A Novel Class of Intensity-based Metrics for Image Functions which Accommodate a Generalized Weber's Model of Perception

Even though the usual L2 image fidelity measurements, such as MSE and PSNR, characterize the mean error for each pixel of the images, these traditional measurements are not designed to predict human visual perception of image quality. In other words, the standard L2-type optimization in the context of best approximation theory is not in accordance with human visual system. To provide alternative methods of measuring image distortion perceptually, the structural similarity image quality measure (SSIM) was established decades ago. In this thesis, we are concerned with constructing a novel class of metrics via intensity-based measures, which accommodate a well-known psychological model, Weber's model of perception, by allowing greater deviations at higher intensity values and lower deviations at lower intensity values. The standard Weber model, however, is known to fail at low and high intensities, which has given rise to a generalized class of Weber models. We have derived a set of "Weberized'' distance functions which accommodate these generalized models. Mathematically, we prove the existence and uniqueness of the density functions associated with the measures which conform to generalized Weber's model of perception. Meanwhile, we consider the generalized Weber-based metrics as the optimization criteria and implement them in best approximation problems, where we also prove the existence and uniqueness of best approximations. We compare the results, which are theoretically adapted to the human visual system, with best L2-based approximations. Using a functional analysis point of view, we examine the stationary equations associated with the generalized Weber-based metrics to arrive at the Fréchet derivatives of these metrics. Finally, we establish an existence-uniqueness theorem of best generalized Weber-based L2 approximations in finite-dimensional Hilbert spaces

On the Optimal Choice of Quality Metric in Image Compression

There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I ; e I) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L p metrics d(I ; e I) = R jI(x) \Gamma e I(x)j p dx are the best, and that the optimal value of p can be selected depending on the expected relative size r of the informative part of the image

On the Optimal Choice of Quality Metric in Image Compression

There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I ; e I) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L p metrics d(I ; e I) = R jI(x) \Gamma e I(x)j p dx are the best, and that the optimal value of p can be selected depending on the expected relative size r of the informative part of the image. 1 Formulation of the Problem 1.1 Image Compression Is Necessary Images tend to take up a lot of computer space, so in many applications, where we cannot store the original images, we must use image compression. Ideally, we would like to use a lossless c..

On the Optimal Choice of Quality Metric In Image Compression: A Soft Computing Approach

Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image e I is, in general, different from the original image I . There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I ; e I) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L p metrics d(I ; e I) = R jI(x) \Gamma e I(x)j p d..

On the Optimal Choice of Quality Metric In Image Compression: A Soft Computing Approach

Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image e I is, in general, different from the original image I. There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I ; e I) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L p metrics d(I ; e I) = R jI(x) \Gamma e I(x)j p d..