43,479 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
Locally adaptive image denoising by a statistical multiresolution criterion
We demonstrate how one can choose the smoothing parameter in image denoising
by a statistical multiresolution criterion, both globally and locally. Using
inhomogeneous diffusion and total variation regularization as examples for
localized regularization schemes, we present an efficient method for locally
adaptive image denoising. As expected, the smoothing parameter serves as an
edge detector in this framework. Numerical examples illustrate the usefulness
of our approach. We also present an application in confocal microscopy
Spatial Smoothing for Diffusion Tensor Imaging with low Signal to Noise Ratios
Though low signal to noise ratio (SNR) experiments in DTI give key information about tracking and anisotropy, e.g. by measurements with very small voxel sizes, due to the complicated impact of thermal noise such experiments are up to now seldom analysed. In this paper Monte Carlo simulations are presented which investigate the random fields of noise for different DTI variables in low SNR situations. Based on this study a strategy for spatial smoothing, which demands essentially uniform noise, is derived. To construct a convenient filter the weights of the nonlinear Aurich chain are adapted to DTI. This edge preserving three dimensional filter is then validated in different variants via a quasi realistic model and is applied to very new data with isotropic voxels of the size 1x1x1 mm3 which correspond to a spatial mean SNR of approximately 3
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