Multispectral image fusion for improved RGB representation based on perceptual attributes

Transcription

1 International Journal of Remote Sensing Vol. 26, No. 15, 10 August 2005, Multispectral image fusion for improved RGB representation based on perceptual attributes V. TSAGARIS and V. ANASTASSOPOULOS Electronics and Computers Division, Physics Department, University of Patras, Patras 26500, Greece; (Received 15 October 2003; in final form 17 February 2005 ) A pixel-level fusion technique for RGB representation of multispectral images is proposed. The technique results in highly correlated RGB components, a fact which occurs in natural colour images and is strictly related to the colour perception attributes of the human eye. Accordingly, specific properties for the covariance matrix of the final RGB image are demanded. Mutual information is employed as an objective criterion for quality refinement. The method provides dimensionality reduction, while the resulting RGB colour image is perceptually of high quality. Comparisons with existing techniques are carried out using both subjective and objective measures. 1. Introduction Various approaches can be found in the literature for pixel-level fusion (Pohl and Van Genderen 1998). Fusion at pixel-level means processing at the raw-data level, as shown in figure 1. The great variety of image fusion methods can be justified by the complexity of the problem, the different types of data involved and the different aims of each application. Fusion can be employed to provide improved visual interpretation, by means of combining different spectral characteristics or image modalities. This is desirable in various applications, such as medical imaging and remote sensing. Pixel-level fusion techniques can also be used to improve the efficiency of classification and detection algorithms. In general, pixel-level fusion methods can be classified into linear methods (Achalakul and Taylor 2001), nonlinear methods (Matsopoulos et al. 1994, Matsopoulos and Marshall 1995, Mukhopadhyay and Chanda 2001), optimization techniques (Solberg et al. 1996), neural networks (Zhang et al. 2001, Shkvarko et al. 2001) and image pyramids (Liu et al. 2001). The proposed fusion method can be categorized into linear ones. The core idea of this method is to yield a final colour image with maximum information from the dataset and enhanced visual features compared with the source multispectral bands. This is achieved by transforming the multispectral data into the 3D RGB space, by means of preserving the basic correlation properties of the RGB components existing in natural colour images. For this purpose the key attributes of human colour perception along with the main properties of natural colour images are presented. These concepts are incorporated into the proposed method by imposing specific restrictions on the covariance matrix of the final colour image. Simultaneously, the non-diagonal terms of this matrix are adjusted for achieving maximum mutual information between the original multispectral bands and the International Journal of Remote Sensing ISSN print/issn online # 2005 Taylor & Francis DOI: /

2 3242 V. Tsagaris and V. Anastassopoulos Figure 1. Information fusion can be carried out in different processing levels: (a) raw data fusion, (b) feature fusion and (c) decision fusion. final RGB image. Cholesky decomposition is employed to derive the transformation of the source multispectral data into the RGB space. The colour image resulting by fusing the source multispectral bands is suitable to be displayed in any RGB device and no additional transformation is needed (Rast et al. 1991, Pohl and Van Genderen 1998, Achalakul and Taylor 2001, Tyo et al. 2003). The paper is organized as follows. Section 2 provides background material on human colour perception and the RGB colour space. Section 3 discusses principal component analysis and introduces the key concept of the proposed fusion technique. The multispectral dataset used in this work is described in 4. Experimental results as well as subjective and objective performance evaluation of the proposed fusion technique are presented in the same section. Finally, the conclusions are drawn in Human colour perception and the RGB colour space 2.1 Colour perception Colour is a rich and complex experience, usually caused by the vision system responding differently to different wavelengths of light. The study of colour is essential in the design and development of colour vision devices. The use of colour in image displays is not only pleasant for the human eye, but it also enables the user to perceive more information. The human eye can perceive only a few dozen grey levels, yet it has the ability to distinguish between thousands of colours. There are two main types of receptor in the retina, called rods and cones. Colour perception is based on the activity of cones. Studies of the genetics of colour vision support the idea that there are three types of cones, called S cones, M cones and L cones (with peak sensitivity at short, medium and long wavelength, respectively). They are occasionally called blue, green and red cones, but this nomenclature is misleading because the sensation of red is not caused by the stimulation of red cones only. The first two receptors have peak sensitivities at quite similar wavelengths. The third receptor, the S cone, has a different peak sensitivity. The response of a receptor to incoming light can be obtained by summing the product of the sensitivity and the

