Level set method with Retinex‐corrected saliency embedded for image segmentation

IET Image ProcessingVolume 15, Issue 7 p. 1530-1541 ORIGINAL RESEARCH PAPEROpen Access Level set method with Retinex-corrected saliency embedded for image segmentation Dongmei Liu, Dongmei Liu orcid.org/0000-0002-8061-1797 School of Information Science and Engineering, Shandong Normal University, Jinan, China School of Control Science and Engineering, Shandong University, Jinan, ChinaSearch for more papers by this authorFaliang Chang, Corresponding Author Faliang Chang flchang@sdu.edu.cn orcid.org/0000-0003-1276-2267 School of Control Science and Engineering, Shandong University, Jinan, China Correspondence Faliang Chang, School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China. Email: flchang@sdu.edu.cnSearch for more papers by this authorHuaxiang Zhang, Huaxiang Zhang orcid.org/0000-0001-6259-7533 School of Information Science and Engineering, Shandong Normal University, Jinan, ChinaSearch for more papers by this authorLi Liu, Li Liu orcid.org/0000-0002-9121-5124 School of Information Science and Engineering, Shandong Normal University, Jinan, ChinaSearch for more papers by this author Dongmei Liu, Dongmei Liu orcid.org/0000-0002-8061-1797 School of Information Science and Engineering, Shandong Normal University, Jinan, China School of Control Science and Engineering, Shandong University, Jinan, ChinaSearch for more papers by this authorFaliang Chang, Corresponding Author Faliang Chang flchang@sdu.edu.cn orcid.org/0000-0003-1276-2267 School of Control Science and Engineering, Shandong University, Jinan, China Correspondence Faliang Chang, School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China. Email: flchang@sdu.edu.cnSearch for more papers by this authorHuaxiang Zhang, Huaxiang Zhang orcid.org/0000-0001-6259-7533 School of Information Science and Engineering, Shandong Normal University, Jinan, ChinaSearch for more papers by this authorLi Liu, Li Liu orcid.org/0000-0002-9121-5124 School of Information Science and Engineering, Shandong Normal University, Jinan, ChinaSearch for more papers by this author First published: 12 January 2021 https://doi.org/10.1049/ipr2.12123AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract It can be a very challenging task when using level set method segmenting natural images with high intensity inhomogeneity and complex background scenes. A new synthesis level set method for robust image segmentation based on the combination of Retinex-corrected saliency region information and edge information is proposed in this work. First, the Retinex theory is introduced to correct the saliency information extraction. Second, the Retinex-corrected saliency information is embedded into the level set method due to its advantageous quality which makes a foreground object stand out relative to the backgrounds. Combined with the edge information, the boundary of segmentation will be more precise and smooth. Experiments indicate that the proposed segmentation algorithm is efficient, fast, reliable, and robust. 1 INTRODUCTION Image segmentation is a process of decomposing an image into multiple areas, which aims to facilitate the extraction of information and interpretation of image contents. It is a fundamental but important task in image analysis and computer vision applications, e.g. object extraction [1], content-based image retrieval [2] and medical image analysis [3]. Over the past decades, a plethora of methods for image segmentation have been proposed, such as clustering [4], region growing [5] and curve evolution [6]. In recent years, active contour method (ACM) [6-8] has been one of the most extensively applied methods for image segmentation. The basic idea is to evolve a curve to approach object and finally converges to object's edge by minimizing its energy functional. Among energy minimization approaches, the level set method (LSM) [9] has been proved an effective way to handle curve evolution. The existing LSM-based image segmentation models can be categorized into two classes: region-based models and edge-based models. The region-based level set models define a region descriptor (e.g. intensity, colour, texture or motion) to guide the motion of the level set function (LSF) to identify each region of interest. One of the early region-based models is proposed by Mumford and Shah [10] which approximates the image using a smooth function inside each region. Chan–Vese (CV) model [6] is one of the most popular region-based models where the image is approximated using a constant function. Some local fitting models have been proposed later