Information content in nonlinear local normalization processing of digital images

In this paper, we investigate the rate at which information is transferred from the scene to the digital processed image in imaging systems using nonlinear Local Normalization. While a formula for the Rate of Information has been used in many studies of linear systems with Gaussian (Normal) signals,1–6 a formula applicable to nonlinear/non-Gaussian systems has not been available until now. We discuss a new formula for the Rate of Information7 developed by the authors for systems with nonlinear Local Normalization processing. The Local Normalization algorithm, which is similar to the Retinex algorithm, is formulated and discussed. As the name implies, this algorithm forms a local average signal and normalizes the detail (high spatial frequency) scene signal by the local average. The scene detail information transferred to the locally normalized image is seen to be at least as high as that transferred to the acquired digital image. Thus, no information loss occurs in using Local Normalization. A case study of the new Rate of Information formula shows that designing the image-gathering system cut-off frequency near or slightly below the Nyquist frequency maximizes the scene detail information transferred to the locally normalized image for all the conditions considered.