Impact analysis of digital watermarking on perceptual quality using HVS models Qi, Pei Graduate student in Electrical&Computering Engineering At University of Wisconsin – Madsion [email protected] Abstract In this project, two improved perceptual quality methods are proposed. One is weighted PSNR (WPSNR). Based on the fact that the human eye will have less sensitivity to modifications in textured areas than in smooth areas, WPSNR uses an additional parameter called the Noise Visibility Function (NVF) that is a texture masking function as a penalization factor. The other method based on Watson HVS models. In his work, Watson defines Just Noticeable Difference (JND) as linear multiples of a noise pattern that produces a JND distortion measure. A perceptually lossless quantization matrix of the DCT transform is generated. Each entries of this matrix represent the amount of quantization that each coefficient can withstand without affecting the visual quality of the image. Introduction All sorts of digital watermarking algorithms or methods have grown greatly in the past twenty years. However, besides designing these approaches, a very important and often neglected issue is how to effectively and precisely measure the perceptual quality of image that has been watermarked. In other words, we need quality metrics to analyze the image degradation introduced by embedding watermarks. However, most popular measures in the field of image coding and compression such as MSE, SNR and PSNR, are objective and independent of the subjective factors like HVS (human visual system). This might be a problem in the application of digital watermarking since sophisticated watermarking methods exploit in one way or the other HVS. Using the above measures to quantify the distortion caused by a watermarking process might therefore result in misleading quantitative distortion measurements. In particular, in the digital watermarking field, the difference between original image and watermarked image is very small. The evaluation of image quality is significantly affected by image contents. Therefore, the present objective measures without considering the effect of HVS do not always provide with reliable quality assessments. In this project, section I briefly introduced some fundamental knowledge regarding human visual system and visual models proposed by Watson [1993]. Section II mainly talked about two current types of measures for perceptual quality, including subjective and objective assessments. And two improved measures which take into account the effect of HVS are proposed in this section. In section III, we evaluate the perceptual quality of different images through several simulations using three perceptual measures (PSNR, WPSNR and JND-based). - 1 -Section I - Human Visual System Models Overview - Human Visual system Much work over the years has been done to understand the human visual system as well as using this knowledge for image and video application. A. Just Noticeable Difference Weber’s law [1]The Difference Threshold (or “Just Noticeable Difference”) is the minimum amount by which stimulus intensity must be changed in order to produce a noticeable variation in sensory experience. Ernst Weber, a 19th century experimental psychologist, observed that the size of the difference threshold appeared to be lawfully related to initial stimulus magnitude. This relationship, known since as Weber’s law, can be expressed as: kII=∆ Where delta I represents the difference threshold, I represents the initial stimulus intensity and k signifies that the proportion on the left side of the equation remains constant despite variations in the I term. Weber’s Law, more simply stated, says that the size of the JND (i.e., delta I) is a constant proportion of the original stimulus value. Weber’s Law can be applied to variety of sensory modalities. The size of the Weber fraction varies across modalities but in all cases tends to be a constant within a specific modality. An empirical value of k equals 0.02 for a wide range of luminance. However, nowadays there are better descriptions of JND, and it is clear that the ratio I / I is not constant but depends on the adaptation level, and can be approximated using Weber’s law just at certain adaptation levels. ∆[2]The mapping function proposed by Greg Ward uses a briefly flashing dot on a uniform background Blackwell to establish the relationship between adaptation luminance, Ia, and just noticeable difference in luminance I (I∆a) as: ∆ I (Ia) = 0.0594(1.219 + La0.4)2.5 - 2 -That means that if there is a patch of luminance Ia + ∆Ia on the background of luminance Ia it will be noticeable, but the patch of luminance Ia + ∆I’, where I’ < ∆∆Ia will not. In fact, the minimal perceptible difference depends on the background luminance. This phenomenon is referred to as luminance or contrast sensitivity. To be precise, Weber-Ferwerda’s law states that “if the luminance of a test stimulus is just noticeable from the surrounding luminance, then the ration of the luminance difference to the surrounding luminance is approximately constant”. Thus, the visibility threshold of a noise is larger for bright areas than for dark ones[3]. [4]Most of the early work on perceptually based image coding has utilized the frequency sensitivity of the human visual system. As far as frequency is concerned, JND thresholds are such that changes in a particular frequency band of an image are not noticeable as long as they remain below the threshold of that particular frequency band. To determine these thresholds, extensive psychovisual measurements have been performed on sinusoidal grating with various spatial frequencies and orientations by given viewing conditions. The goal is to determine the contrast thresholds of gratings by the given frequency and orientation. Contrast as a measure of relative variation of luminance for periodic pattern such as a sinusoidal grating is give by the equation as: minmaxminmaxLLLLC+−= Where Lmax and Lmin are maximal and minimal luminance of a grating. Reciprocal values of contrast thresholds express the contrast sensitivity (CS), and the contrast sensitivity as a function of spatial frequency determines the contrast sensitivity function (CSF) defined by the equation: ])114.0([1.1)114.00192.0(6.2)(feffCSF−+= Where f is the spatial frequency in