on, such as local binary fitting (LBF) [11], local image fitting (LIF) [12], Markov random field (MRF) embedded [13] etc. Li et al. [11] proposed a region-based ACM (LBF) that draws upon intensity information in local regions at a controllable scale. Zhang et al. [14] presented a level set method for image segmentation with intensity inhomogeneity by exploiting local image region statistics, in which they defined a mapping from the original image domain to another domain so that intensity probability model is more robust to noise while suppressing the intensity overlapping to some extent. Ding et al. [15] presented an active contour model using local pre-fitting energy for fast image segmentation, and the core idea of local pre-fitting energy is to define two pre-fitting functions by computing average image intensities locally before the evolution of curve. The edge-based level set models often use an image gradient to control the motion of the active contours and stop the contour on the desired object's boundaries. Li et al. [16] proposed an distance regularization level set evolution model (DRLSE) to solve the periodical re-initialization problem. Wang et al. [17] introduced an enhanced distance regularized level set evolution completely free of the re-initialization procedure based on analysing these recent regularization models. Liu et al. [18] proposed a weighted edge-based level set method based on multi-local statistical information to better segment synthetic and real images that have added different types and levels of noise. The region-based models usually rely on the statistical information of the image, which are sensitive to the intensity inhomogeneity of the image. The edge-based models depend on the object edge information, which suffer to boundary leakage problem with weak edges. Recently, image saliency detection, which aims at locating important and semantic areas or objects from a complicated circumstance, has been beneficial for computer vision applications including object recognition [19], image and video compression [20], object detection [21], to name a few. In terms of the used models, saliency detection methods can be categorized into two classes: top-down methods (task-driven) and bottom-up methods (stimuli-driven). Top-down models [22, 23] are driven by task, which use prior knowledge to find information relevant to the ongoing tasks or goals. These methods have achieved encouraging performance, but it is expensive to generate pixel-wise training data [24]. By comparison, bottom-up methods [25-34] are more extensively studied and used. These methods are usually triggered by stimulus such as colour, intensity, orientation, shape etc. Saliency information is sensitive to human visual system, and it can be taken into account to yield promising results in image segmentation. In this paper, a new hybrid model for image segmentation which combines the saliency information with the level set segmentation method is proposed. The saliency information of an image is extracted after Retinex-based inhomogeneity correction and embedded into the region-based level set function, and then the evolution of the curve is driven by an improved level set equation combining both region and edge information. The remainder of this paper is summarized as follows. Related works and motivation of the proposed algorithm is presented in Section 2; In Section 3, the Retinex-corrected saliency extraction and the proposed level set method are described in detail. Experimental results and discussions are given in Section 4. The paper is then concluded in Section 5. 2 BACKGROUND AND MOTIVATION In this section, some back ground knowledge of related works are first briefly introduced: the Retinex theory, the saliency detection model, the CV model and DRLSE model. And the motivation of this work is given in Section 2.4. 2.1 Retinex theory The Retinex theory was first proposed by Land and McCann [35]. This theory attempts to explain colour constancy phenomenon of the human visual system and compensates illumination effects in images. It is now widely used in tone mapping [36], image enhancement [37], image segmentation [38] etc. The Retinex theory assumes that an observed image I i n ( x , y ) can be decomposed into an illumination component L ( x , y ) and a reflectance component R ( x , y ) , such that: I in ( x , y ) = L ( x , y ) R ( x , y ) (1) Reflectance describes the nature property of objects, which is considered to be consistent under any lightness conditions. The illumination represents the various lightness on objects. The primary goal of Retinex-based algorithm is