Hereafter, we present several contour/texture separation using Morphological Component Analysis (MCA)

Left, original image; middle, piecewise smooth content part and right, texture part. The addition of the texture part and the piecewise smooth part reproduces the original image.

Left, Canny edge detection on previous original image and right, Canny edge detection on the piecewise smooth part.

Left, original image; middle, piecewise smooth content part and right, texture part. The addition of the texture part and the piecewise smooth part reproduces the original image.

Left, original image; middle, piecewise smooth content part and right, texture part. The addition of the texture part and the piecewise smooth part reproduces the original image.

Upper, left original image + noise and right, piecewise smooth content part. Bottom, left texture part and right, residual part. Residual + texture part + piecewise smooth content part = input data.

Decomposition in a Curvelet + DCT dictionnary :

References :

1. ❖J. Bobin, J.-L. Starck, J. Fadili, Y. Moudden, and D.L. Donoho, "Morphological Component Analysis : An Adaptive Thresholding Strategy", IEEE Transactions on Image Processing, Vol.16, N°11, p. 2675 - 2681, November 2007.
   

2. ❖M. Elad, J.-L Starck, D. Donoho and P. Querre, "Simultaneous Cartoon and Texture Image Inpainting using Morphological Component Analysis (MCA)", Journal on Applied and Computational Harmonic Analysis ACHA , Vol. 19, pp. 340-358, November 2005.
   

3. ❖J.-L. Starck, M. Elad, and D.L. Donoho, "Image Decomposition Via the Combination of Sparse Representation and a Variational Approach", IEEE Transaction on Image Processing , Vol. 14, N°10, 2005.
   

4. ❖J.-L. Starck, M. Elad, and D.L. Donoho, "Redundant Multiscale Transforms and their Application for Morphological Component Analysis", Advances in Imaging and Electron Physics , 132, 2004.

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