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.

• References

The algorithm is based on a filter developed by Weickert, using a formula from Schmidt

1. J. Weickert. Anisotropic Diffusion In Image Processing. B.G. Teubner Stuttgart, 1998.
2. 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

• Formula

The filter develop by Weickert is a diffusion process using a PDE (Partial Differential Equation)