to obtain reflectance component R ( x , y ) from observed image, which is an ill-posed problem. Multi-scale Retinex with colour restoration (MSRCR) [39] is one of centre/surround approaches to solve this problem, and it is widely used to achieve simultaneous dynamic range compression, colour consistency and lightness rendition. Mathematically, R msrcr ( x , y ) = C i ( x , y ) ∑ n = 1 N w n { log | I in ( x , y ) | − log | F ( σ n ) ∗ I in ( x , y ) | } (2) C i ( x , y ) = ρ { log [ γ I in ( x , y ) ] − log [ ∑ i = 1 U I in ( x , y ) ] } (3)where N is the number of scales, w n and F ( σ n ) are respectively the weight and Gaussian function associated with the nth scale, and a log operation is applied to simplify the calculation. C i is the ith band of colour restoration function, where ρ is a gain constant, and γ controls the strength of the non-linearity. 2.2 Saliency detection methods Saliency detection aims to locate the important and conspicuous areas or objects of natural scenes. Itti et al. [25] introduced a biologically inspired saliency model by evaluating the contrast of low-level features (colour, orientation of edges and intensity). FT [27] is a frequency-tuned approach of finding salient objects in images using low level features of colour and luminance. Cheng et al. [29] introduced a regional contrast (RC) based salient object detection algorithm, which simultaneously evaluates global contrast differences and spatial weighted coherence scores. Ishikura et al. [31] present a saliency detection technique, which can maintain high detection performance on images containing objects of various sizes and salient sub-objects by using a combination of multiscale perceptual-colour-difference extrema and a measure of global saliency based on directional-rarity and colour-rarity. Wu et al. [34] proposed a novel propagation model via deformed smoothness constraint to deal with the problem that some object regions with low contrast to background will miss during saliency detection. Some saliency detection models [41-43] have been proposed based on deep learning [44]. Li et al. [41] presented a multi-scale cascade network to identify the most visually conspicuous objects in an image. Luo et al. [42] introduced a webly-supervised learning method utilizing large amounts of web data for salient object detection. Figure 1 shows results of some saliency detection models: Itti (IT) model [25], graph-based (GB) model [26], frequency-tuned (FT) model [27], context-aware (CA) model [40], wavelet transform saliency detection (WTS) model [28] and non-subsampled contourlet transform saliency detection (NSCTS) model [30]. The pixels with higher values in bright of these typical results of saliency detection models are salient. FIGURE 1Open in figure viewerPowerPoint The saliency detection results of different models. The first row: original image and its ground truth. The second row: results of different saliency detection models In comparison, the FT method is chosen in this work, because it outputs full resolution saliency maps with well-defined boundaries of salient objects and is simple to implement, which is computationally efficient. 2.3 Traditional level set models for image segmentation The level set method was first introduced by Osher et al. [9] for capturing moving fronts, and it is an effective approach to handle curve evolution. In two-dimension image segmentation, the LSM represents a closed curve C ( t ) = { ( x , y ) | ϕ ( x , y , t ) = 0 } as the zero level set of a level set function (LSF) ϕ ( x , y , t ) in three dimension. The curve moves toward its interior or exterior normal direction and stop at the edge of object. The level set equation (LSE) which defines the evolution function can be written as: ∂ ϕ ∂ t = | ∇ ϕ | F (4)where F is the speed of evolving the curve for solving the differential equation, ∇ is the gradient operator and t is the optimization step. Chan et al. [6] proposed a classic region-based active contour model which used the mean values of different regions to guide contour evolution, and the level set formulation is expressed as follows: E CV = μ ∫ Ω δ ( ϕ ) | ∇ ϕ | d x d y + ν ∫ Ω H ( ϕ ) d x d y + λ 1 ∫ Ω | I ( x , y ) − c 1 | 2 H ( ϕ ) d x d y + λ 2 ∫ Ω | I ( x , y ) − c 2 | 2 ( 1 − H ( ϕ ) ) d x d y (5)where μ ≥ 0 , ν ≥ 0 , λ 1 > 0 , λ 2 > 0 are fixed parameters; the first and second integral items are the length of the curve C and the area of the region inside C respectively; the constants c 1 and c 2 are the averages of image I inside C and outside C respectively; H is the Heaviside function: H ( ϕ ) = 1 , when ϕ ( x , y ) ≥ 0 ; H ( ϕ ) = 0 , when ϕ ( x , y ) < 0 . Li et al. [16, 45] proposed an edge-based level set active contour model with a regularization term, which is used to solve the periodic re-initialization problem, and the energy functional is expressed as follows: E DRLSE = λ ∫ Ω g δ ( ϕ ) | ∇ ϕ | d x d y + α ∫ Ω g H ( − ϕ ) d x d y + β ∫ Ω 1 2 ( | ∇ ϕ | − 1 ) 2 d x d y (6)where g = 1 1 + | ∇ G σ ∗ I | 2 is an edge detector depending on the gradient of the image and G σ is a Gaussian kernel with standard deviation σ. 2.4 Motivation The CV model [6] is a region-based level set model, which is less sensitive to noise and the initial placement of evolving contour, but may not work well for segmenting some images with intensity inhomogeneity. The DRLSE model [16] is an edge-based level set model with a regularization term to avoid periodical re-initialization, but may have problems to segment images in the presence of noise and weak object edges. The human visual system can effectively select important information from complex scenes for further processing. Inspired by this biological capability, visual saliency detection, which can locate important and semantic areas or objects from an complicated circumstance, can be taken into account in image segmentation to yield promising results. Qin et al. [46] combined the region saliency based on entropy rate superpixel with the affinity propagation clustering algorithm, and use random walks method to obtain the segmentation results. Zhi et al. [8] presented a two-stage level set evolution protocol with both saliency map and colour intensity, but this work doesn't consider the problem of intensity inhomogeneity in saliency detection and segmentation. Wang et al. [47] extracted saliency map to determine the initial contour, and the level set function is obtained by computing the local average Renyi entropy and Canny operator. Therefore, motivated by aforementioned works, a synthetical level set model based on the combination of edge information and region information is proposed, wherein the region-based information is constituted by Retinex-corrected saliency information and colour intensity. Saliency information embedded into the energy functional can make the foreground objects more distinct to be segmented, with Retinex corrected, it can also address challenges presented by intensity inhomogeneity. The combination of region information and edge information can make the segmentation insensitive to the initializations, robust and fast. 3 PROPOSED MODEL The overview of the proposed image segmentation model is illustrated in Figure 2. The saliency information of the input image is firstly generated after Retinex inhomogeneity correction. Then the saliency information is embedded into the region-based level set function. The final energy functional contains both region and edge information and the segmentation is guided by minimizing the proposed energy functional. FIGURE 2Open in figure viewerPowerPoint Overview of the proposed image segmentation method As described above, the primary contributions of this method can be summarized as follows: Retinex theory is introduced to correct image inhomogeneity and enhance saliency detection, which shows beneficial effect and promote the performance of the proposed model. The improved saliency information is embedded as the region information of the energy function, which makes the foreground objects more distinct and the segmentation results more reliable. With saliency information embedded, a synthetic level set model based on the combination of region information and edge local information is proposed. Experiments demonstrate its effectiveness and robustness in image segmentation. 3.1 Retinex-corrected saliency detection The FT method proposed by Achanta et al. [27] is employed to extract the saliency information in this work. It can output full resolution saliency maps with well-defined boundaries of salient objects, which is easy to implement and computationally efficient. But it does not work well under the circumstance of the illumination problems such as poor illumination or occurrence of shadow like some other saliency detection models. In addition, intensity inhomogeneity is one of significant challenges to some region-based LSM image segmentation. In this paper, we use Retinex to ameliorate intensity inhomogeneity of the image and to suppress the influence of illumination on saliency detection. The Retinex theory originally dealt with colour constancy, which in human vision ensures that the perceived colours of objects remain relatively constant under varying illumination conditions. The Retinex