Edge Enhancing Coherence Filter in the Image Filters Panel

Perform Anisotropic Non-Linear Diffusion filtering on a 2D gray/color or 3D image stack. Anisotropic Non-Linear Diffusion filtering should reduce the noise while preserving the region edges, and also enhancing the edges by smoothing along them.

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Contents Coherence Filter Toolbox description

Image Edge Enhancing Coherence Filter based on the Image Edge Enhancing Coherence Filter Toolbox written by Dirk-Jan Kroon and Pascal Getreuer. This is one of the most advanced image enhancement methods available, and also contains HDCS (Hybrid Diffusion With Continuous Switch), from October 2009. The result looks like an artist painted the image, with clear brush strokes along the image edges and ridges.

The basis of the method used is the one introduced by Weickert.

1. Calculate Hessian from every pixel of the Gaussian smoothed input image
2. Gaussian Smooth the Hessian, and calculate its eigenvectors and values (image edges give large eigenvalues, and the eigenvectors corresponding to those eigenvalues describes the direction of the edge)
3. The eigenvectors are used as diffusion tensor directions. The amplitude of the diffusion in those 3 directions is based on the eigen values and determined by Weickerts equation
4. A Finite Difference scheme is used to do the diffusion
5. Back to step 1, till certain diffusion time is reached

Diffusion schemes:

There are several diffusion schemes available: standard, implicit, nonegative discretization, and also a rotation invariant scheme, and a novel diffusion scheme with new optimized derivatives.

Coherence Filter Parameters

Schemes, available numerical diffusion schemes:

• 'R', Rotation Invariant, Standard Discretization (implicit) 5x5 kernel;
• 'O', Optimized Derivative Kernels;
• 'I', Implicit Discretization (only works in 2D);
• 'S', Standard Discretization;
• 'N', Non-negativity Discretization.

Eigenmode, different equations to make a diffusion tensor:

• '0', Weickerts equation, line like kernel (similar to 3);
• '1', Weickerts equation, plane like kernel;
• '2', Edge enhancing diffusion (EED) (similar to 4);
• '3', Coherence-enhancing diffusion (CED) (similar to 0);
• '4', Hybrid Diffusion With Continuous Switch (HDCS) (similar to 2).

Other parameters

• 'T', The total diffusion time;
• 'dt', Diffusion time stepsize, in case of scheme H,R or I defaults to 1, in case of scheme S or N defaults to 0.15.;
• 'sigma', Sigma of gaussian smothing before calculation of the image Hessian;
• 'rho',Rho gives the sigma of the Gaussian smoothing of the Hessian;
• 'C', amplitude of the diffusion smoothing in Weickert equation (Default 1e-10);
• 'm', amplitude of the diffusion smoothing in Weickert equation (1);
• 'alpha', amplitude of the diffusion smoothing in Weickert equation (0.001);
• 'lambda_e', Default 0.02, planar structure contrast (CED, EED, HDCS modes);
• 'lambda_c', Default 0.02, tube like structure contrast (CED, EED, HDCS modes);
• 'lambda_h', Default 0.5 , threshold between structure and noise (CED, EED, HDCS modes);

Effective combinations

• Scheme=N, eigenmode=2/4 or 1, T=5, dt=0.15, Sigma=5, rho=1
• Scheme=O, eigenmode=1, T=5, dt=1, Sigma=5, rho=1
• Scheme=R, eigenmode=2/4, T=5, dt=1, Sigma=5, rho=1
• Scheme=S, eigenmode=2 or 4, T=5, dt=0.15, Sigma=5, rho=1

Coherence Filter Usage

Anisotropic Diffusion is fairly slow process and search of best parameters may be hard. In order to speed up the process there is a possibility to perform a Test run to define the best parameters.

Test run

• Zoom in into the area of interest with a mouse wheel.
• Press the Test run button.
• Check the region that will be used for the test filtering. • Define the variation of Parameters (T, dt, sigma, rho, C, m, alpha, lambda_e, lambda_c, lambda_h) using standard Matlab notation (start:step:end). By default the script will save middle slice of the selected dataset to a file, however this may be changed in the Save frame numbers editbox. The filter parameters for each image are fused into the saved image and will also be added into the ImageDescription field. • Press the Test Run button.
• Define desired Scheme and Eigenmode values. • Give a template for saving
• Stay patient...

Coherence Filter References

• Kroon and Slump, "Coherence Filtering to Enhance the Mandibular Canal in Cone-Beam CT Data", IEEE-EMBS Benelux Chapter Symposium, 2009.
• Kroon et al, "Optimized Anisotropic Rotational Invariant Diffusion Scheme on Cone-Beam CT", MICCAI, 2010
• Weickert, "A Scheme for Coherence-Enhancing Diffusion Filtering with Optimized Rotation Invariance"
• Mendrik et al, "Noise Reduction in Computed Tomography Scans Using 3-D Anisotropic Hybrid Diffusion With Continuous Switch", October 2009
• Weickert, "Anisotropic Diffusion in Image Processing", Thesis 1996
• Laura Fritz, "Diffusion-Based Applications for Interactive Medical Image Segmentation"
• Siham Tabik et al, "Multiprocessing of Anisotropic Nonlinear Diffusion for filtering 3D image"

Parallel processing

There is a small optimization for parallel processing for final runs in 2D mode. The improvement factor is about x3-5 times for 8 cores. Parallel processing should be enabled by pressing the Turn on parallel processing button in the im_browser toolbar .

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