Significant edges in the case of non-stationary Gaussian noise

  • Authors:

  • I. Abraham;R. Abraham;A. Desolneux;S. Li-Thiao-Te

  • Affiliations:

  • CEA/DIF, 91680 Bruyères le Chatel, France;Laboratoire MAPMO, Fédération Denis Poisson, Université d'Orléans, B.P. 6759, 45067 Orléans cedex 2, France;Laboratoire MAP5, Université René Descartes, 45 rue des Saints-Pères, 75270 Paris cedex 06, France;Laboratoire CMLA, ENS Cachan, 61 avenue du Président Wilson, 94235 Cachan cedex, France

  • Venue:
  • Pattern Recognition
  • Year:
  • 2007

Quantified Score

Hi-index 0.01

Visualization

Abstract

In this paper, we propose an edge detection technique based on some local smoothing of the image followed by a statistical hypothesis testing on the gradient. An edge point being defined as a zero-crossing of the Laplacian, it is said to be a significant edge point if the gradient at this point is larger than a threshold s(@e) defined by: if the image I is pure noise, then the probability of @?@?I(x)@?=s(@e) conditionally on @DI(x)=0 is less than @e. In other words, a significant edge is an edge which has a very low probability to be there because of noise. We will show that the threshold s(@e) can be explicitly computed in the case of a stationary Gaussian noise. In the images we are interested in, which are obtained by tomographic reconstruction from a radiograph, this method fails since the Gaussian noise is not stationary anymore. Nevertheless, we are still able to give the law of the gradient conditionally on the zero-crossing of the Laplacian, and thus compute the threshold s(@e). We will end this paper with some experiments and compare the results with those obtained with other edge detection methods.