Illumination-independent descriptors using color moment invariants

Transcription

1 482, February 2009 Illumination-independent descriptors using color moment invariants Bing Li De Xu Beijing Jiaotong University Institute of Computer Science & Engineering Beijing China Weihua Xiong OmniVision Technologies 1341 Orleans Drive Sunnyvale, California Songhe Feng Beijing Jiaotong University Institute of Computer Science & Engineering Beijing China Abstract. Color-based object indexing and matching is attractive because color is an efficient visual cue for characterizing an object. However, different light sources will lead to color deformation of objects, which will inevitably degrade the performance of recognition. In order to circumvent this confounding influence, we present three effective illumination-independent descriptors that are substantially insensitive to the variations of light conditions, object geometric transformation, and image blur level. To this end, we define two new two-dimensional color coordinate systems, the central color coordinate system and the edgebased color coordinate system, based on the diagonal-offset reflectance model. By introducing normalized moment invariants, this paper then provides two color-constant descriptors in each system separately. Either descriptor is a feature vector consisting of several normalized moment invariants of the color pixels distribution with different orders. Furthermore, the combination thereof can characterize not only color content but also color edges in an image, so it serves as a third descriptor of the image. Experiments on real image databases with object recognition and image retrieval show that our descriptors are robust and perform very well under various circumstances Society of Photo- Optical Instrumentation Engineers. DOI: / Subject terms: illumination-independent descriptor; color invariants; color constancy; moment invariant; blur-robust. Paper R received Jul. 26, 2008; revised manuscript received Jan. 5, 2009; accepted for publication Jan. 7, 2009; published online Feb. 19, /2009/$ SPIE 1 Introduction Color has proven to be simple, straightforward tool for object matching, but different light sources can result in different colors of the same object. Consequently, to successfully index objects, the effect of illumination color variation should be canceled out. There are two major approaches: The first one is estimating the illumination characteristics and directly mapping the image into that under a canonical illumination. Although a variety of illumination estimation methods have been proposed in the past decades, 1,2 their performance and generality are not enough for systematic application to recognition among a large number of objects. 3 The second approach is representing images by features that are independent of the light source, so they do not depend on the performance of the color constancy algorithm. A number of techniques belonging to this category have been reported in the literature Swain and Ballard 15 developed an indexing scheme that recognizes the object using color histogram intersections. Although this method is insensitive to geometric transformation, its performance will inevitably degrade when light conditions change. To address this problem, Funt and Finlayson 4 deduced a set of color-constant derivatives based on a physical reflection model. They presented an algorithm, named color-constancy color indexing CCCI, matching histograms of color ratios between neighboring pixels. Gevers and Smeulders 5 extended the CCCI technique to take account of the effect of both illumination color and shading. Adjeroh and Lee 6 proposed another color-ratio-based feature to be calculated by integrating the variation between each pixel and its neighbors. van de Weijer and Schmid 8 introduced the ratio of image derivatives into edge-based color-constant descriptors. Although these methods have been shown to be superior to Swain and Ballard s method in the presence of illumination change, they work along the image edges while ignoring the color content information of the images themselves. When the image is blurred and the edge sharpness is degraded, the derivatives will be easily affected by noise for darker regions, and are close to 0 for blurred or uniform regions. Consequently, these methods are too sensitive to image quality, especially for the blurred images that are frequently encountered due to poor focus, to relative motion between camera and object, and to other causes. Another category of illumination independent descriptors are based on image color information. Healey and Slater 7 gave an object recognition algorithm using highorder color distribution information. Finlayson et al. 9 sorted the pixels in increasing order of their RGB responses and associated them with a rank measure. They further proved that such rank measures are invariant to the illumination change and can be used as descriptors of images for object matching. Muselet et al. 10 discovered that the intersection of ranks so estimated cannot provide satisfactory results; they introduced the concept of fuzzy spatial rank and utilized the histogram of such ranks to characterize the image for object recognition. Based on a blackbody model, Fin

