An adaptive Bilateral Filter for Predicting Color Image Difference

Color image difference metrics are of great importance in the field of color image reproduction. In this study, we introduce an adaptive bilateral filter for predicting color image difference. This filter is simple, employing two Gaussian smoothing filters in different domains, which avoids the loss of edge information when smoothing the image. However, the challenge is to select appropriate parameters to result in a better performance when applying for color image deference prediction. We propose a method to optimize the parameters, which are designed to be adaptive to the corresponding viewing conditions, and the quantity and homogeneity of information contained in an image. We have conducted psychophysical experiments to evaluate the performance of our approach. The experimental sample images are reproduced with variations in six image attributes: Lightness, Chroma, Hue, Compression, Noise, and Sharpness. The Pearson’s correlation value between the predicted difference and the z-score of visual judgments was employed to evaluate the performance and compare it with that of s-CIELAB and iCAM. Background Theories of spatial characterization of the human visual system are of much current interest in the development of image difference metrics [1-4]. They all involve the conception that the human visual system is optimally designed to process the spatial information in images or complex scenes. The study [5] of the human visual system has shown that the human visual system is composed of spatial frequency channels. The light sensors of the human visual system, cones and rods, are sensitive to the spatial changes of stimuli. Both contrast sensitivity and color appearance vary as a function of the spatial pattern [6, 7]. Attempts to computationally assess color image difference have typically created models of human perception suitable for determining the discriminations introduced by spatial alteration, such as image compression, halftone reproduction, etc. On the other hand, the successful applications of color difference formulae, such as CIELAB 1976 color difference, CIE94, and CIEDE2000, have encouraged researchers to apply them also to image difference evaluation. An important motivation of our work is the development of an image difference metric on various image reproduction tasks. Image difference may originate due to different image reproduction methods, such as the discriminations from chromatic and spatial modifications. Several studies [8-12] have measured the discriminations introduced by chromatic changes of the images alone. In this work, we study the general statistics over both spatial and chromatic image reproductions. Spatial filtering was introduced into the color difference formula for measuring image reproduction errors, and later, replaced with the simulator of the human contrast sensitivity functions (CSFs) [2, 13, 14]. There are many models developed for simulating the CSFs. The model developed by Movshon and Kiorpes [15] was suggested [2] and also adopted by the CIE TC802 [16]. Generally, the spatial filters (or CSF models) are applied in the opponent color space to deduct the high frequency components in an image. The decrease in sensitivity at higher frequencies has been attributed to blurring because of the optical limitation of the eye and spatial summation in the human visual system [17]. Thus, a blurrier image is the output, in which the imperceptible information is attenuated, including, inevitably, high frequency edges. There is a broad consensus, however, that the human visual system is particularly sensitive to the edges in an image. Edge detection is believed to be necessary to distinguish objects from their background, and establish their shape and position. It has been proved to be a crucial early step in the process of scene analysis by the human visual system. To overcome the undesirable loss of edges whilst using the spatial filter, recent studies [3, 18] employed edge enhancement in the workflow for spatial localization. Many image processing methods have been developed to smooth the image and keep the edges. Recently, Tomasi and Manduchi [19] described an alternative bilateral filter which extended the concept of Gaussian smoothing by weighting the filter coefficients with their corresponding relative pixel intensities. Two Gaussian filters are applied at a localized pixel neighborhood, one in the spatial domain (domain filter) and the other in the intensity domain (range filter). The result is a blurrier image than the original while preserving edges. However, the behavior of this filter is governed by a number of parameters which need to be selected with care for color image difference evaluation. In this paper, we propose an adaptive bilateral filter for color image difference evaluation and design the parameters based on the spatial frequency and the quantity and the homogeneity of the information contained in a certain image. We describe a psychophysical experiment to validate its performance and compare it with other two models, sCIELAB and iCAM, which are both recognized as the human visual system based models. The testing images are reproduced in terms of both spatial and chromatic attributes. The evaluation is based on the Pearson’s correlation value between the visual psychophysical judgments and the predicted difference. Adaptive Bilateral Filter The idea behind the bilateral filter is to combine domain and range filters together. Pixels in the neighborhood which are geometrically closer and photometrically more similar to the filtering centre will be weighted more. Given a color image f(x), the bilateral filter [19] can be expressed as: ξ ξ ξ ξ d x f f s x c f x k x h )) ( ), ( ( ) , ( ) ( ) ( ) ( 1 ∫ ∫ ∞