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developpement:productions:logiciels:anisotropicblur [2014/12/05 09:09]
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 ====== Image processing : Anisotropic Blur ====== ====== Image processing : Anisotropic Blur ======
 +  * **Anisotropic Blur** : PDE-based algorithm to reduce noise in grey-scale image (2D or 3D) from biology, using a diffusion process.
 +  * **Why ?**
 +To study plant morphogenesis,​ we need to follow the evolution of a plant during time. We can use real-time imaging and image segmentation to reconstruct the plant development at a cell level. ​
 +The real-time 3D images obtained by confocal microscopy are noisy. In order to segment them, we need to reduce this noise. ​
 +The easiest way is to use a gaussian blur, which will smooth the image intensity. It will indeed remove the noise, but we might also lose some important informations,​ as the localization of the cell walls. That's why we implement an anisotropic blur, which reduce the noise without blurring the cell walls.
 +The filter develop by Weickert is a diffusion process using a PDE (Partial Differential Equation). The image will evolve in time according to its gradient and a diffusion tensor (anisotropic) or a diffusion coefficient (isotropic). ​
 +The diffusion process is similar to a smoothing or blurring process.
 +The filter develop by Schmidt is anisotropic and heterogeneous : there is a diffusion tensor D for each voxel. D is compute using the eigenvectors and the eigenvalues of the Hessian matrix (second derivative of the image intensity). The diffusion tensor D is a 3 by 3 matrix with values between 0 and 1. 
 +Inside the cells, where the image is globally homogeneous,​ the diffusion is isotropic and equal to 1.
 +Near the cell walls, the diffusion is anisotropic : it is strong along the walls, and small perpendicularly to the walls.
 +  * **Results**
 +From left to right :
 +  - original image
 +  - anisotropic blur K=0.1 / sigma=6 / gamma=1 / nb_it=150
 +  - gaussian blur
 +{{ :​developpement:​productions:​logiciels:​original_zoom.png?​nolink&​650 |}}
 +  * **References**
 +The algorithm is based on a filter developed by Weickert, using a formula from Schmidt
 +  - J. Weickert. Anisotropic Diffusion In Image Processing. B.G. Teubner Stuttgart, 1998.
 +  - Schmidt, T., Pasternak, T., Liu, K., Blein, T., Aubry-Hivet,​ D., Dovzhenko, A., Duerr, J., Teale, W., Ditengou, F. A., Burkhardt, H., Ronneberger,​ O. and Palme, K. (2014), The iRoCS Toolbox – 3D analysis of the plant root apical meristem at cellular resolution. The Plant Journal, 77: 806–814. doi: 10.1111/​tpj.12429
 +<note important>​This project has been performed during the stage of Master of **Typhaine Moreau** at ENS Lyon (Reproduction et Developpement des Plantes and Centre Blaise Pascal) coordinated by **Annamaria Kiss and Cerasela Calugaru**
developpement/productions/logiciels/anisotropicblur.1417766992.txt.gz · Dernière modification: 2015/01/07 10:04 (modification externe)