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An ideal image edge detection scheme

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Abstract

This paper introduces a scale-invariant and contrast-invariant multi-scale differential edge detector. The method is a direct consequence of two key discoveries: (1) a precise scale normalization method and (2) a formula to verify scale-invariant detectors. The new scale normalization method provides differential operators with respect to scale, among them the scale-invariant edge detectors. To investigate these differential detectors quantitatively, mathematical functions were used to represent the edges and to solve for the parameters, including position, width, contrast, offset, and orientation, in closed form. Noise is filtered as a low-contrast feature. The method has been tested with various kinds of synthesized edge functions and can extract edge features accurately. It is suitable for real-world images of several kinds of degradation.

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References

  • Canny, J. (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6), 679–698.

    Article  Google Scholar 

  • Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman lectures on physics. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Gebäck, T., & Koumoutsakos, P. (2009). Edge detection in microscopy images using curvelets. BMC Bioinformatics, 10, 75.

    Article  Google Scholar 

  • Guo, C., Zhu, S. C., & Wu, Y. N. (2007). Primal sketch: Integrating structure and texture. Computer Vision and Image Understanding, 106(1), 5–19.

    Article  Google Scholar 

  • Hajiaboli, M. R., Ahmad, M. O., & Wang, C. (2012). An edge-adapting Laplacian Kernel for nonlinear diffusion filters. IEEE Transactions on Image Processing, 21(4), 1561–1572.

    Article  MathSciNet  Google Scholar 

  • Ham, B., Min, D., & Sohn, K. (2012). Robust scale-space filter using second-order partial differential equations. IEEE Transactions on Image Processing, 21(9), 3937–3951.

    Article  MathSciNet  Google Scholar 

  • Haselhoff, A., & Kummert, A. (2012). On filtering by means of generalized integral images: A review and applications. Multidimensional Systems and Signal Processing, 23(1), 291–312.

    Article  MATH  MathSciNet  Google Scholar 

  • Hu, Q., He, X., & Zhou, J. (2005). Multiscale edge detection with bilateral filtering in spiral architecture. In Proceedings of the Pan-Sydney area workshop on visual information processing (pp. 29–32).

  • Koenderink, J. J. (1984). The structure of images. Biological Cybernetics, 50(5), 363–370.

    Article  MATH  MathSciNet  Google Scholar 

  • Kokkinos, I., Maragos, P., & Yuille, A. (2006). Bottom-up & top-down object detection using primal sketch features and graphical models. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2, 1893–1900.

    Google Scholar 

  • Lindeberg, T. (1998). Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision, 30(2), 117–154.

    Google Scholar 

  • Liu, X., Wang, C., Yao, H., & Zhang, L. (2012). The scale of edges. In IEEE conference on computer vision and pattern recognition (CVPR) (pp. 62–469).

  • Mahmoodi, S. (2011). Scale-invariant filtering design and analysis for edge detection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 467(2130), 1719–1738.

    Article  MATH  MathSciNet  Google Scholar 

  • Mairal, J., Leordeanu, M., Bach, F., Hebert, M., & Ponce, J. (2008). Discriminative sparse image models for class-specific edge detection and image interpretation. ECCV, Lecture Notes in Computer Science, 5304, 43–56.

    Article  Google Scholar 

  • Marr, D., & Hildreth, E. (1980). Theory of edge detection. Proceedings of the Royal Society of London Series B, Biological Sciences, 207(1167), 187–217.

    Article  Google Scholar 

  • Miller, E., & Willsky, A. S. (1997). Multiscale, statistical anomaly detection analysis and algorithms for linearized inverse scattering problems. Multidimensional Systems and Signal Processing, 8(1), 151–184.

    Article  MATH  Google Scholar 

  • Verma, O. P., Hanmandlu, M., et al. (2013). A novel fuzzy system for edge detection in noisy image using bacterial foraging. Multidimensional Systems and Signal Processing, 24(1), 181–198.

    Article  MATH  MathSciNet  Google Scholar 

  • Witkin, A. P. (1983). Scale-space filtering. In 8th International joint conference on artificial intelligence (vol. 2, pp. 1019–1022).

  • Yi, S., Labate, D., Easley, G. R., & Krim, H. (2009). A shearlet approach to edge analysis and detection. IEEE Transactions on Image Processing, 18(5), 929–941.

    Article  MathSciNet  Google Scholar 

  • Yu, P., Qin, A. K., & Clausi, D. A. (2012). Unsupervised polarimetric SAR image segmentation and classification using region growing with edge penalty. IEEE Transactions on Geoscience and Remote Sensing, 50(4), 1302–1317.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Xiaochun Zhang & Chuancai Liu

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  1. Xiaochun Zhang
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  2. Chuancai Liu
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Correspondence to Xiaochun Zhang.

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Zhang, X., Liu, C. An ideal image edge detection scheme. Multidim Syst Sign Process 25, 659–681 (2014). https://doi.org/10.1007/s11045-013-0224-9

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  • DOI: https://doi.org/10.1007/s11045-013-0224-9

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