theory can be used to correct intensity inhomogeneity when illumination is recovered and removed from the image. The saliency detection of this paper consists of the following steps: (1) Convert the input image I in from RGB colour space to CIELAB colour space. (2) Apply MSR method to the L-channel of the input image to estimate and remove the luminance component in this channel, while the colour channels A and B remain unchanged: I = ( R msrcr ( I in L ) , I in A , I in B ) . (3) Calculate the saliency map of the improved image I of step (2) by FT model: S ( x , y ) = | | I m − I ω ( x , y ) | | (7)where I m is the arithmetic mean pixel value of the image I, I ω ( x , y ) is the corresponding image pixel vector value in the Gaussian blurred version (using a 5 × 5 separable binomial kernel, to eliminate fine texture details as well as noise and coding artefacts) of the original image, and ∥ · ∥ is the L 2 norm. Three examples are given to show the effect of Retinex-correction in saliency detection in Figure 3. The saliency maps are converted into heat maps to get a better visual display. The Retinex method enhances the contrast between the salient objects and background, and ameliorate intensity inhomogeneity of the image. In the example of boat, the boat and people on the boat of Figure 3d show higher saliency than that of Figure 3b while the saliency of the object reflection in the water much lower, which is beneficial in the later segmentation process (Figure 7f). In the second example, some texture details around the tiger are eliminated and the contrast of tiger and background is enhanced, meanwhile, the entire tiger is intensity homogeneous. In the third case, the saliency map after Retinex-corrected of the entire object is more homogeneous than that of before Retinex-corrected. With Gaussian filter operation in Retinex, the background noise is also suppressed. The quantitative comparison between saliency detection with and without Retinex-correction is carried out on dataset MSRA1000 [27]. The average accuracy, average recall and F-Measure are shown in Table 1, and it can be seen that the corrected saliency detection shows better performance. TABLE 1. Comparison of average accuracy, average recall and F-Measure before and after Retinex correction Methods Average accuracy Average recall F-measure FT 0.8125 0.6829 0.8211 Retinex+FT 0.8778 0.7553 0.8826 FIGURE 3Open in figure viewerPowerPoint Saliency detection with and without Retinex-correction (a) The original image; (b) The saliency map without Retinex-correction; (c) The CIELAB images after Retinex-correction; (d) The saliency map with Retinex-correction FIGURE 4Open in figure viewerPowerPoint Retinex-correction saliency effects on image segmentation (a) Original images; (b) CV model; (c) SE model; (d) RSE model; (e) RSED model FIGURE 5Open in figure viewerPowerPoint The Dice and HD values for the images shown in Figure 4(a) the Dice values; (b) the HD values FIGURE 6Open in figure viewerPowerPoint Some images and their ground truths of the MSRA1000 dataset, PASCAL-S dataset and DUT-OMRON (a) 10 examples of MSRA1000 dataset; (b) five examples of PASCAL-S dataset; (c) five examples of DUT-OMRON dataset FIGURE 7Open in figure viewerPowerPoint Comparison between the proposed model and other models on MSRA1000 (a) CV model results; (b) LBF model results; (c) DRLSE model results; (d) LPF model results; (e) SDREL model results; (f) RC model results; (g) DSC model results; (h) The proposed RSED model results 3.2 Saliency-embedded region energy In light of the above discussion, we can take the Retinex-corrected saliency information into account to improve segmentation results, which can make an object stand out relative to its neighbours with well-defined boundaries and saliency homogeneity. Thus, under the framework of CV models, the new saliency-embedded region energy arises: E SE = μ ∫ Ω δ ( ϕ ) | ∇ ϕ | d x d y + ν ∫ Ω H ( ϕ ) d x d y + λ 1 ∫ Ω | I ( x , y ) − c 1 | 2 H ( ϕ ) d x d y + λ 2 ∫ Ω | I ( x , y ) − c 2 | 2 ( 1 − H ( ϕ ) ) d x d y + λ 3 ∫ Ω | S ( x , y ) − s 1 | 2 H ( ϕ ) d x d y + λ 4 ∫ Ω | S ( x , y ) − s 2 | 2 ( 1 − H ( ϕ ) ) d x d y (8)where λ 3 , λ 4 > 0 , S is the saliency map generated from Section 3.1, s 1 and s 2 are the averages of saliency map S inside and outside contour C respectively. The further and detailed discussion on the Retinex-correction saliency effect on the level set method is given in Section 4.1. 