2 layson et al. 11 proposed another descriptor under outdoor illumination for shadow removal. But this method requires strict assumptions about the camera and light sources, and it requires calibrating the camera s parameters, which is inconvenient for practical applications. Moment invariants have also been introduced to get color invariants by Mindru et al. 12 However, they pay attention mainly to image color content, ignoring the contour and edge information in the image. In this paper, we propose two new two-dimensional color coordinate systems derived from a more general diagonal-offset model. One is based on image color content; the other is based on image edge information. In these two systems, two illumination-independent descriptors, represented by feature vectors, are given after introducing the normalized moment invariants. Every descriptor includes several normalized moment variants with different orders, each summarizing the shape of the color distribution of the image. Furthermore, the combination of the two descriptors can characterize not only color content but also color edges in the image. Experiments using several real image databases show that our scheme is robust to illumination, affine transformation, and image blur change and works very well in various situations. The remainder of this paper is organized as follows. In Sec. 2, the diagonal-offset model is described. Then, in Sec. 3, we explain the details of illumination-independent descriptors using color moment invariants. Section 4 discusses the robustness of the proposed descriptors. The experimental results are presented in Sec. 5. Section 6 concludes this paper. 2 Diagonal-Offset Model According to the Lambertian reflectance model, the image f =R,G,B T can be computed as follows: fx = esx,d, 1 where X is the spatial coordinate, is the wavelength, represents the visible spectrum, e is the spectral power distribution of the light source, SX, is the surface reflectance, =R,G,B is the camera sensitivity function of the three responses, and is the shading factor depending on the angle between the normal to a surface patch and the illumination direction. Because the Lambertian model is unrealistic, Shafer 13 proposed to add a diffuse light term to this model. The diffuse light has a lower intensity and comes equally from all directions: 13 fx = esx,d d, 2 + where is the function that models the diffuse light. This equation can model objects under daylight well, since daylight consists of both a point source the sun and diffuse light coming from the sky. So this model is much better for natural images and much more robust than Eq. 1. The aim of many color constancy applications is to transform all colors of the input image f 1, taken under a light source e 1, to colors in an image f 2 as they would appear under a reference light e 2. This transformation can be modeled by a diagonal model called the von Kries model: 1 f 1 = D 1,2 f 2, 3 where D 1,2 is a diagonal matrix. In the R,G,B T color space, the transformation can be written as R R2 = B 0 0 B = e 1 R/e 2 R 0 0 B R2 0 e 1 G/e 2 G e 1 B/e 2 G 1 G 2 2, B 4 where e 1 R,e 1 G,e 1 B, and e 2 R,e 2 G,e 2 B, are the light colors of illumination e 1 and e 2, respectively. However, this diagonal model is too strict. It cannot describe some conditions, for example, saturated colors. To overcome these problems, Finlayson et al. proposed a more robust diagonal-offset model by adding an offset term to the diagonal model: 14 R R2 = o1 + B 0 0 B G 1 G 2 o 2 o 3. Interestingly, the diagonal-offset model also takes diffuse lighting into account, consistently with Eq. 2. Thus the illumination color changes can be considered as comprising scaling combined with an offset for each color band. 3 Illumination-Independent Descriptors Using Moment Invariants 3.1 Two New Color Coordinate Systems (Central and Edge-Based) Here we introduce two novel two-dimensional color coordinate systems, each removing the additional offset term in Eq. 5 through a different method. The first new one, called the central color coordinate or chc, is defined by subtracting from each pixel the average of the image: chc R = R R, chc G = G Ḡ, chc B = B B, 6 where R Ḡ,B is the average pixel value of the whole image in the R G,B channel separately. In order to extract the color intensity information as in Ref. 16, we express it in two dimensions: chc R chc G chc = chc r,chc g =, 7 chc B chc B. Here chcr, chcg are two color components of the central color coordinate chc. G

