Full-reference image quality assessment metrics with signal strength quantification capabilities

Most image processing and computer vision applications necessitate objective quality assessment of the input images during pre-processing or post-processing. This important inquiry promotes effective selection of quality images by imaging and vision machines for accurate image processing, analysis and interpretation. On this ground, peak signal-to-noise ratio (PSNR) has traditionally been used in a range of image enhancement and restoration problems, including denoising and super-resolution, to gauge quality of images. Despite its wide application, PSNR is an unbounded metric and cannot be intuitively interpreted with respect to ideal conditions of the input images. PSNR increases with an image quality, but fails to inform an upper bound of a quality value that an image can achieve. Additionally, PSNR explodes to an unreasonably large number under ideal situations (when mean squared error equals zero, or when original and restored images are equal). Furthermore, PSNR resonates poorly with the human visual system. These observations limit the scope of interpreting the metric, especially in situations where we intend to understand the performance degree of restoration methods. In this work, we have re-defined PSNR to ensure boundedness and, based on this new definition, three other alternative image quality assessment (IQA) metrics have been proposed: absolute percentage error, symmetric mean absolute percentage error and logarithmic relative error. In addition, we have introduced a normalized IQA metric, which ranges between 0% and 100%, based on the re-defined bounded PSNR metric (PSNRB). Empirical results show that our IQA metrics remain robust under varying degradation conditions. Furthermore, PSNRB correlates with PSNR within the established lower and upper bounds of PSNRB – an important observation highlighting the significance and validity of PSNRB. These metrics expand our understanding on quantifying and qualifying quality of features contained in the images. To allow for reproducibility of our results, we have shared implementation codes and datasets in the MATLAB File Exchange: https://www.mathworks.com/matlabcentral/fileexchange/136574-bounded-peak-signal-to-noise-ratio.