Computing a perceptual score

The model [ 18 ] used here was designed for colour images and uses the opponent colour representation [ 13 ] but in this paper we restrict the discussion to monochrome images and use only the B/W channel (which is extremely close to the luminance (Y) channel). A schematic of the system is shown in Figure  2 .

   
Figure 2: Schematic of the human vision model

Both the original image and the error are filtered into perceptual channels. The contrast of the original image is then evaluated and used to mask the error. This gives a distortion measure that is averaged in a manner that crudely models the fovea. The blocks labelled ``Perceptual decomposition'' consist of a set of Gabor filters. The first band-pass filter in the set is isotropic with zero response at wavenumber (to model insensitivity to global luminance level),

where k is the wavenumber measured in radians per degree of visual of angle and rad deg , rad deg .

   
Figure 3: Response of the Gabor filter set in Fourier space. Axes are labelled in cycles per degree of visual angle.

The other filters have a bandpass response centred on wavenumber ,

where , . The filters, shown in Figure  3 , are chosen to model the visual channels [ 8 ]. Each channel of the distorted image is compared to the same channel from the original image and a masking model applied [ 5 ].

The masking model used here allows only within-channel masking and uses masking weights computed as the inverse the normalised detection threshold:

where is the detection threshold of the error in the absence of the masker. C is the error contrast and is the contrast sensitivity function,

where a =0.0192, c =1.1, d = 2.6 and rad deg are experimentally determined constants [ 9 ]. is the contrast of the original image (the masker).

The masked error contrast is averaged using a disc shaped filter. The disc is chosen to subtend 2 so as to approximate the fovea. The final distortion is computed as

where there are N channels, is the set of M pixels in the foveal disc and e ( x , y ) is the masked error signal at position x , y . The Minkowski sum in ( 5 ) is an attempt to weight errors in the same way as human observers [ 18 ]. E ( x , y ) is called the Visual Difference Score.