Difference magnitude is not measured by discrimination steps for order of point patterns

We have shown in previous work that the perception of order in point patterns is consistent with an interval scale structure (Protonotarios, Baum, Johnston, Hunter, & Griffin, 2014). The psychophysical scaling method used relies on the confusion between stimuli with similar levels of order, and the resulting discrimination scale is expressed in just-noticeable differences (jnds). As with other perceptual dimensions, an interesting question is whether suprathreshold (perceptual) differences are consistent with distances between stimuli on the discrimination scale. To test that, we collected discrimination data, and data based on comparison of perceptual differences. The stimuli were jittered square lattices of dots, covering the range from total disorder (Poisson) to perfect order (square lattice), roughly equally spaced on the discrimination scale. Observers picked the most ordered pattern from a pair, and the pair of patterns with the greatest difference in order from two pairs. Although the judgments of perceptual difference were found to be consistent with an interval scale, like the discrimination judgments, no common interval scale that could predict both sets of data was possible. In particular, the midpattern of the perceptual scale is 11 jnds away from the ordered end, and 5 jnds from the disordered end of the discrimination scale

A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing

Since its introduction in 2004, the Structural Similarity (SSIM) index has gained widespread popularity as an image quality assessment measure. SSIM is currently recognized to be one of the most powerful methods of assessing the visual closeness of images. That being said, the Mean Squared Error (MSE), which performs very poorly from a perceptual point of view, still remains the most common optimization criterion in image processing applications because of its relative simplicity along with a number of other properties that are deemed important. In this thesis, some necessary tools to assist in the design of SSIM-optimal algorithms are developed. This work combines theoretical developments with experimental research and practical algorithms. The description of the mathematical properties of the SSIM index represents the principal theoretical achievement in this thesis. Indeed, it is demonstrated how the SSIM index can be transformed into a distance metric. Local convexity, quasi-convexity, symmetries and invariance properties are also proved. The study of the SSIM index is also generalized to a family of metrics called normalized (or M-relative) metrics. Various analytical techniques for different kinds of SSIM-based optimization are then devised. For example, the best approximation according to the SSIM is described for orthogonal and redundant basis sets. SSIM-geodesic paths with arclength parameterization are also traced between images. Finally, formulas for SSIM-optimal point estimators are obtained. On the experimental side of the research, the structural self-similarity of images is studied. This leads to the confirmation of the hypothesis that the main source of self-similarity of images lies in their regions of low variance. On the practical side, an implementation of local statistical tests on the image residual is proposed for the assessment of denoised images. Also, heuristic estimations of the SSIM index and the MSE are developed. The research performed in this thesis should lead to the development of state-of-the-art image denoising algorithms. A better comprehension of the mathematical properties of the SSIM index represents another step toward the replacement of the MSE with SSIM in image processing applications

Calibrating MS-SSIM for Compression Distortions using MLDS

International audienceIn this paper, we describe a recently developed method for assessing perceived image quality, Maximum Likelihood Difference Scaling (MLDS), and use it to assess the performance of MS-SSIM on compression distored images. MLDS allows us to quantify supra-threshold perceptual differences between pairs of images and to examine how perceived image quality, estimated through MLDS, changes as the compression rate is increased. We show how the data collected by MLDS allows us to recalibrate MS-SSIM to improve its performance