Multifractal measures of image quality

This paper proposes image quality measures based on multifractality preservation. Image quality measures play critical roles in designing and evaluating image processing schemes and performance, especially in which the resulting images deviate from the original ones. Examples of such schemes include image denoising and lossy compression. Traditional quality or distortion measures have been based on mean square error (MSE) measure or its derivatives, e.g., signal to noise ratio (SNR) or peak SNR (PSNR). Although such measures often lead to optimal schemes (with respect to MSE or PSNR), they are known to remove image parts that has noise-like appearances. Furthermore, they treat image singularities such as sharp edges or high textures (that are more important visually and diagnostically) and other image parts (that are less important) uniformly. In contrast, multifractal measures proposed in this paper characterize image singularities. This means the measures pay attention more on important image features, such as sharp edges and high textures. Furthermore, it can distinguish noise from noise-like signals through their differences in their types of singularities. As a result, the measure can be used to assess image quality of sensitive images resulting from processing schemes. The paper shows various ways of defining the measure that reveals multifractality of different aspects of images. It reports the use of the multifractal measure to compare a joint photographic expert group (JPEG) scheme and a variant of differential pulse code modulation (DPCM) coding showing that the DPCM scheme is superior in multifractal preservation for comparable compression ratios. As a result, the DPCM coding has been selected for a database of aerial ortho images.