3 Multispectral image fusion based on perceptual attributes 3243 spectral radiance of the light over all the wavelengths that correspond in the visible region of the electromagnetic spectrum. 2.2 The RGB colour space Various colour spaces have been standardized for different practical reasons, namely RGB, YIQ, HSV, Lab, etc. The RGB colour space is the dominant colour space and the most frequently used in colour cameras, scanners, displays, etc. Its advantages are its simplicity as well as the fact that other colour representations have to be transformed to RGB in order to be displayed on a colour monitor. The single wavelength primaries used in the RGB colour space are nm for red, nm for green and nm for blue. The colour matching functions for the primaries of the RGB system are depicted in figure 2. The negative values mean that subtractive matching is required to match colour lights at the same wavelength with the RGB primaries. On the other hand, the RGB colour matching functions present similarities to the raw L, M and S responses of the cones. One of the properties that characterize the RGB space in applications involving a natural colour image is the high degree of correlation between its components. The term high correlation means that if the intensity changes, all three components will change accordingly. This is a consequence of the overlapping sensitivity curves of the different types of cone in the human eye (Forsyth and Ponce 2002 p. 105), as well as the colour matching functions for the primary colours of the RGB system given in figure 2. This high correlation is studied in this paper using the two-dimensional correlation coefficient r, given by: P P A mn {A Bmn {B m n r~ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P 2 P P ð1þ 2 A mn {A B mn {B m n m n Figure 2. Colour matching functions for the primaries of the RGB system (Data obtained from the Colour & Vision Research Laboratories, University College London, UK, wwwcvrl.ucsd.edu).

4 3244 V. Tsagaris and V. Anastassopoulos where A is the mean of A and B is the mean of B and A,B can be any two components of the multispectral entity. The values of the correlation coefficient satisfy the relation 21(r( Correlation properties in natural colour images The correlation properties of natural colour images were examined by means of the Imagine Macmillan database (Macmillan Technical Publishing, which consists of a great variety of images covering several themes. In this work a set of 100 images is used and the images are categorized subjectively according to their variety of colour. The selected scenes were those displaying perceptually rich information content. The first category consists of images with rich colour. By the term rich colour, natural colour images with a great variety of colours and hues are described. The other three categories are formed by images with one of the primary colours dominant. For example, a jet ski in the sea is an image where the blue colour is dominant. The statistical results for the entire set, consisting of 25 images in each category, can be found in table 1. The evaluation of the correlation matrix is based on equation (1). The degree of correlation is high (higher than 0.6) for all pairs of colour components and all types of image. The selection of the correlation coefficients was based on their mean value, which is a sufficient estimator since the corresponding variance is quite small. 3. Linear pixel-level fusion techniques In the context of colour image fusion of multispectral data, most of the linear methods employ principal components analysis (PCA) (Rast et al. 1991, Achalakul and Taylor 2001, Tyo et al. 2003). The main drawback of these methods is that the principal components cannot be used to produce an RGB image without an additional transformation. This transformation is used to convert the pixels values from an appropriate chosen colour space (e.g. IHS, HSV) to RGB values. In this section the basic properties of the PCA are presented. On the other hand, the core idea of the proposed transformation originates from PCA but the correlation properties among the RGB components of the obtained fused image are similar to those of natural colour images and, thus, no additional transformation for RGB representation is necessary. In this way the dimensionality of the multispectral vector space is reduced because only three components are used to represent the information contained in the multispectral image set. 3.1 Multidimensional image representation and dimensionality reduction The statistical properties of a multispectral entity with MN pixels per channel and K different channels can be studied if each pixel is described by a vector whose components are the individual spectral responses to each multispectral channel: Table 1. Correlation coefficient for natural colour images. Corr(R, G) Corr(R, B) Corr(G, B) Mean Variance

