  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 $s(\eps)$ defined by: if the image $I$ is pure noise, then
$\P(\norm{\nabla I}\geq s(\eps) \bigm| \Delta I = 0) \leq\eps$. 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 $s(\eps)$ can be explicitly
computed in the case of a stationary Gaussian noise. In 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. But in this case again, we will be able to give the law of the
gradient conditionally on the zero-crossing of the Laplacian, and thus compute
the threshold $s(\eps)$. We will end this paper with some experiments and
compare the results with the ones obtained with some other methods of edge
detection.
