On Monotonicity of Image Quality Metrics

Perceptual image quality assessment (IQA) is an important research topic of visual signal processing both in its own right and for its utility in designing various optimal image processing and coding algorithms. This work is concerned with an issue that has been largely overlooked by the research community of IQA, that is, the monotonicity, or lack of it, between the subjective scores and the predictions of image quality metrics (IQM) for images with compression artifacts. We analyze the data of several well-known databases for IQA and expose among them a large number of instances of non-monotonicity between subjective and objective quality scores. Further, we observe that a nonlinear dynamical model of 3D cusp catastrophe can well explain the intricate relationship between the subjective and objective quality scores. Our findings identify an inherent flaw of current signal-distance or fidelity-based IQMs, which neglect the psycho-physiological aspect of human visual perception. This research suggests a new direction of IQA research and it also sheds light on the design of subjective quality evaluation process.