• the degraded image signal is the zero-mean Radon Projection of the image along the column axis, called luminance cross-section
• the scratch profile on the cross-section is well-modelled by a damped sinusoid whose equation is:
  
  where i is the horizontal abscissa (column number), cp and bp are respectively the column position and brightness of the scratch on the cross-section, kp is the decay of the line profile and wp is the line width
• the scratch is an area of partially missing data: its destroying effect is almost complete in correspondence to the peak of the sinusoid and diminishes moving away from it, according to the coefficient kp; moreover the higher the amplitude of the scratch, the more evident is its destroying effect (measured by the coefficient gamma).

  Thus the model is

  

    where I is the degraded image signal and G the original image one

The Algorithm

• Image luminance cross-section computation
• Hierarchical representation on the cross-section (peaks sequence: maxima for white scratches, minima for the black ones)
• Width Selection: peaks which are mainlobe of sinusoids having sidelobes distance in the range [3,10] are selected,
• Height Selection: peaks having amplitude over the average of the heigth of the signal are selected;
• Weber's law (Energy) Selection: peaks having an energy value greater than the minimum one for a perceivable scratch (according to the Weber's law) are selected
• False alarms rejection: lines ending roughly on the image are rejected

Scratches Classification

• Principal Scratches extending vertically on more than 95% of the image
  • not alone , having another scratch at distance of few pixels with sidelobes influencing each other;
    
  • alone , viceversa.
    
  • Secondary scratches: length up to 95% of image (They can be alone or not alone)

   

  Experimental Results

   

  The proposed algorithm
  • detects principal and secondary scratches because there are not thresholds on the length of the scratch; see the ones in the middle of the portion of the frame of STAR sequence;
    STAR sequence, portion of FRAME no.1
  • detects slight scratches thanks to the Weber’s law, expecially if they are alone; see the one at column number 146 of the seventh frame of SITDOWN sequence;
    SITDOWN sequence, portion of FRAME no.7
  • has no limit on the number of scratches to be detected;
  • employs a lower computing time: O(MN) for the cross-section computation and O(N) for the thresholding phases

   

   

    Slides

  (see V. Bruni, D. Vitulano, A Generalized Model for Scratch Detection, IEEE Trans. on Image Processing, Vol. 12, No. 11, November 2003)

   

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