This strategy only enforces uncorrelation of the recto text and the verso text at each channel.
The estimated cross-spectra highlighted a significant correlation among recto and verso text patterns.
However, note the slight residual interference in the second output, clearly indicating that the recto text and the verso text are actually correlated.
In this case, employing ICA to solve each subsystem only entails assuming independence of the recto and verso text at each individual channel, as done for the grayscale case, and no unrealistic uncorrelation is assumed among the various colour maps of the recto (verso) text.
Indeed, if no blur is accounted for, two homologous patterns in the two different sides cannot match exactly; on the other side, this could also indicate that the recto and verso text are actually correlated at each channel.
Analogously, s r C (t) and s v C (t) are the clean recto and verso text patterns at pixel t, channel C. The positive elements a nm C, n = (r,v) and m = (r,v), of the so-called mixing matrix A, represent the unknown percentage of ink intensity attenuation of the two texts in the two sides, due to ageing factors, or transparency of the paper or ink seeping from the back to the front page.
By further assuming to neglect, at this stage, the attenuation and blurring of the recto (verso) text in the recto (verso) side, at each channel C the model we consider in the space domain is given by following 2 × 2 system: x r C t = s r C ( t ) + a C h C ( t ) ⊕ s v C ( t ) + μ r C ( t ) x v C t = a C h C ( t ) ⊕ s r C ( t ) + s v C ( t ) + μ v C ( t ) (2).
Furthermore, in our case, they can also be used for estimating the cross-correlation of the clean, ideal recto and verso foreground texts.
A reason for that could be the low correlation index between the recto and verso clean foreground texts that, as estimated from the ground-truth masks, results to be -0.0336.
He observed that all these texts but I and G verso consist predominantly of shared phrases (sequences of glyphs), which occur in different orders and contexts on different tablets.
