Multidimensional Systems and Signal Processing

, Volume 25, Issue 4, pp 659–681 | Cite as

An ideal image edge detection scheme

  • Xiaochun Zhang
  • Chuancai Liu


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.


Edge Scale space Gradient magnitude Laplacian of Gaussian  Heat diffusion equation Error function Scale invariance Scale normalization  Multi-scale 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Computer Science and EngineeringNanjing University of Science and TechnologyNanjingChina

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