• a scratch is caused by light diffraction: it is produced by the projector light that passes through the slit (i.e. the damaged region) of the film material.
   

   

    Therefore,

• the scratch appears as an area of partially missing data , where the original information has not been completely removed

• the scratch profile on the luminance cross-section is well-modelled by a sinc² whose equation is:
   

   

    where y is the horizontal abscissa (column number), c_p and b_p are respectively the column position and brightness of the scratch on the cross-section, and m_p is the line width

  Thus the model is

   

   

    where I is the degraded image signal and G the original image one (see BW model)

  COLOR FILM is based on the subtractive synthesis:

       it filters colors from white light through three separate layers of sensitive emulsions that are respectively sensitive to blue, green and red

         and the printed images are obtained using the subtractive color synthesis, i.e. yellow, magenta and cyan.

Hence,

If the mechanism acts on the opposite (negative) part of the support, it firstly removes the support and then the cyan layer providing a red scratch.

 

Degraded frame. From left to right: blue, red and cyan scratches.  

 

Portion of a degraded frame: white scratch  

 

  The range of width of color scratches differs from the BW model because of the change of resolution and the diffraction effect.

In correspondence to blue scratches, blue light (i.e. wavelength l ~ .4 m m) is not absorbed. For red scratches ( l ~ .7 m m) it is the opposite, since the filter has been removed from the mechanism causing the scratch.

For that reason, the maximum width allowed for blue scratches, in the pure case, is about half of the maximum width allowed for red scratches.

 

The Algorithm

• Apply the BW detection algorithm on the Magenta component (downsampled by 4) of the CMYK color space using the diffraction model for the degradation (white scratches are searched!)

  Let C the set of candidates. For each element c_p of C:

• Select the color component (among R,G,B) whose cross section has the highest value in correspondence to c_p;

• compute the undecimated wavelet decomposition of the selected component;

• restore the wavelet low pass A and vertical detail bands V by attenuating scratch contribution under the local visibility threshold using the model equation

• Invert the wavelet decomposition using the restored bands and let I_p be the resulting partially restored image;
• extract the luminance component of I_p and evaluate the energy value in correspondence to c_p in the cross section of this component, as done at step 5 of the detection algorithm. If the scratch is still visible, go to step 1 only considering the remaining color components.

 

 

Experimental Results

Good visual quality

Blue, red and cyan scratches have been removed from the image.

Textures are preserved

Left) Portion of the degraded frame around the red scratch. Right) Restored scratch using the proposed algorithm

False colors are not introduced

Left) Portions of the degraded frame around the blue scratch. Right) Restored scratch using the proposed algorithm