Development and evaluation of perceptually adapted colour gradients

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/236131515 Development and Evaluation of Perceptually Adapted Color Gradients ArticleinImage Processing, IET · June 2013 DOI: 10.1049/iet-ipr.2012.0085 CITATIONS 15 READS 95 4 authors, including: Some of the authors of this publication are also working on these related projects: Computer assisted surgery View project Aurora Sáez Universidad de Sevilla 32 PUBLICATIONS245 CITATIONS SEE PROFILE Begoña Acha Universidad de Sevilla 90 PUBLICATIONS1,170 CITATIONS SEE PROFILE Carmen Serrano Universidad de Sevilla 105 PUBLICATIONS1,357 CITATIONS SEE PROFILE All content following this page was uploaded by Begoña Acha on 31 May 2014. The user has requested enhancement of the downloaded file. Development and evaluation of perceptually adapted color gradients for color edge detection Aurora S´aez, Carlos S. Mendoza, Bego˜na Acha, Carmen Serrano Abstract Although several color edge detectors have been proposed, most of them utilized Euclidean color distances in different color spaces to measure color differences. In this paper a set of color gradients based on color visual perception is proposed. These color gradients are designed in uniform color spaces and use perceptual color difference equations. In order to be able to study the gradients performance, they have been applied in a variational level set formulation. A comparative study has been performed. A set of synthetic images, generated for this purpose, has allowed carrying out an extensive evaluation. Both quantitative and qualitative measures are used. It can be conclude that detectors based on CIE94 color difference equation are the best regarding to the correlation with color visual perception. Our main contributions are: the derivation of perceptual color gradients, the design of a perceptual evaluation with a specific synthetic dataset and the comparison between detectors based on different color differences. Keywords: perceptual color gradients, perceptual evaluation, color difference equations 1. Introduction Edge detection is one of the fundamental operations in computer vision. Edges correspond to abrupt discontinuities in physical quantities such as gray-level, color, texture or motion. In order to analyze an image, the human visual system detects changes in it, that is, discontinuities. Nowadays, the majority of the image processing tasks are developed for color images. The advantage of color edge detection schemes over grayscale approaches is easily demonstrated by considering the fact that those edges that exist at the boundary between regions of different colors cannot be detected in grayscale Preprint submitted to Elsevier July 1, 2011 images if there is no change in intensity [1]. The color edge detectors can be classified into two groups: those techniques extended from grayscale edge detectors which apply the detection method in each color plane and combining the results, and those techniques that take into account the vector nature of the color images [2]. Several color edge detectors preserving this vector nature have been proposed [2] but none of them take into account recent advances in measuring perceptual color differences. Different algorithms that extend the concept of derivative operator to three-color-component pixels have been developed in the literature. One of simplest approximations consists in generalizing the operators based on the first derivative, e.g. Sobel, commonly applied in the grayscale images into the multidimensional case. Wesolkowski compared several edge detectors in multiple color spaces, and he drew the conclusion that the performance of Sobel operator is superior to others [3]. This is the reason why Sobel operator is chosen in this paper. As results correlated with perceptual color differences are intended, RGB space is avoided because it is not a perceptually uniform color space. Instead, we make use of a perceptual uniform color space (CIE L∗a∗b∗) and the CIELAB, CIE94 and CIEDE2000 color difference equations [4],[5]. A comparative study between these gradients is carried out. To evaluate the performance of them, a variational Level Set technique where these color gradients control external energies is developed. As the aim is to measure how the detectors are correlated with the human visual perception, an extensive evaluation is performed. A database formed by 96 images has been generated and both quantitative and qualitative measures are used to test the correlation between the detector output and the visually perceived color difference. Other authors have approached to the field of perceptual color edge detectors. However, in their work, there is lack of a thourogh evaluation[6], [7], [8]. The rest of the paper is organized as follows: Section 2 summarizes the color gradients proposed. The variational Level Set technique implemented to evaluate the color gradients is introduced briefly in Section 3. In Section 4 the complete developed method is exposed. The experimental results are explained in Section 5. Some conclusions are presented in Section 6. 