3 The second new color coordinate system is described after using color derivatives to remove the offset term. We name it the edge-based color coordinate system, or che: che R = dr dx, dg che G = dx, db che B = dx, where d/ dx means first-order spatial differentiation with respect to neighborhoods. Then the two-dimensional che is defined as che R che G che = che r,che g =, 9 che B che B. It is obvious that the two new two-dimensional color coordinate systems still conform well to the diagonal transformation model: chc r 1 chc g 1 = 0 0 chc r 2 chc g 2, che r 1 che g 1 = 0 0 che r 2 che g 2, where =/ and =/. Here chcr 1, chcg 1 and chcr 2, chcg 2 represent the colors in the chc color coordinate system under illumination e 1 and e 2, respectively, and cher 1, cheg 1 and cher 2, cheg 2 represent the corresponding colors in che color coordinate system. 3.2 Normalized Moment Invariant After defining two new color coordinate systems from the diagonal-offset model, we introduce a novel color moment invariant, which is the basis of illumination independent descriptor. The u+v-order color moment M C uv for the image f is defined as follows: M C uv =r u g v pr,gdr dg, 12 where Cchc,che, is the selected color space. We have r,g=chcr,chcg when C=chc, while r,g =cher,cheg when C=che. The density function pr,g is defined as the fraction of each color value in f: pr,g = Numr,g pixnum, 13 where pixnum is the image size of f, while Numr,g is the total number of pixels with value r,g T in the image. According to the Eqs , the relationship between M C uv 1, the color moment in r 1,g 1 under illumination e 1, and M C uv 2, the color moment in r 2,g 2 under illumination e 2, can be obtained as M C uv 1 =r 2 u g 2 v Pr 2,g 2 = u+1 v+1 M C uv 2, where dg 0 dr 14 is the Jacobi determinant. The scale factors, describe the change of lighting color, so they must be removed to get the moment invariants in Eq. 14. Consequently, the normalized moment invariants are defined as C uv = M C 00 u+v+2/2 C. M C 20 u+1/2 M C 02 v+1/2m uv 15 In Eq. 15, all scale factors for each color band in C uv have been normalized, so it stays constant across a change of illumination. 3.3 Implementation of Moment Invariants in Discrete Space All the derivation in the previous subsection is based on continuous space. In this section, we discuss how to implement the moment invariants in discrete color space. The integral is replaced with a sum and dr and dg are discarded. Consequently, the moment M C uv in Eq. 13 is implement as C in discrete color space: DM uv DM uv r max g max C = r u g v pr,g, r=0 g=0 16 where r max and g max represent the maxima r and g in the specific image. The relationship between M C uv 1 and M C uv 2 in Eq. 14 is now changed to a relationship between DM C uv 1 and DM C uv 2 : DM C uv 1 = r 2 u g 2 v Pr 2,g 2 = u v DM C uv So in the discrete color space, DM C 00 =1, and the normalized moment invariants are computed as C uv = C DM uv DM C 20 u/2 DM 02 C v/ Illumination-Independent Descriptor Having obtained the normalized moment invariants, we discuss how to use them to construct an illuminationindependent descriptor of any image. To ameliorate the effect from noise, the descriptor should include as many loworder moment invariants as possible and keep the moment order, u+v, as low as possible. According to these two principles, 10 candidate moment invariants are used to compose the image description vector J C in this paper. Because C 02 = C 20 =1 according to Eq. 18, these two moment invariants are not used in J C :

4 J C = C 01, C 10, C 11, C 12, C 21, C 22, C 03, C 30, C 13, C From different selections of C, this color-constant descriptor framework J C can be decomposed as follows: Image color constant descriptor OJ=J chc. In this case, the central color coordinate system, chc, is used to get moment invariants. This descriptor describes color features of the image. Edge image color constant descriptor EJ=J che. This descriptor is defined on the color coordinate system, i.e., C=che which is about image edge. So J che is an edge-derived descriptor. Combined color constant descriptor CJ=OJ,EJ. Itis composed of the image color constant descriptor OJ and edge image descriptor EJ. This descriptor can describe not only color content but also color edges in the image. 