The Weber-Fechner and Michelson contrast laws are widely used for measuring contrast of test tar- gets, but they do not describe complex image contrast ad-.
A MEASURE FOR PERCEPTUAL IMAGE QUALITY ASSESSMENT Ronaldo de Freitas Zampolo and Rui Seara LINSE – Circuits and Signal Processing Laboratory Federal University of Santa Catarina 88040-900 – Florian´opolis-SC Brazil E-mail: {zampolo, seara}@linse.ufsc.br
ABSTRACT This paper addresses the issue of perceptual image quality assessment in image restoration systems. Firstly, experiments are conducted to evaluate perceived quality in images degraded only by frequency distortion. Based on the resulting experimental data, a distortion quality measure (DQM) is proposed. Then another experiment, whose test images present frequency distortion and noise injection, is achieved. From this latter experiment, a composed quality measure (CQM) is developed to assess perceived quality of images degraded by combined effects of frequency distortion and noise injection. The CQM is derived from DQM and NQM (noise quality measure), this latter has been recently proposed, and it can be used as a tool for evaluation and optimization of image restoration systems according to human visual perception.
1. INTRODUCTION Image quality assessment plays a key role in evaluating and optimizing image processing systems. Considering an image system designed for human consumers, the measure used to assess quality of such a system should follow visual perception characteristics. Nevertheless, the measures mostly used are based on mean-squared error (MSE), which are not accurate in predicting perceptual quality [1]. The reason for such procedure is that MSE-based measures result in lower computational burden and simpler mathematical expressions than the ones that use more sophisticated metrics. Although psychovisual measures are difficult to develop, due to inherent complexity of the human visual system (HVS), they are necessary for keeping consistency between numerical improvements and perceived quality in image systems. Therefore, intensive efforts have been made in psychovisual metric research, specially in contrast measurement. The Weber-Fechner and Michelson contrast laws are widely used for measuring contrast of test targets, but they do not describe complex image contrast ad-
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equately. Anyway, the measuring principle used by WeberFechner and Michelson, foreground target against background, forms the basis from which other contrast measures are derived. As experiments show that the perception of contrast depends on spatial frequency, this component has been increasingly taken into account in contrast measures. The mentioned dependency is expressed by the so called contrast threshold function (CTF) and its inverse, the contrast sensitivity function (CSF), which can be used to include environmental conditions and visualization device features in image quality metrics [2], [3]. Hess and Pointer explicitly address the problem of complex image contrast perception at different spatial frequency, proposing a contrast metric defined in the frequency domain [4]. However, the Hess and Pointer metric cannot capture the local nature of contrast changes [5]. Attempting to join local masking effects and spatial frequency dependency into a single metric, Peli [4] presents an approach to assess contrast in complex images, called local bandlimited contrast, in which an image is analyzed by a bank of band pass filters. Then the output images are used to determine the contrast of every pixel as a function of the spatial frequency. In [5], a noise quality measure (NQM) and a distortion measure (DM) are proposed to quantify, respectively, noise injection and frequency distortion in image restoration systems. In such an approach, noise injection and frequency distortion are considered decoupled psychovisual effects. The NQM is based on the Peli’s contrast and has shown better performance than the signal-to-noise ratio (SNR), peak SNR (PSNR) and weighted SNR (WSNR). In this paper, we present evidences that DM is not suitable to represent perceived frequency distortion and therefore propose a distortion quality measure (DQM), which is based on the NQM with modified inputs. In [5], the authors have pointed out that the definition of a quality metric that combines the two measures of frequency distortion and noise injection is still an open problem. In this way, the present paper also develops a composed quality measure (CQM), using NQM and DQM. Both DQM and CQM are validated by experimentation.
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2. IMAGE QUALITY ASSESSMENT IN IMAGE RESTORATION SYSTEMS In [5], the authors present a procedure for image quality assessment in restoration systems, in which the noise injection and frequency distortion are considered decoupled effects. In this way, a noise quality measure (NQM) and a distortion measure (DM) are developed in order to quantify perceived noise injection and frequency distortion, respectively. The referred metrics require that the original image and a noiseless version of the degraded image are available. Figure 1 illustrates the structure used in [5] and adopted here from now on, where x(m, n), ν 0 (m, n), η(m, n), ν(m, n), c(m, n), x ˆ0 (m, n) and x ˆ(m, n) are, respectively, the original image, noiseless blurred image, additive noise, blurred image, point spread function (PSF) of the blurring system, model restored image [5] and restored image.
The CSF [6] used here for DM evaluation is given by CSF (f ) = 2.6 (0.0192 + 0.114f ) exp [−(0.114f )1.1], (2) where f denotes the radial spatial frequency (cycles/degree). Thus, by using (1), DM is evaluated by experimentation. The experiments are conducted under the following conditions: • four 256×256 original images (“Lena”, “Baboon”, “Peppers” and “Bridge”) are degraded only by frequency distortion, generating four sets of nine images each; • each image is ranked in perceived quality by seven volunteers, according to Table 1; • the referred volunteers are 20 to 50 years old with normal or corrected vision; • a 15 inch monitor, 800×600 pixel resolution, is used to visualize the test images; • the viewing distance is about 60 cm.