5 Multispectral image fusion based on perceptual attributes x 1 x 2 x~ ð2þ with mean vector given by m x ~Efxg~ 1 MN x i. The dimensionality of the mean i~1 value m x is K, with its components corresponding to the mean value of each multispectral channel. While the mean vector is used to define the average or expected position of the pixels in the vector space, the covariance matrix describes their scatter x K PMN C x ~ 1 X MN x i x T i {m x m T x MN i~1 ð3þ The covariance matrix can be used to quantify the correlation between the multispectral bands. In the case of a high degree of correlation the corresponding off-diagonal elements in the covariance matrix will be large. The diagonal elements of the covariance matrix are the variances of the multispectral components. The correlation between the different multispectral components can also be described by means of the correlation coefficient given by equation (1). The correlation coefficient r is related to the corresponding covariance matrix element, since it is the covariance matrix element divided by the standard deviation of the corresponding multispectral component (r ij 5c ij /s i s j ). The correlation coefficient matrix R x has as elements the correlation coefficient between the ith and jth multispectral component. Accordingly, all the diagonal elements will be 1 and the matrix is symmetric r 12 r 1K r 21 1 r 2K R x ~ ð4þ 4. 5 r K1 r K2 1 In the literature several different linear transforms can be found, based on the statistical properties of vector representation. An important case is the Karhunen Loewe transform, also known as principal components analysis (PCA). For this transformation the matrix C x is real and symmetric thereby finding a set of orthonormal eigenvalues is always possible. Let e i and l i, i51,2,3...k, be the eigenvectors and the corresponding eigenvalues of C x arranged in descending order. Furthermore, let A be a matrix whose rows are formed by the eigenvectors of C x ordered so that the first row of A is the eigenvector corresponding to the largest eigenvalue, and the last row is the eigenvector corresponding to the smallest one. The matrix A is the transformation matrix that maps x into vectors denoted by y as follows y~aðx{m x Þ ð5þ

6 3246 V. Tsagaris and V. Anastassopoulos The mean of y resulting from that transformation is zero and the covariance matrix C y is given by C y ~AC x A T ð6þ The resulting covariance matrix C y will be diagonal and the elements along the main diagonal are the eigenvalues of C x ; that is 2 3 l l 2 0 C y ~ ð7þ l K The off diagonal elements of the covariance matrix are zero, denoting that the elements of the vector population y are uncorrelated. This transformation will establish a new coordinate system whose origin is at the centroid of the population and whose axes are in the direction of the eigenvectors of C x. This coordinate system clearly shows that the transformation in equation (5) is a rotation transformation that aligns the data with the eigenvectors, and this alignment is exactly the mechanism that decorrelates the data. The transform is optimal in the sense that the first principal component will have the highest contrast and it can be displayed as a greyscale image with the bigger percentage of the total variance and thus the bigger percentage of visual information. The above property does not hold in the case of a colour image. If the three principal components are used to establish an RGB image (first component as red, second as green and third as blue) the result is not optimal for the human visual system. The first principal component (red) will exhibit a high degree of contrast, the second (green) will display only a limited range of the available brightness value, whilst the third one (blue) will demonstrate an even smaller range. In addition, the three components displayed as R, G and B are totally uncorrelated and this is an assumption that does not hold for natural images (Chavez 1989, Gonzalez and Woods 2002, Forsyth and Ponce 2002). 3.2 The proposed method A different approach for RGB image formation using multispectral data is not to totally decorrelate the data, but to control the correlation between the colour components of the final image. This is achieved by means of the covariance matrix. The proposed transformation distributes the energy of the source multispectral bands, so that the correlation between the RGB components of the final image is similar to that of natural colour images. In this way no additional transformation is needed and direct representation to any RGB display can be applied. This can be achieved using a linear transformation of the form y~a T x ð8þ where x and y are the population vectors of the source and the final images, respectively. The relation between the covariance matrices is C y ~A T C x A ð9þ where C x is the covariance of the vector population x and C y is the covariance of the arising vector population y. The required values for the elements in the resulting

