Removing artefacts from color and contrast modifications

Julien Rabin (1) , Julie Delon (2) and Yann Gousseau (2)
(1) CMLA, École Normale Supérieure de Cachan
(2) CNRS LTCI, Télécom ParisTech




This work is concerned with the modification of the gray level or color distribution of digital images. A common drawback of classical methods aiming at such modifications is the revealing of artefacts or the attenuation of details and textures.
In this work we propose a generic
filtering method enabling, given the original image and the radiometrically corrected one, to suppress artefacts while preserving details. The approach relies on the key observation that artefacts correspond to spatial irregularity of the so-called transportation map, defined as the differencebetween the original and the corrected image. The proposed method draws on the non-local Yaroslavsky filter to regularize the transportation map. The eff iciency of the method is shown on various radiometric modifications:
contrast equalization, midway histogram, color enhancement and color transfer.

For more details, see [1] and



• Let u : Ω → R^n be a discrete image, with n = 1 for a gray level image, n = 3 for a color image, and where Ω ⊂ Z^2 is the bounded image domain.

• Let T(u) be the image after color or contrast modification (Histogram equalization, color transfer, gamma transform, etc).

• We define M(u) := T(u) − u as the transportation map of the image u.


The image T(u) often exhibits some unpleasant artefacts, such as JPEG blocs, color inconsistancies, noise enhancement or loss of details (texture washing).

We propose to regularize the transportation map M thanks to the operator Y_u, a weighted average with weights depending on the similarity of pixels in the original image u. The effect of this operator on an image v : Ω →
R^n with n ≥ 1 is defined as

Y_u (v) : x ∈ Ω → R^n = 1 / c(x) * Σ_{y ∈ N (x)} v(y) · w_u (x, y)

with weights w_u (x, y) = exp { || u(x)−u(y) ||^2 / σ^2 },
where ||.|| stands for the Euclidean distance in R^n ,
where N (x) = x+N (0) ⊂ Ω  with N (0) a spatial neighborhood of 0,
where σ is a tuning parameter of the method and
C(x) is the normalization constant c(x) =
Σ_{y ∈ N (x)} w_u (x, y) .

Observe that if we apply Y_u to the image u, we obtain the Yaroslavsky filter.

The regularization of the image T(u), referred to as Transportation Map Regularization (TMR), is then defined as

TMR_u ( T(u) ) := u + Y_u ( M(u) ) = Y_u ( T(u) ) + u − Y_u (u) .

The TMR filter is iterated to remove the aforementioned artefacts. In order to control the iterations of the TMR filter, we compute at each iteration a convergence map, written C and defined at each pixel as follows:

C(x) = || Y_u^k [ M(u(x)) ] − Y_u^(k-1) [ M(u(x)) ]  || .

We then consider that there is numerical convergence in pixel x when C(x) < τ, and the TMR filter is only
applied to pixels for which the convergence map is greater than the threshold τ.

Experimental settings

For all the following experiments, the parameters have been set to:
  •   σ = 10 ,
  •   ρ = 10 ,
  •   τ = 1
for 8n-bits images (i.e. when n=3, the RGB color space is [0, 255]^3).

For more details, see [1] and

List of experiments:

'Book' experiment                                         book.jpg           book_eq_TMR.jpg

'Renoir-Gauguin' experiment      book.jpg      

'Lena-Barbara' experiment               

'ClownFish-SeaScape' experiment           

'Lena-Olive' experiment                    

'Budgerar-Parrot' experiment           

'Oxford-NewYork' experiment            


[1]   J. Rabin, J. Delon and Y. Gousseau, “Regularization of transportation maps for color and contrast transfer.”
       Proceedings of the IEEE International Conference on Image Processing, 2010. [BibTeX]

[2]   J. Rabin, J. Delon and Y. Gousseau, “Artefact-Free color and contrast modification.”
       HAL preprint, 2010 [WebPage].

Julien Rabin © 2011