Table 1. Values used to rank images Rank 4 3 2 1 0
Fig. 1. Image degradation, restoration and quality assessment blocks.
3. DISTORTION MEASURE (DM) EVALUATION The DM [5] is defined as follows ( ) X X ˆ 0(u, v) 1− DM = 20 log10 CSF (u, v) , (1) X(u, v) (u,v)
ˆ 0 (u, v) and X(u, v) are the model restored image where X and original image Fourier transforms, respectively.
Perceived Quality Excellent Good Regular Bad Unacceptable
Figure 2 illustrates the mean perceived quality for the evaluated image sets as a function of DM. The curves presented seem meaningless, since images with lower DM are expected to be perceived as having higher quality. Probably, this unexpected behavior occurs because the DM formulation, defined only in the frequency domain, cannot take into account the resulting contrast masking effects in the luminance domain. These statements are reinforced by the experimental data presented in the next section, in which a distortion quality measure (DQM) is proposed. 4. DISTORTION QUALITY MEASURE (DQM) The DQM proposed in this paper is based on the NQM; this latter is described in [5]. Originally designed to assess perceptual quality in images degraded only by noise injection, the NQM procedure can also be used for frequency
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Fig. 5. DQM evaluation for set #3.
distortion measurement. This can be accomplished by using the NQM procedure in the frequency distortion assessment block (Fig. 1), thus replacing the original NQM inputs x ˆ(m, n) and xˆ0 (m, n) by x ˆ0 (m, n) and x(m, n), respectively. The evaluations of Section 3 are depicted in Figs. 3 to 6, as a function of the DQM, for the image sets #1 to #4, respectively. Superimposed on the experimental data, a straight line is plotted obtained by linear regression. The correlation coefficients between the regression line and data are presented in Table 2. The results obtained have shown a quasi-linear variation of the perceived quality in images degraded by frequency distortion with respect to DQM, for the DQM range considered in the experiments.
5. COMPOSED QUALITY MEASURE (CQM)
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As pointed out in [5], the development of a metric that combines frequency distortion with noise injection measures is an open problem. This issue is addressed here by proposing a composed quality measure (CQM), which is derived from the NQM and DQM. A set of 81 test images is obtained from the “Lena” image by combining frequency distortion with addition of uniform Gaussian noise at different levels. Each of the 81 images is classified 7 times according to its perceived quality in the same conditions stated in Section 3. In Fig. 7, the mean perceived quality is plotted as a function of NQM and DQM. The proposed CQM model is expressed in (3). The bidimensional Gaussian function with non-correlated variables has been chosen among several
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Correlation Coefficients 0.9871579 0.9681562 0.9825474 0.9688865
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Fig. 7. Mean perceived quality as a function of the NQM and DQM. measure (CQM), is based on both the noise quality measure (NQM) [5] and DQM, being also ratified by experimental data. 7. REFERENCES [1] P. C. Teo and D. J. Heeger, “Perceptual image distortion,” in Proc. IEEE Int. Conf. Image Processing, 1994, vol. 2, pp. 982–986.
tested functions due to its correlation coefficient (0.935770) and variance (0.174635) values with respect to experimental data. " # (N − µ1 )2 (D − µ2 )2 CQM = k · exp − − , (3) 2σ12 2σ22 where N and D denote NQM and DQM, respectively; µ1 , µ2 , σ12 and σ22 denote the means and variances of N and D, respectively; and k is a normalization constant used to keep CQM values within the 0 to 4 range (Table 1).
6. CONCLUSIONS We have addressed the problem of perceived image quality in image restoration systems. Firstly, experiments have shown that the distortion measure (DM) [5] does not predict adequately perceptual quality in images degraded only by frequency distortion. Therefore, a distortion quality measure (DQM) has been proposed and confirmed experimentally. Finally, a measure to assess perceived quality in images degraded by both frequency distortion and noise injection is developed. This metric, named composed quality
[2] P. G. J. Barten, “The effects of picture size and definition on perceived quality,” IEEE Trans. Electron Devices, vol. 36, no. 9, pp. 1865–1869, Sept. 1989. [3] P. G. J. Barten, “Effects of quantization and pixel structure on the image quality of color matrix displays,” in Proc. Int. Display Research Conf., 1991, pp. 167–170. [4] E. Peli, “Contrast in complex images,” J. Opt. Soc. Am. A, vol. 7, no. 10, pp. 2032–2040, Oct. 1990. [5] N. Damera-Venkata, T. D. Kite, W. S. Geisler, B. L. Evans, and A. C. Bovik, “Image quality assessment based on a degradation model,” IEEE Trans. Image Processing, vol. 9, no. 4, pp. 636–650, Apr. 2000. [6] T. Mitsa and K. L. Varkur, “Evaluation of contrast sensitivity functions for the formulation of quality measures incorporated in halftoning algorithms,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, 1993, vol. 5, pp. 301–304.