2 2. Color gradients In this paper several perceptual color gradients are proposed and compared. These color gradients are developed in a uniform color space and preserve the vector nature of the color images in that space. 2.1. Perceptual Uniform Color Space and Color Difference Equations In 1976, International Commission on Illumination (CIE) standardized L∗a∗b∗space as perceptually uniform [9]. A color space is perceptually uniform if perceptual color differences can be measured with Euclidean distances in this space. The three coordinates of L∗a∗b∗represent the lightness of the color (L∗), its position between red/magenta and green (a∗) and its position between yellow and blue (b∗). It can also be expressed in terms of cylindrical coordinates with the perceived lightness L∗, the chroma C∗ ab and the hue h∗ ab, defined in (1) and (2) respectively. Cab ∗=pa∗2+b∗2(1) hab =arctan b∗2 a∗2(2) CIELAB color difference, also known as ∆E∗ ab, is calculated using (3). ∆E∗ ab =p∆L∗2+ ∆a∗2+ ∆b∗2(3) where ∆L∗=L∗ 1−L∗ 2(∆a∗and ∆b∗are defined in the same manner for coordinates a∗and b∗). However, subsequent experiments demonstrated that Euclidean distance ∆E∗ ab is not an accurate measure of perceived color difference between two stimuli. To correct the problem a new difference formula was recommended by CIE [4] in 1994. ∆E94 ∗=s∆L∗ kLSL2 +∆C∗ ab kCSC2 +∆H∗ ab kHSH2 (4) SL= 1,(5) SC= 1 + 0.045 C∗ ab ,(6) 3 SH= 1 + 0.015 C∗ ab .(7) The factors kL,kCand kH, are included to match the perception of the background conditions. Later, CIEDE2000 was developed to correct defficiencies of previous color difference equations [10]. Its accuracy to predict small perceived color differences have been demonstrated [11] ∆E00 =s∆L0 KLSL2 +∆C0 KCSC2 +∆H0 KHSH2 +RT∆C0 KCRC ∆H0 KHSH (8) where ∆C0and ∆H0are defined in [5]. 2.2. Proposed color gradients In color gradients, the vector nature of color is preserved throughout the computation. Color images are viewed as a two-dimensional three channel vector field. Each channel in this vector is characterized by a discrete integer function f(x, y). The value of this function at each point is defined by a three dimensional vector in a given color space [2]. Therefore, a pixel is defined as in (9). f(x, y) =   C1(x, y) C2(x, y) C3(x, y) (9) where Ci(x, y) represents the value of the pixel in the i-th color plane (i= 1,2,3), and (x, y) refers to the spatial dimensions in the 2-D plane. The operator based on the firs derivative, commonly applied in the grayscale imaging, is generalized into multidimensional case in [2]. Plataniotis extends the Sobel operator, with the horizontal and vertical masks shown in (10), by constructing the vectors: H+=f7+ 2f3+f8,H−=f9+ 2f2+f6, V+=f6+ 2f4+f8,V−=f9+ 2f5+f7, according to the notation used in Figure 1. They calculate the color vector gradient as H+−H−and V+−V−, respectively. In order to estimate the color variation in the vertical and horizontal directions, the following scalars are calculated: kH+−H−k ,kV+−V−k. The magnitude Bof the maximun variation is estimated as: 4 B=pkH+−H−k2+kV+−V−k2. f9f5f7 f2f1f3 f6f4f8 Figure 1: Sliding window X1=  −1 0 1 −2 0 2 −1 0 1  , X2=  −1−2−1 000 121 (10) In this paper, we propose calculating the gradient along xand ydirection as shown (11) and (12). Gx= ∆EH+,H−(11) Gy= ∆EV+,V−(12) where ∆Edenotes the color difference between two vectors. Then, the gradient magnitude can be computed as shown in (13). G=qG2 x+G2 y(13) In this paper three color gradients are studied, each one of them is obtained by applying: •f(x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Edetermined by Euclidean distance (CIELAB). •f(x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Edetermined by CIE94 color difference equation. •f(x, y) = [L∗(x, y), a∗(x, y), b∗(x, y)] and ∆Edetermined by CIEDE2000 color difference equation. 5 3. Variational level set Once a color gradient is estimated, the simplest edge detector is obtained by thresholding this gradient. In the three proposed color gradient estimators, the dynamic range of the color gradient differs between the three color difference measures. This implies that a different threshold should be chosen to detect edges with the different gradient estimators and the quality of edges detected from each gradient estimator depends strongly on the choice of this threshold. Therefore, in order to make the comparison between the three gradient estimators independent from this choice, a level set formulation has been applied. Level set methods [12] have been widely used as global approaches towards the optimization of active contours for the segmentation of objects of interest from the background. In these methods, in each time tedges are considered to be in the zero-level of a scalar function φ(t), called level-set function. The challenge of a level-set algorithm is to make φevolve along tso that its zero level converge at the real boundaries in the image. The general level set equation is presented in (14), ∂φ ∂t +F|∇φ|= 0 (14) where Frepresents the speed