7 Multispectral image fusion based on perceptual attributes 3247 covariance matrix C y are based on the study of natural colour images as explained previously. The selection of a covariance matrix based on the statistical properties of natural colour images guarantees that the resulting colour image will be pleasing for the human eye. The RGB correlation coefficients depend on the scenes depicted in the images. However, since a large variety of images with different scenes, perceptually pleasing for the observer, have been chosen from the database, the mean value of the correlation coefficients is not affected by the selection of the scenes. The matrices C x and C y are of the same dimension and, if they are known, the transformation matrix A can be evaluated using the Cholesky factorization method. Accordingly, a symmetric positive definite matrix S can be decomposed by means of an upper triangular matrix Q, so that S~Q T : Q ð10þ The matrices C x, C y using the above factorization can be written as C x ~Q T x Q x C y ~Q T y Q y ð11þ and equation (9) becomes Q T y Q y~a T Q T x Q xa~ ðq x AÞ T Q x A ð12þ thus Q y ~Q x A ð13þ and the transformation matrix A is A~Q {1 x Q y ð14þ The final form of the transformation matrix A implies that the proposed transformation depends on the statistical properties of the original multispectral dataset. Additionally, in the design of the transformation the statistical properties of natural colour images are taken into account. The resulting population vector y is of the same order as the original population vector x, but only three of the components of y will be used for colour representation. The evaluation of the desired covariance matrix C y for the transformed vector is based on the statistical properties of natural colour images, discussed in 2.3, and on requirements imposed by the user or the visual expert. The relation between the covariance C y and the correlation coefficient matrix R y is given by C y ~~R y ~ T ð15þ where 2 s y1 0 0 : 0 0 s y2 0 : 0 ~~ 0 0 s y3 : : : : : : : s yk ð16þ

8 3248 V. Tsagaris and V. Anastassopoulos is the diagonal matrix with the variances (or standard deviations) of the new vectors in the main diagonal and r R,G r : R,B 0 r R,G 1 r : G,B 0 R y ~ r R,B r G,B 1 : : : : : : : 1 ð17þ is the desired correlation coefficient matrix. The steps that one has to follow in order to apply the proposed method can be summarized as follows: 1. Determine the desired R y in equation (17) and evaluate the corresponding C y from equation (15). 2. Evaluate C x from the source multispectral data. 3. Calculate Q x and Q y from C x and C y using Cholesky decomposition. 4. Evaluate the required transformation matrix A using equation (14). For high visual quality the final colour image produced by the transformation must have a high degree of contrast. In other words the energy of the original data must be sustained and equally distributed in the RGB components of the final colour image. This requirement is expressed as follows X K i~1 s 2 xi ~ X3 s 2 yi i~1 ð18þ with s y1 5s y2 5s y3 approximately. The remaining K-3 bands should have negligible energy (contrast) and will not be used in forming the final colour image. Their variance can be adjusted to small values say s yi s y1 for i54 K. 3.3 Selection of primary bands The selection of the initial spectral bands that will help to determine the primary axes for projecting the multispectral information is of paramount importance for the visual quality of the final colour image. In principal components analysis this selection is based on the three largest eigenvalues and the corresponding eigenvectors. Consequently, the direction of the three new axes used for projection is different from that of the initial bands and simultaneously the information is totally decorrelated. According to the proposed transformation, the projection is carried out giving special importance to those of the initial axes (spectral bands) which possess the largest amount of energy. It is preferable that these bands have the smallest possible correlation with all the other spectral bands. A method proposed by Chavez et al. (1982) takes into consideration the previously mentioned requirements. Specifically, this selection method is based on