3.3 Improved LSM The CV model often fails to segment images with intensity inhomogeneity or whose objects have similar colour information with background, and the contour can be trapped in a local minimum. The saliency information corrected by Retinex method is embedded into the level set function to solve these problems, and then combing the edge-based DRLSE model because it has a penalty term to solve the LSF's periodic re-initialization problem, and the segmentation results of this model often have smooth boundaries. The final energy functional is written as follows: E = η E SE + κ E DRLSE = η μ ∫ Ω δ ( ϕ ) | ∇ ϕ | d x d y + ν ∫ Ω H ( ϕ ) d x d y + λ 1 ∫ Ω | I ( x , y ) − c 1 | 2 H ( ϕ ) d x d y + λ 2 ∫ Ω | I ( x , y ) − c 2 | 2 ( 1 − H ( ϕ ) ) d x d y + λ 3 ∫ Ω | S ( x , y ) − s 1 | 2 H ( ϕ ) d x d y + λ 4 ∫ Ω | S ( x , y ) − s 2 | 2 ( 1 − H ( ϕ ) ) d x d y + κ λ ∫ Ω g δ ( ϕ ) | ∇ ϕ | d x d y + α ∫ Ω g H ( − ϕ ) d x d y + β ∫ Ω 1 2 ( | ∇ ϕ | − 1 ) 2 d x d y (9)where H is the Heaviside function, and it is usually replaced by its smooth approximation function: H ε ( z ) = 1 2 1 + 2 π arctan z ε , ε → 0 (10) The minimization of the energy functional is an unconstrained optimization problem, so it can be minimized with respect to the fitting variables c 1 , c 2 , s 1 , s 2 and ϕ, and the steepest descent method is used to minimize them. Keeping ϕ fixed and minimizing the energy functional with respect to c 1 , c 2 , s 1 and s 2 , we can obtain: c 1 = ∫ Ω I ( x , y ) H ε ( ϕ ) d x d y ∫ Ω H ε ( ϕ ) d x d y , (11) s 1 = ∫ Ω S ( x , y ) H ε ( ϕ ) d x d y ∫ Ω H ε ( ϕ ) d x d y , (12)if ∫ Ω H ε ( ϕ ) ) d x d d y > 0 , i.e. the curve C has a non-empty interior in Ω, and c 2 = ∫ Ω I ( x , y ) ( 1 − H ε ( ϕ ) ) d x d y ∫ Ω ( 1 − H ε ( ϕ ) ) d x d y , (13) s 2 = ∫ Ω S ( x , y ) ( 1 − H ε ( ϕ ) ) d x d y ∫ Ω ( 1 − H ε ( ϕ ) ) d x d d y , (14)if ∫ Ω ( 1 − H ε ( ϕ ) ) d x d y > 0 , i.e. the curve C has a nonempty exterior in Ω. Keeping c 1 , c 2 , s 1 and s 2 fixed, and minimizing the energy functional with respect to ϕ. According to the Euler–Lagrange equation ∂ ϕ / ∂ t = 0 , The evolution equation of level set function ϕ is computed as follows: ∂ ϕ ∂ t = − ∂ E ∂ ϕ = η δ ε ( ϕ ) μ div ∇ ϕ | ∇ ϕ | − ν − λ 1 ( I − c 1 ) 2 + λ 2 ( I − c 2 ) 2 − λ 3 ( S − s 1 ) 2 + λ 4 ( S − s 2 ) 2 ∇ ϕ | ∇ ϕ | + κ { λ δ ε ( ϕ ) div g ∇ ϕ | ∇ ϕ | + α g δ ε ( ϕ ) + β Δ ϕ + div ∇ ϕ | ∇ ϕ | } (15)where δ ε is a smooth Dirac function that is the derivative of H ε : δ ε ( z ) = H ε ′ ( z ) = ε ( ε 2 + z 2 ) π (16) 4 EXPERIMENTAL RESULTS In this section, we implemented some experiments to evaluate the proposed Retinex-corrected saliency embedded level set image segmentation method. The experiments are implemented using the MATLAB R2018a on a personal computer, with CPU 2.59 GHz Intel Core-i7, 16 GB RAM, and Windows 10 operating system. 4.1 Effects of Retinex-correction saliency on image segmentation Saliency information is embedded into the proposed level set segmentation model, which is intensity inhomogeneity corrected by Retinex method in advance (shown in Figure 3). With these operations, this model is expected to acquire better segmentation results. In order to demonstrate this, the following experiment is designed. By setting different parameters of Equation (9) and different inputs, we can obtain different level set active contour models. In particular, when η = 1 , κ = 0 , λ 1 ≠ 0 , λ 2 ≠ 0 , λ 3 = 0 , λ 4 = 0 , it becomes traditional CV model; when η = 0 , κ = 1 , it becomes traditional DRLSE model. The specific parameters are carefully chosen and are given in Table 2. The second column lists the inputs of each model, where "img" refers to the original image, "sm" refers to the saliency map obtained by ref. [27] and "Rsm" refers to the Retinex-corrected saliency map. The Δ t of all models are set to 0.1 and a checkerboard shape is defined to initialize all level set functions: ϕ 0 ( x , y ) = sin π × H × x 1500 sin π × W × y 1500 (17)where H and W are respectively the height and width of input image. TABLE 2. Parameters setting of Equation (9) Models Input λ 1 λ 2 λ 3 λ 4 η κ CV img 0.01 0.01 N/A N/A 1 N/A SE img+sm 0.01 0.01 0.06 0.06 1 N/A RSE img+Rsm 0.01 0.01 0.06 0.06 1 N/A RSED img+Rsm 0.01 0.01 0.06 0.06 0.1 0.9 Figure 4 shows the segmentation results obtained from using the CV model and the proposed SE model, RSE model and RSED model. Figure 4a are the input images from MSRA1000 [27], Figure 4b–e are the segmentation results of these models respectively. The first image contains a tomato illuminated by sidelight, which has high intensity inhomogeneity. In this case, the CV model cannot handle very well high intensity variation; the SE (saliency-embedded) model also shows poor performance in segmenting tomato, because the saliency map without Retinex-correction is in