4 Robustness Analysis Various illumination-independent descriptors have been proposed. Evaluating and analyzing them should adhere to the following criteria: Photometric robustness: The descriptor should be independent of the spectral power distribution SPD of the illumination. Normalized moments defined in color space guarantee that our proposed descriptors adhere to this requirement. 2. Geometric robustness: The descriptor should be invariant with respect to geometrical changes, such as zoom, rotation, and affine transformation caused by change of viewpoint. Our descriptors are global descriptors, which come from the color distribution of the whole image. Obviously they are not affected by geometric changes. 3. Photometric stability: The descriptor should adequately handle the instabilities in the imaging process. Blurred images with different levels are most frequently encountered. In this paper, we always assume that image blur is caused by the PSF of the imaging system and ignore any blur due to motion. The central color coordinate system is defined with respect to color information of the image color content, so the presented descriptor using this color coordinate generally has much better robustness. However, the edge-based color coordinate system is based on image derivatives, which may be affected by the image blur level. Is it still robust? The following analysis yields a positive answer. To simulate the PSF of the blurred image, a Gaussian filter G with different standard deviation of is applied; the image fx becomes a blurred one on convolution with the Gaussian filter, fx G. We assume that an edge can be modeled by a step edge 8,17 fx=a I x+b, where A I indicates the amplitude of the step edge for the different channels I. We take R, B channels for instance; their value of cher in the edge-based color coordinate system after blurring is equal to Fig. 1 Examples from the image data set pixels. First row: examples from group A. Second row: examples from group B. che R che r = che B = R X B = X = A A R B X AR x + b G x X AB x + b G x X x G x X x G x = A R x G x A B x G x, 20 where the derivative of a step edge is equal to the delta function, x/x=x. Let us consider the ratio response exactly at the edge 17 x=0. The preceding equation is equivalent to che R che r = che B = R X B = AR x G x X A B x G x = AR G 0 A B G 0 = AR A B. 21 This result clearly shows that both cher and cheg, which are independent of, are robust to Gaussian smoothing. Consequently, the edge-based color coordinate system is robust to blur change. 5 Experiments To evaluate the performance of the proposed descriptors, object recognition and image retrieval experiments based on two image databases are conducted with respect to their robustness to three conditions: light source change, geometric affine transformation, and image instability. Group A consists of 172 images of 17 scenes under 11 different light sources, which are picked out from the 321 images of 30 scenes 2 after removing some darker images. Group B consists of 220 images of 20 scenes under 11 light sources, 18 which have rotation and viewpoint changes. Both of them can be downloaded from Refs. 19 and 20. Figure 1 shows some example images of the two groups. The images in both groups will also be synthetically transformed to simulate affine transformation and different blur levels. 5.1 Experiments on Object Recognition In this subsection, the experiment on the proposed illumination-independent descriptors considers the perfor

5 Table 1 Performance comparison of our proposed descriptors with four other descriptors in terms of robustness to illumination color. Group data set Descriptor RR % k=1 k=3 k=5 k=7 Dimensions Mean RR % A Existing: P p m m Proposed: OJ EJ CJ B Existing: P p m m Proposed: OJ EJ CJ mance under both synthetic transformation and real changes in illumination. Recognition of a pattern is performed by means of a k-nearest-neighbor KNN classification scheme based on feature vectors consisting of moment invariants. The performance is assessed with reference to the recognition ratio RR. Here k means we use the first k matches in the increasing sort of matching distance values. If k is set to 1, the image from the first rank is selected as matching object; otherwise, the most numerously matched object will be selected. In this paper, we set k to 1, 3, 5, and 7. We also compute the average RR for the performance over these four different k values Robustness to illumination color Here we test the image descriptors with respect to robustness to illumination color variations. In the two image groups, since images