Multispectral Anisotropic Diffusion (MultiAD)


Abstract:

A novel way to denoise multispectral images is proposed via an anisotropic diffusion based partial differential equation (PDE). A coupling term is added to the divergence term and it facilitates the modelling of interchannel relations in multidimensional image data. A total variation function is used to model the intrachannel smoothing and gives a piecewise smooth result with edge preservation. The coupling term uses weights computed from different bands of the input image and balances the interchannel information in the diffusion process. It aligns edges from different channels and stops the diffusion transfer using the weights. Well-posedness of the PDE is proved in the space of bounded variation functions. Comparison with the previous approaches is provided to demonstrate the advantages of the proposed scheme. The simulation results show that the proposed scheme effectively removes noise and preserves the main features of multispectral image data by taking channel coupling into consideration.

Related projects: VTV-Denoise

Example 1:

Noisy Channels

Restored Channels with the Scheme [1]

Combined multispectral image (3 channels combined):

Noisy image

Denoised image [1]

Example 2:

Comparison with other schemes (from [1]):

Acton & Landis

[4]

Boccignone et al.

[8]

Pope & Acton

[5]

Tschumperle & Deriche [9]

Lennon et al.

[6]

Bresson & Chan

[10]

Wang et al.

[7]

Proposed scheme

[1]

If you use the images presented here kindly cite Reference [1] below.

References:

[1] V. B. S. Prasath, A. Singh. Multispectral image denoising by well-posed anisotropic diffusion with channel coupling. International Journal of Remote Sensing, 31(8), 2091-2099, Mar 2010. doi:10.1080/01431160903260965

[2] V. B. S. Prasath. Weighted Laplacian differences based multispectral anisotropic diffusion. IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2011. doi:10.1109/IGARSS.2011.6050119

[3] V. B. S. Prasath, J. C. Moreno, K. Palaniappan. Color image denoising using chromatic edges based vector valued anisotropic diffusion improves perceptual visual quality. Preprint, 2013. Very preliminary version at arXiV, April 2013. doi:10.48550/arXiv.1304.5587. Supplementary files, data set containing images, results are available at figshare: 10.6084/m9.figshare.658958.

Bibliography:

[4] S. T. Acton and J. Landis, Multi-spectral anisotropic diffusion. International Journal of Remote Sensing, Volume 18, pp. 2877-2886, 1997.

[5] K. Pope and S. T. Acton, Modified mean curvature motion for multispectral anistropic diffusion. In Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation, 5-7 April 1998, Tucson, AZ, USA, pp. 154-159, 1998.

[6] M. Lennon, G. Mercier and L. Hubert-Moy, Nonlinear filtering of hyperspectral images with anisotropic diffusion. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, 25-29 July 2002, pp. 2477-2479, 2002.

[7] Y. Wang, L. Zhang and P. Li, Nonlinear multispectral anisotropic diffusion filters for remote sensed images based on MDL and morphology. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, 25-29 July 2005, pp. 4327-4330, 2005.

[8] G. Boccignone, M. Ferraro and T. Caelli, Generalized spatio-chromatic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, pp. 1298-1309, 2005.

[9] D. Tschumperle and R. Deriche, Vector-valued image regularization with PDE's: A common framework for different applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, pp. 1-12, 2005.

[10] X. Bresson and T. Chan, Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems and Imaging, 2, pp. 455-484, 2008.

For anisotropic diffusion of mono channel (gray-scale images), please visit this project page.