9 Multispectral image fusion based on perceptual attributes 3249 the optimum index factor (OIF), which considers the source spectral bands in triplets and is defined as OIF~ P 3 s i i~1 P 3 j~1 jr j j ð19þ where s i is the standard deviation of each of the three selected bands and r j is the correlation coefficient between any pair formed by these bands. The OIF factor is evaluated for all possible combinations of groups with three bands. The group of bands with higher OIF is selected for projecting the information content of the multispectral data. In this work the information quality of each of the original bands is assessed using the factor MEMC, which stands for maximum energy minimum correlation, defined on each separate source band as MEMC~ P K s i j~1,i=j r i,j ð20þ for each band i51,...,k where s i is the standard deviation of the band and r i,j is the correlation coefficient between band i and the rest of the bands. The three source spectral bands with the largest MEMC index span the maximum of the original spectral space. According to the proposed method the source spectral bands are ordered with descending MEMC index before applying the transformation given by equation (14). 3.4 Objective performance evaluation The performance evaluation of image fusion methods and the testing of the achieved results is a relatively complex issue because of the different sources of data and the different aims of fusion processes. The method proposed in this work aims to derive a colour image of improved quality and fidelity that will be used mainly for visual interpretation. Therefore, the overall performance evaluation is based on perceptual evaluation as in Achalakul and Taylor (2001), Tyo et al. (2003), Bogogni and Hansen (2001) and Toet and Franken (2003). In recent years, a few objective measures for the evaluation of fused methods have been proposed (Xydeas and Petrovic 2000, Qu et al. 2002). These measures have been developed for the assessment of greyscale fusion techniques, thus their use in colour fusion is not straightforward. A numerical quality assessment of image fusion based on mutual information has been recently introduced in Qu et al. (2002). Each source multispectral band X and each colour component of the final colour image Y, can be treated as discrete random variables distributed according to probabilities p X (x) and p Y (y), respectively. Thus, the mutual information shared by a source multispectral image and one of the final colour components is given by I XY ~ X x X p XY ðx,yþlog p XY ðx,yþ p X ðxþp Y ðyþ y ð21þ

10 3250 V. Tsagaris and V. Anastassopoulos It can be proved that mutual information is always a positive quantity that vanishes only if p XY (x,y)5p X (x)p Y (y). Therefore, it can be interpreted as a measure of the statistical dependence between the variables X and Y. The physical significance of mutual information is that it quantifies the amount of common information between two images. In Qu et al. (2002) the mutual information between each source image and the final greyscale image is evaluated. The fusion performance measure is the total mutual information. In this work the total mutual information between the original multispectral bands and each colour component of the final image is evaluated. An iteration process is employed in order to maximize the total mutual information by adjusting the elements of the resulting correlation matrix. For this purpose each element of the correlation matrix C y takes its value in a range that is defined by the corresponding variance given in table 1. In this way not only the perceptual attributes, related to the correlated bands in the RGB colour space, are incorporated in the method, but also the objective condition of the maximization of mutual information is satisfied. 4. Experimental procedure 4.1 Multispectral data description The multispectral dataset used in this work consists of four multispectral bands and is available by Space Imaging ( and acquired from IKONOS-2 sensor. The analysis of each band is 11 bits per pixel and the size is pixels. The ground resolution provided by IKONOS-2 for the multispectral imagery is 4 m. The spectral range of the sensor is depicted in table 2. The area covered in this multispectral image is mainly an urban area with a structured road network, a forest, a stadium, a park, etc. The correlation among the source multispectral components is shown in table 3. Obviously, a high degree of correlation is present mainly between the three components that lie in the visible region of the electromagnetic spectrum. The selection of primary bands for projecting the multispectral information is carried out here on a perceptual as well as on a statistical basis. According to the perceptual approach bands 1, 2 and 3, given in table 2, are used to determine Table 2. Spectral range of IKONOS-2 data. Band number Spectral range (mm) 1 (blue) (green) (red) (near infrared) Table 3. Correlation coefficient matrix for IKONOS data. Band number