are taken under 11 light sources, the colors of the same object have large differences as shown in Fig. 1. The images of the same white paper under three light sources appear to be white, blue, and red respectively. The performances of the three proposed descriptors are compared with four other kinds of illumination-invariant descriptors, 4,8,15 which are as follows: P = p 1,p 2,p 3 = R X R, G X G, B X B, 22 m = m 1,m 2 = R XG G X R, G XB B X G, 23 RG BG p = p 1, p 2 =arctan p 1 p 2,arctan p 2 p 3, 24 m =arctan m 1 25 m 2. Histograms of these four descriptors are constructed to represent an image. There are three dimensions for P, two dimensions for m and p, and one dimension for m. Each dimension of each descriptor is divided into 16 equal bins, and uniform quantization is adopted to construct the descriptor vector. The recognition performance is estimated by means of a leave-one-out procedure. 12 The RRs of the proposed descriptors with different values of k are shown in Table Robustness to affine transformation In this experiment, we test the robustness to geometric affine transformation, which is usually encountered for realworld images. To simulate geometric affine transformation, each image pixel s location x,y is changed into x,y, where y=sx+y. That is, the new vertical coordinate is acquired by a shift of sx pixels along the vertical direc

6 Fig. 2 First row: affine transformation examples with different s. Second row: examples using Gaussian blur with different. tion while the horizontal coordinate is kept untouched. The scale factor is chosen from five different values 0.2, 0.4, 0.6, 0.8, 1. Some transformed example images are shown in Fig. 2. For each scale factor s, the transformed images compose the training set, while the original images are used as test ones. That is, we use the transformed images to recognize the original ones based on the OJ, EJ, and CJ descriptors, respectively. The changing performance RR with the selection of different values of k is shown in Fig. 3 and Fig. 4. From these two graphs, we can draw the conclusion that the RR performance of the each descriptor shows nearly no loss with increase of s. The numerical details of the affine transformation are shown in Table 2. The maximum change ranges of OJ, EJ, and CJ are 0%, 5.1%, and 1.2%, respectively, for image group A, and 2.3%, 2.8%, and 3.2%, respectively, for image group B. So OJ, EJ, and CJ are all robust to affine transformation. Fig. 3 The object recognition ratio of image group A as a function of affine transformation

7 Fig. 4 The object recognition ratio of image group B as a function of affine transformation Robustness to Gaussian blur Next we evaluate the performance of the proposed descriptors with respect to changing blur level. To simulate the blur change, Gaussian smoothing with standard deviation is applied to the PSF of the imaging device before processing the images in groups A and B. The value of is selected from 2, 4, 6, 8, 10. Some blurred image examples are shown in Fig. 2. As in the previous experiment, the original images serve as the test set while the blurred images are used as the training set. The performance variations in terms of RR for k=1,3,5,7 are shown in Fig. 5 and Fig. 6 for groups A and B, respectively. They tell us that the performance of OJ, EJ, and CJ always keeps stable as increases. The numerical at results are shown in Table 3. The maximal reductions in performance are only 2.3% for image group A and 5.9% for image group B. Thus, it is seen that the descriptors proposed here are very robust to blur. In Sec. 4, the robustness to blur of descriptor EJ was proved theoretically; the experiment results here confirm this conclusion. Table 2 Object recognition ratio change range. MAX means the maximal change among defined ranges. RR % Group Descriptor k=1 k=3 k=5 k=7 MAX % A OJ 100, 98.8, , , EJ 94.9, 91.4, , , CJ 100, 99.4, 95.3, , B OJ 99.5, 93.1, , , EJ 90.9, , , , CJ 99.0, , , ,

8 Fig. 5 The object recognition ratio of image group A as a function of image blur level. 5.2 Experiments on Image Retrieval In this subsection, we evaluate the performance of three proposed descriptors in an image retrieval task. We use the images from group B, and follow same experiment procedure as proposed in Ref. 8. The performance is assessed and compared by reviewing the rank results of correct matches, which indicate the number of correctly retrieved images. The normalized average rank 8 for a single Fig. 6 The object recognition ratio of image group B as a function of image blur level

