illustrate the power of the Generalized EM inpainting algorithm, we
applied it to the Barbara textured image, which is particularly
challenging. Texture is naturally handled in our EM inpainting algorith
using teh appropriate representation in the dictionary. As stationary
textures are efficiently represented by the local DCT, the dictionary
contained both the curvelet (for the geometry part) and the LDCT
transforms. The penalty function was the l1 norm
(see the papers for details).
The algorithm is not only able to recover the geometric part (cartoon),
but particularly performs well inside the difficult textured areas,
e.g. trousers. Note also the performance despite the difficulty on the
2 and 3
GEM inpainting algorithm was applied to other synthetic images without
locally-stationary textures, from which we present few examples (here
Lena and Claudia images). The dictionary contained the curvelet
transform and again the convex l1 penalty was used. The algorithm
converged after 100 iterations. Remaining artefacts on Claudia image
are mainly due to the JPEG compression of the original image.
algorithm was finally applied to a real old degraded
photograph. The missing areas (mask of degraded
parts to be recovered) were manually plotted. Here,
the dictionary contained the undecimated
DWT. Curvelets yield similar results. The quality of the inpainted
image is very promising.
the bird ! This
example was used for comparative purposes with vector-valued
regularization PDE methods (see D. Tschumperlé demo page),
where authors found it particularly challenging. We again applied our
GEM inpainting with a dictionary containing the UDWT and the local DCT
transforms. Note the quality of the reconstructed texture at the right
of the bird's
eye. See here for comparison with the
5: Free the Zebra !
is a toy example. We again applied our
GEM inpainting with a dictionary containing the fast curvelet transform.