function. One of the main challenges in the employment of level set techniques is to overcome the generation of shocks in φ, very sharp or flat shape during the evolution, which can result in less than accurate contours. Many authors avoid this problem by re-initializing the function φto a signed function periodically. In this paper, this problem is overcome with the method developed by Li et al [13]. In the reported work, a new term is introduced into (14) to maintain the level set function near the signed distance function, thus avoiding the need for re-initialization of the level set function. It has been shown that the resulting expression is the following gradient flow: ∂φ ∂t =µ∆φ−div ∇φ |∇φ|+λδ(φ)div g∇φ |∇φ|+νgδ(φ) (15) where µdetermines the deviation of φfrom a signed distance function, λand νare the coefficients of the weighted length of the zero level curve and of the 6 weighted area inside the zero level curve respectively, and tis the time step of the experiment. The second and the third term in the right hand side of (15) are responsible of driving the zero level curve towards the object boundaries. gis the edge indicator function, usually defined as: g=1 1 + |∇Gσ∗I|2(16) where Gσis the Gaussian kernel with standard deviation σand Iis the test image. In the proposed method, the edge indication function ghas been modified to: g=1 1 + |V D(diff{I})|2(17) where diff is an anisotropic diffusion filter and V D are the proposed color gradients that are applied to the diffused image. Therefore, modifying the edge indicator function includes two aspects: •The Gaussian filter smothing is substituted by an color anisotropic diffusion filter [15]. Both smoothing were tested but the color anisotropic diffusion filter obtained better results according experiments. •Gradients the diffused image are computed with the three proposed color gradients approaches explained in Section 2. 4. Methodology The data flow diagram in Figure 2 gives an overview of the main steps of the perceptual color detectors based on proposed color gradients. a. Uniform color space transform. The RGB image is transform in to the uniform color space CIE L∗a∗b∗, previously described. b. Anisotropic diffusion filtering. In the anisotropic diffusion [14] a withinregion smoothing is largely performed without blurring between-region boundaries. In this paper an extension of the method to color image is implemented [15], where a separate anisotropic diffusion of chromatic 7 Figure 2: Proposed system and achromatic channels is performed. This way finds its rationale in the models of color vision: the human visual system senses color information through photoreceptors which can be regarded as three sets of filters tuned to the wavelengths of red, green and blue; this information is then split into chromatic (2-D) and achromatic (1 -D) channels before being further and independently processed. Neurophysiological evidence shows that there exists a perfect agreement between the second Human Visual System processing stage and the opponent-colors theory based on the three antagonistic mechanisms red-green, blue-yellow and black-white. These stimuli can also be conveniently expressed in terms of hue, saturation and lightness. Hue and saturation are processed together using the formalism of phasors: hue is the phase and saturation is the magnitude of a complex function defined as the complex chromaticity. The scalar achromatic information represented by lightness is separately diffused. c. Perceptual color gradients computation. The proposed color gradients explained in Section 2 are computed from diffused image. d. Level set technique. The level set formulation explained in Section 3 is applied with the edge indicator function as: g=1 1 + |V D(diff{I})|2(18) 8 (a) (b) (c) (d) Figure 7: a) Test image. b) Output of detector based on CIELAB. c) Output of detector based on CIE94. d) Output of detector based on CIEDE2000. 6. Conclusions In this paper three different perceptually adapted color gradients have been proposed. These gradients have been integrated in a level-set framework to color edge detection. This color edge detection algorithm is used to evaluate the three color gradients with two evaluation tests: a subjective test and a quantitative evaluation measure. To this purpose, a synthetic image database following CIE guidelines for coordinated research on color difference evaluation [17] has been developed. The edge detector using the color gradient based on CIE94 resulted the best both according to the subjective test and the perceived quantitative measure (perceived FP ratt). An additional advantage of CIE94 color difference equation is its low computational cost when compared to CIEDE2000 difference equation. 15 References [1] A.N. Evans, X.U. Liu, A morphological gradient approach, IEEE Transaction on Image Processing, 15(6) (2006) 1454-1563. [2] K.N. Plataniotis, A.N. Venetsanopoulos, Color Image Processing and Applications, Springer-Verlag, Berlin, 2000. [3] S. Wesolkowski, M.E. Jernigan, R.D. 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