Interpolation using a Threshold-based variable number of gradients

Interpolation using a Threshold-based variable number of gradients

This algorithm is described in [21].

Basic procedures :

a set of gradients is determined from the color values in the 5x5 neighborhood centered at the pixel under consideration. Each gradient corresponds to a different direction.
for each set of gradients, a threshold value is determined and the threshold is used to select a subset of gradients. Low-valued gradients indicate pixels having similar color values whereas high-valued gradients would be expected in regions of the image where there are many fine details or sharp edges.
the subset of gradients is used to locate regions of pixels that are most like the pixel under consideration. The pixels in these regions are then weighted and summed to determine the average difference between the color of the actual measured center pixel value and the missing color.

Interpolation of the green,red/blue value at the blue/red pixel : consider figure 8 below, we want to estimate G13 and B13 at R13.

figure 8

Form eight gradients as follows :

We show a numerical examples here too :

Gradient	N	E	S	W	NE	SE	NW	SW
Value	12	13	7	8	4	7	12	14

table 1

Determine a threshold and select a subset of gradients :

₁

₂

₁

₂

Here k₁*Min accounts for the case in which the gradients are all very similar, so that we wish to inclue all of them by setting a threshold that exceeds them. k₂ * (Max - Min) accounts for the case in which there is a significant difference between the maximum and minimum gradient values.

consider the numerical example illustrated in table 1, Min = 4, Max = 14 and T = 11 consequently. Therefore the selected subset of gradients consists of those with value less than 11 :
Gradient subset = {S, W, NE, SE}

Locate the pixels in the regions corresponding to the subset of gradients and to use those pixels to determine a color difference between the center pixel color and the color to be recovered.

Determine the average green, blue and red values in the gradient subset regions :

	G	B	R
S	G18	( B17 + B19 ) / 2	( R13 + R23 ) / 2
W	G12	( B7 + B17 ) / 2	( R11 + R13 ) / 2
NE	( G4 + G8 + G10 + G14 ) / 4	B9	( R13 + R5 ) / 2
SE	( G14 + G18 + G20 + G24 ) / 4	B19	( R13 + R25 ) / 2

Form the average color values in the gradient subset regions to get G_sum, B_sum and R_sum

_sum

Find the normalized color difference by dividing the difference of two sums by the number of gradients in the threshold subset, and add this normalized color difference to the pixel value under consideration to form the other two missing color components.

_sum

Interpolation of the blue/red value at the green pixel : consider figure 9 below, we want to estimate R13 and B13 at G13.

figure 9

Form eight gradients as follows :

As described earily, determine a threshold and select a subset of gradients. Again, T = k₁*Min + k₂ * (Max - Min), where k₁= 1.5 and k₂ = 0.5

Again, Locate pixels in the selected regions and use those pixels to determine a color difference between the center pixel color and the color to be recovered, finally add this color difference to produce an estimate for the missing color value.