1,874 research outputs found
Significant edges in the case of a non-stationary Gaussian noise
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 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
Tomography: mathematical aspects and applications
In this article we present a review of the Radon transform and the
instability of the tomographic reconstruction process. We show some new
mathematical results in tomography obtained by a variational formulation of the
reconstruction problem based on the minimization of a Mumford-Shah type
functional. Finally, we exhibit a physical interpretation of this new technique
and discuss some possible generalizations.Comment: 11 pages, 5 figure
Differential Phase-contrast Interior Tomography
Differential phase contrast interior tomography allows for reconstruction of
a refractive index distribution over a region of interest (ROI) for
visualization and analysis of internal structures inside a large biological
specimen. In this imaging mode, x-ray beams target the ROI with a narrow beam
aperture, offering more imaging flexibility at less ionizing radiation.
Inspired by recently developed compressive sensing theory, in numerical
analysis framework, we prove that exact interior reconstruction can be achieved
on an ROI via the total variation minimization from truncated differential
projection data through the ROI, assuming a piecewise constant distribution of
the refractive index in the ROI. Then, we develop an iterative algorithm for
the interior reconstruction and perform numerical simulation experiments to
demonstrate the feasibility of our proposed approach
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