Multiscale relevance of natural images

We use an agnostic information-theoretic approach to investigate the statistical properties of natural images. We introduce the Multiscale Relevance (MSR) measure to assess the robustness of images to compression at all scales. Starting in a controlled environment, we characterize the MSR of synthetic random textures as function of image roughness H and other relevant parameters. We then extend the analysis to natural images and find striking similarities with critical (H approximate to 0) random textures. We show that the MSR is more robust and informative of image content than classical methods such as power spectrum analysis. Finally, we confront the MSR to classical measures for the calibration of common procedures such as color mapping and denoising. Overall, the MSR approach appears to be a good candidate for advanced image analysis and image processing, while providing a good level of physical interpretability.