9 Table 3 Object recognition ratio change range. MAX means the maximal change among defined ranges. Group Descriptor RR % k=1 k=3 k=5 k=7 MAX % A OJ 97.1, 94.2, , , EJ 99.4, 95.9, , , CJ 100, 99.4, , , B OJ 74.8, , , , EJ 71.7, , , , CJ 84.0, , , , query is defined as NAR = 1 N R R NN R i N RN R +1, 26 i=1 2 where N is the total number of images in the database, the number of images relevant to the candidate is N R, and R i is the rank at which the i th relevant image is retrieved. The smaller NAR is, the better the retrieval result is. Perfect retrieval occurs when NAR=0, and random retrieval results in NAR=0.5. The average NAR result over all queries, ANAR, is also given. We also compare the performance of our proposed descriptors with that of the four descriptors mentioned in Sec The comparison is in two respects: robustness to illumination color change and robustness to natural blurring effects Comparison in robustness to illumination change We compare the descriptors with respect to robustness to illumination color variations. In each of the 20 scenes, the first image is picked out as query image and the remaining ones are used as the image database. Therefore, for each query image, there are 10 relevant images of the same object, but under different light sources and orientations. The results are summarized in Table 4. The descriptor P performs best with ANAR= The performance of our descriptors is comparable to that of the others. In particular, the descriptor CJ has ANAR= 0.011, which outperforms p, m, and m. Although CJ s ANAR is larger than P, the dimensions used in CJ are much less than P, so it is much easier to implement. Table 4 Rank and ANAR for robustness to illumination color. The columns headed 1 10, 11 20, and 20 display the numbers of images in those rank ranges for all queries. indicates that the descriptor is robust to illumination change. The results of other descriptors, marked *, are from Ref. 8. Descriptor No. of images Ranks ANAR Feature dimensions Robustness to illumination P * p * m * m * OJ EJ CJ

10 Fig. 7 Examples in the natural blur image data set: a, b out-of-focus blur; c change in focus from foreground to background Comparison in robustness to real blurring effects In the experiment in Sec. 5.1, we synthetically simulated the natural image blurring effects. In this subsection, a natural image data set with real blurring effects is used. 8,21 This data set includes 20 pairs of images. Each pair consists of two images of the same scene: One is clear; the other is blurred. The blur is caused by changing the acquisition parameters, such as the shutter time and aperture. Figure 7 gives some example images in this data set. As in Ref. 8, the clear image nonblurred in each scene is selected as the query image; the others compose the image database for retrieval. Consequently, for each query there is only one matching image in the database. Table 5 provides the comparison results. All of our descriptors can work well under various blur level, while the descriptors P and m are not robust, as has been reported in Ref. 8. In particular, the combinational descriptor CJ outperforms all other descriptors; its ANAR is smaller by 44.4% than that of the second-best descriptor p. The experiments show that, although the real-world blurring effects are often not well modeled by a predefined Gaussian smoothing, the proposed blur robust descriptor CJ still obtains good results. 6 Conclusion Object recognition is a fundamental task in computer vision, and color can provide valuable clues for it. However, the color of objects will vary with the illumination incident on them. To address this problem, three independent descriptors are presented in this paper. Firstly, two new twodimensional color coordinate systems, the central color coordinate system and the edge-based color coordinate system, are defined, based on the diagonal-offset reflectance model. After introducing moment invariants, we proposed two color-constant descriptors in the new systems. Both descriptors are robust to illumination, affine transformation, and image blur change. In addition, the combina- Table 5 Rank and ANAR for robustness to natural blurring effects. indicates that the descriptor is is not robust to blurring. The results of other descriptors marked * are from Ref. 8. Descriptor No. of images Rank ANAR Feature dimensions Robustness to blurring P * p * m * m * OJ EJ CJ

