Statistically and perceptually motivated nonlinear image representation

Abstract

We describe an invertible nonlinear image transformation that is well-matched to the statistical properties of photographic images, as well as the perceptual sensitivity of the human visual system. Images are first decomposed using a multi-scale oriented linear transformation. In this domain, we develop a Markov random field model based on the dependencies within local clusters of transform coefficients associated with basis functions at nearby positions, orientations and scales. In this model, division of each coefficient by a particular linear combination of the amplitudes of others in the cluster produces a new nonlinear representation with marginally Gaussian statistics. We develop a reliable and efficient iterative procedure for inverting the divisive transformation. Finally, we probe the statistical and perceptual advantages of this image representation, examining robustness to added noise, rate-distortion behavior, and artifact-free local contrast enhancement.

Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization

“…Although RG is unlikely to remain optimal in the presence of channel noise, we expect that a globally extended RG transform might still be effective for image compression. In previous work, we found that divisively normalized representations can produce improvements in the rate-distortion trade-off (for MSE and in terms of visual quality) compared with their linear counterparts (Lyu & Simoncelli, 2007).…”

“…Empirically, it has been shown that locally dividing bandpass-filtered pixels by local standard deviation can produce approximately gaussian marginal distributions (Ruderman, 1996) and that a weighted DN nonlinearity can reduce statistical dependencies of oriented bandpass filter responses (Simoncelli, 1997;Buccigrossi & Simoncelli, 1999;Schwartz & Simoncelli, 2001;Valerio & Navarro, 2003). Recently, several authors have developed invertible image transformations that incorporate DN (Malo et al, 2000;Malo, Epifanio, Navarro, & Simoncelli, 2006;Gluckman, 2006;Lyu & Simoncelli, 2007). Since DN provides a nonlinear means of reducing dependencies in bandpass representations of images, it is natural to ask how it is related to the RG methodology introduced in this article.…”

“…We show that RG produces much more substantial reductions in dependency, as measured with multi-information of pairs or blocks of nearby bandpass filter responses, than does ICA. Finally, we show that the RG transformation may be closely approximated by divisive normalization (DN), which was developed as a description of the nonlinear response properties of visual neurons (Heeger, 1992;Geisler & Albrecht, 1992), and which has been shown empirically to reduce higherorder dependencies in multiscale image representations (Malo, Navarro, Epifanio, Ferri, & Artigas, 2000;Schwartz & Simoncelli, 2001;Wainwright, Schwartz, & Simoncelli, 2002;Valerio & Navarro, 2003;Gluckman, 2006;Lyu & Simoncelli, 2007). Thus, RG provides a more principled justification of these previous empirical results in terms of a specific source model.…”

Change detection on SAR images using divisive normalization-based image representation

“…The DNT is built upon linear transform models, where each coefficient (or neuronal response) is normalized (divided) by the energy of a cluster of neighboring coefficients (neighboring neuronal response) [14]. This procedure can explain nonlinearities in the responses of mammalian cortical neurons, and nonlinear masking phenoma in human visual perception, and was also empirically shown to produce approximately Gaussian marginal distributions and to reduce the statistical dependencies of the original linear representation [19]. Therefore, we proposed a change detection method for SAR images in the DNT domain rather than in the wavelet domain due to the superior properties of the DNT as mentioned above.…”

SSIM-inspired image restoration using sparse representation

“…This normalization is conceptually consistent with the light adaptation (also called luminance masking) and contrast masking effect of HVS. It has been recognized as an efficient perceptually and statistically non-linear image representation model [32,33]. It is shown to be a useful framework that accounts for the masking effect in human visual system, which refers to the reduction of the visibility of an image component in the presence of large neighboring components [34,35].…”