11 Multispectral image fusion based on perceptual attributes 3251 Table 4. OIF index for the multispectral dataset. Band combination OIF 1, 2, , 2, , 3, the projection directions, since their spectral range is lying in the visible region of the electromagnetic spectrum. In this way the information contained in band 4 (near infrared) is distributed on the three primary bands, thus sustaining all the visually perceivable information of the original bands. Statistically based band selection is implemented using both OIF and MEMC indexes. The values of the OIF index for all combinations of source spectral bands are displayed in table 4, while index MEMC is shown for each of the four bands in table 5. The OIF index indicates that bands 2, 3 and 4 are the most important for primary axes evaluation. On the other hand the MEMC index designates bands 1, 4 and Experimental results The fusion results are demonstrated in figure 3. In the upper left image a false colour composite using only the first three bands of the data is shown. The image in figure 3(b) is derived from PCA analysis. The two images in the second row of figure 3 have resulted according to the proposed method using the perceptual selection and the MEMC index, respectively. The transformation matrix A calculated by means of equation (14) was based on the following correlation coefficient matrix :8487 0: : : R y ~ 6 7 ð22þ 4 0:7040 0: according to table 1. The result transformation matrix A is depicted in table 6 for the case of using channels 1, 2 and 3 as primary bands. Apparently, in the perceptual case the final colour image possesses more natural colours, while the image resulting on the MEMC selection is more expressive for the human eye. Subjectively, the proposed method produces a colour image that can be characterized as a rich colour image with similar properties to those of natural colour images. Another important property of the colour images resulting from the proposed transformation is that areas with the same spectral signature (urban area, sea, forestry, etc.) are depicted with variations of the same colour. In other words, Table 5. MEMC index for the multispectral dataset. Band number MEMC (610 4 )

12 3252 V. Tsagaris and V. Anastassopoulos (a) (b) (c) (d ) Figure 3. Detail image (a) false colour composite of the first three bands, (b) first three PC components from PCA transformation, (c) proposed method, (d) proposed method with MEMC selection. the overall colour balance of the area is preserved but the colours are presented with more shading. In addition, the proposed method outperforms the other two, because the resulting image has a greater variety of colours and hues that are perceivable by the human eye, especially in dark areas of the source images. The objective evaluation of the proposed method is based on the measure described in 3.4 and the results are displayed in table 7. The proposed method outperforms PCA-based approaches in both realizations. The amount of informa- Table 6. Transformation table for IKONOS data in the case of selecting multispectral bands 1, 2 and 3 for projection :1024 {2:5622 {1:7097 0: :5480 {0:3595 {0:2209 A~ :1217 0: :0433

13 Multispectral image fusion based on perceptual attributes 3253 Table 7. Mutual information between source multispectral bands and the final colour image. PCA Proposed Proposed using MEMC Red Green Blue Red Green Blue Red Green Blue Sum tion conveyed in the fused colour image, as described by mutual information, is greater in all cases. In addition, the information of the source multispectral images is almost uniformly distributed among the RGB components of the fused image. This property is a result of the attributes of the human visual system that have been incorporated in the proposed transformation. Further improvement in the visual quality of the resulting colour image could be achieved by means of a post-processing step. This step includes the use of a histogram equalization technique in order to improve the contrast of the final colour image. In the case of PCA the second and the third principal components are always narrow because of the energy compaction property of the KL transform. The proposed method outperforms PCA due to the fact that the three components produced by the transform (8) have improved contrast. The results reveal that the visual appearance along with the discrimination capability is enhanced. 5. Conclusions The main purpose of this paper is to present a new fusion technique for multispectral images. The fusion process results in a colour image suitable for visual interpretation and provides a novel scheme for the display of multispectral imagery. Its basic idea is to control the terms of the covariance matrix of the output colour image so that attributes related to human colour perception are incorporated. For this purpose correlation properties in natural colour images are taken into consideration in the design of the transform. The perceptual attributes of the obtained image are not sensitive to small variations of the correlation coefficient values. In addition, the proposed technique is well suited for direct representation to any RGB-based device. The projecting directions have been derived according to the MEMC index introduced in this paper. This index reveals the multispectral bands that play a dominating role in the proposed transformation, since they have the maximum energy and the smallest correlation among all the other bands. In order to establish the proposed fusion technique, both subjective and objective performance evaluations have been carried out. The objective evaluation is based on mutual information and justifies the proposed method as meaningful. Specifically, the total mutual information is proposed and used as a measure for maximizing the information conveyed from the source multispectral bands to the final colour image. Subjectively, the experimental results demonstrate that the proposed method produces a colour image with a large variety of colours and hues. In this way the ability of the human eye to perceive millions of colours is fully exploited. Another main advantage of the technique is that the resulting colour image is formed in the RGB colour space and no further transformation is needed.

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