11 tion of the two descriptors can characterize not only color content but also color edges in an image. Our experiments show that the proposed descriptors provide good performance under changes of illumination, object geometry, and image blur level. Furthermore, the proposed descriptors can be easily applied to other computer vision tasks. Acknowledgments We would like to thank Computational Vision Laboratory of Simon Fraser University for providing the image data set. We also thank Dr. Joost van de Weijer of the LEAR Team, INRIA, for providing the natural-blur data set. This work is supported by the National Natural Science Foundation of China , the National High Technology Research and Development Program of China 2007AA01Z168, and the Science Foundation of Beijing Jiaotong University 2007XM008. References 1. K. Barnard, V. Cardei, and B. V. Funt, A comparison of computational color constancy algorithms part 1: methodology and experiments with synthesized data, IEEE Trans. Image Process. 119, K. Barnard, L. Martin, A. Coath, and B. V. Funt, A comparison of computational color constancy algorithms part 2: experiments with image data, IEEE Trans. Image Process. 119, B. V. Funt, K. Barnard, and L. Martin, Is colour constancy good enough, in 5th Eur. Conf. on Computer Vision (ECCV), pp B. V. Funt and G. D. Finlayson, Color constant color indexing, IEEE Trans. Pattern Anal. Mach. Intell. 175, T. Gevers and A. Smeulders, Color based object recognition, Pattern Recogn. 32, D. A. Adjeroh and M. C. Lee, On ratio-based color indexing, IEEE Trans. Image Process. 1010, G. Healey and D. Slater, Global color constancy: recognition of objects by use of illumination-invariant properties of color distribution, J. Opt. Soc. Am. A 1111, J. van de Weijer and C. Schmid, Blur robust and color constant image description, in 2006 IEEE Int. Conf. on Image Processing (ICIP), pp G. D. Finlayson, S. Hordley, G. Schaefer, and G. Y. Tian, Illuminant and device invariant colour using histogram equalization, Pattern Recogn. 38, D. Muselet, B. Funt, and L. Macaire, Object recognition and pose estimation across illumination change, in 2nd Int. Conf. on Computer Vision Theory and Applications, pp G. D. Finlayson, S. D. Hordley, C. Lu, and M. S. Drew, On the removal of shadows from images, IEEE Trans. Pattern Anal. Mach. Intell. 281, F. Mindru, T. Tuytelaars, L. V. Gool, and T. Moons, Moment invariants for recognition under changing viewpoint and illumination, Comput. Vis. Image Underst. 941, S. Shafer, Using color to separate reflection components, Color Res. Appl. 104, G. Finlayson, S. Hordley, and R. Xu, Convex programming colour constancy with a diagonal-offset model, in 2005 IEEE Int. Conf. on Image Processing (ICIP), pp M. J. Swain and D. H. Ballard, Color indexing, Int. J. Comput. Vis. 71, G. Finlayson, S. Hordley, and P. Hubel, Color by correlation: a simple, unifying framework for color constancy, IEEE Trans. Pattern Anal. Mach. Intell. 2311, J. van de Weijer and C. Schmid, Coloring local feature extraction, in Proc. Eur. Conf. on Computer Vision (ECCV), Part II, pp K. Barnard, L. Martin, B. V. Funt, and A. Coath, A data set for colour research, Color Res. Appl. 273, colour_constancy_synthetic_test_data Bing Li received the BE in computer science from Beijing Jiaotong University in He is pursuing the PhD degree at the Institute of Computer Science and Engineering, Beijing Jiaotong University, Beijing, China. His current research interests include color constancy, visual perception, and computer vision. De Xu received the ME in computer science from Beijing Jiaotong University in He is now a professor at the Institute of Computer Science and Engineering, Beijing Jiaotong University, Beijing, China. He has published more than 100 papers in international conferences and journals. His research interests include database systems, computer vision, and multimedia processing. Weihua Xiong is now an imaging scientist in Omnivision Technologies, USA. He received his PhD from Simon Fraser University in He received his master s degree from Beijing University 1996 and bachelor s degree from Beijing Information University His primary research interests are color science, automatic white balancing, stereo vision and image processing. He has applied for five U.S. patents, and has published eleven papers in international conference, seven papers in journals, and four Chinese books. One of his papers, Stereo Retinex, was named the Best Vision Paper in the 3rd Canadian Conference on Computational and Robot Vision. He is a reviewer for international journals, including and the Journal of Electronic Engineering. He is also a member of the Digital BioColor Society and the Society of Imaging Science and Technology. Songhe Feng received the BE in computer science from Beijing Jiaotong University in He is pursuing the PhD degree at the Institute of Computer Science and Engineering, Beijing Jiaotong University, Beijing, China. His current research interests include image processing, image annotation, and computer vision