao, A wavelet-based edge detection method by scale multiplication. IEEE 16th Int. Conf. Pattern Recogn. 3, 501504 (2002)
Z. Zhang et al., An edge detection approach based on directional wavelet transform. Comput. Math. Appl. 57(8), 1265–1271 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Noras, P., Aghazadeh, N. Directional Schemes for Edge Detection Based on B-spline Wavelets. Circuits Syst Signal Process 37, 3973–3994 (2018). https://doi.org/10.1007/s00034-018-0753-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-018-0753-4