A genetic algorithm for MRF-based segmentation of multi-spectral textured images

Pattern Recognition Letters 20 (1999) 1499±1510

www.elsevier.nl/locate/patrec

A genetic algorithm for MRF-based segmentation of multi-spectral textured images q Din-Chang Tseng *, Chih-Ching Lai Institute of Computer Science and Information Engineering, National Central University, Chung-li 320, Taiwan, ROC

Abstract A segmentation approach based on a Markov random ®eld (MRF) model is an iterative algorithm; it needs many iteration steps to approximate a near optimal solution or gets a non-suitable solution with a few iteration steps. In this paper, we use a genetic algorithm (GA) to improve an unsupervised MRF-based segmentation approach for multispectral textured images. The proposed hybrid approach has the advantage that combines the fast convergence of the MRF-based iterative algorithm and the powerful global exploration of the GA. In experiments, synthesized color textured images and multi-spectral remote-sensing images were processed by the proposed approach to evaluate the segmentation performance. The experimental results reveal that the proposed approach really improves the MRF-based segmentation for the multi-spectral textured images. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Unsupervised texture segmentation; Markov random ®eld; Genetic algorithm; Multi-spectral remote-sensing images

1. Introduction In the last decade, multi-spectral image analysis has received a great deal of attention in remotesensing and industrial applications because it signi®cantly improves discrimination and recognition capability over pure intensity-based methods. With the widespread availability of multi-spectral images, many techniques have been proposed for these applications to extract useful information. Image segmentation is an important process for scene analysis and image understanding. Many approaches (Beulieu and Goldberg, 1989; Carlotto, 1989; Haralick and Shapiro, 1985; Pal and Pal, q Electronic Annexes available. See www.elsevier.nl/locate/ patrec. * Corresponding author. E-mail address: [email protected] (D.-C. Tseng)

1993) have been proposed for the monochrome image segmentation. Among these approaches, histogram thresholding and the clustering methods have been extensively used for the multi-spectral images (Celenk, 1990; Pal and Pal, 1993). Texture plays an important role in image segmentation. The goal of texture segmentation is to separate an image into regions with distinct contextual structures or statistical behavior. Nontextured multi-spectral images can be segmented well with only spectral information; however, textured multis-pectral images (e.g., remote-sensing images) can only be exactly segmented with combining spatial and spectral information. Markov random ®elds (MRFs) utilize both spectral and spatial information to model the local structure of an image. Several MRF-based segmentation approaches (Andrey and Tarroux, 1998; Bouman and Liu, 1991; Chellappa and Jain, 1993;

0167-8655/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 8 6 5 5 ( 9 9 ) 0 0 1 1 7 - 8

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D.-C. Tseng, C.-C. Lai / Pattern Recognition Letters 20 (1999) 1499±1510

Dubes et al., 1990; Huang et al., 1992; Li, 1995; Liu and Yang, 1994; Manjunath and Chellappa, 1991; Panjwani and Healey, 1995; Solberg et al., 1994; Yamazaki and Gingras, 1995; Zhang et al., 1990) have been proposed to segment textured images. An important property of the MRF model is that they use a ®nite number of parameters to characterize spatial interactions of pixels to describe an image region. The image textures can be viewed as realizations of samples from a parametric probability distribution in the image space. Thus, an MRF-based segmentation generates image regions being homogeneous in spectral distribution and textural properties. Manjunath and Chellappa (1991) divided an intensity textured image into a number of nonoverlapped regions and used a Gauss Markov random ®eld (GMRF) to model every region. Then a simple clustering method was used to obtain a coarse segmentation result and a pixel-based scheme was used to re®ne the segmentation. Liu and Yang (1994) proposed a coarse-to-®ne multiresolution color image segmentation based on an MRF model. At ®rst, the scale space ®lter (SSF) is employed to get the coarse segmented result. The MRF-based multi-resolution segmentation method using a simulated annealing technique is then used to re®ne the segmentation result. Panjwani and Healey (1995) used an MRF model that captured spatial interactions within and between spectrum bands of a color image to model color textured images. A maximum pseudolikelihood scheme was then used to estimate model parameters for every image block based on the MRF model. At last, a stepwise optimal merging process was used to complete the segmentation. Many MRF-based segmentation methods have been proposed for remote-sensing images. Zhang et al. (1990) presented a multi-spectral image context classi®cation algorithm based on a stochastic relaxation algorithm and Markov±Gibbs random ®eld. The favorable features of the algorithm are that the random model arises from the joint probability distribution of the variates in a neighborhood and the algorithm is highly parallel. Solberg et al. (1994) presented an MRF model for multi-source classi®cation of remote-sensing im-

ages. The MRF model provides a methodological framework that allows the images gotten from di€erent sensors and map data to be merged in a consistent way. Yamazaki and Gingras (1995) proposed a criterion for classifying multi-spectral remote-sensing images based on a hierarchical MRF model. The maximizing a posteriori distribution probability (MAP) criterion is one of the most popular statistical criteria for optimality and has been the most popular choice for the MRF modeling (Li, 1995). An essential method using the MAP criterion for image segmentation is a stochastic or deterministic relaxation algorithm. Among all existed MAP-criterion algorithms, simulated annealing (SA) and the iterated conditional modes (ICM) algorithms are the two commonly used methods for image-pixel labeling. However, the SA algorithm su€ers from intensive computation and the ICM algorithms su€ers from inaccurate estimation (Bouman and Liu, 1991; Hu and Dennis, 1992). It has been shown that SA can converge to the global optimum with the proper annealing schedule, but such a schedule converges too slow to be practically useful. On the other hand, a result obtained from the ICM algorithm represents a local maximum and heavily depends on the initial state (Li, 1995). Hu and Dennis (1992) proposed selective and con®dence enhanced update schemes to reduce the computation demand for SA and to improve the estimation accuracy for the ICM algorithm. However, the method needs to judge whether the image regions are homogeneous or not and the segmentation result still has a few incorrectly classi®ed regions. In this paper, we use a genetic algorithm to improve the ICM algorithm for segmenting multispectral textured images. Genetic algorithms (GAs) (Goldberg, 1989; Michalewicz, 1992) are probabilistic search methods guided by the principles of evolution and natural genetics. Originally, GAs were modeled and developed by Holland (1975), and they have been emerged as general purpose and robust optimization techniques. GAs are well known for their ability to eciently and adaptively explore large search spaces (Michalewicz, 1992). GAs have the following advantages over the traditional search methods: (i) GAs

D.-C. Tseng, C.-C. Lai / Pattern Recognition Letters 20 (1999) 1499±1510

directly work with a coding of the parameter set; (ii) search is carried out from a population of points; (iii) payo€ information is used instead of derivatives or auxiliary knowledge, and (iv) probabilistic transition rules are used instead of deterministic ones (Goldberg, 1989). The initialization of the ICM algorithm is often obtained to label each pixel without considering neighboring pixel labels (Besag, 1986); thus, the ICM algorithm is shown to be sensitive to the initialization (Li, 1995). Here, we use a GA as a search algorithm in which the spatial correlation between a pixel and its neighbors is embedded in it to provide a better initialization for the ICM algorithm. The hybrid method has the advantage that combines fast convergence of the ICM algorithm with the global exploration of the GA. The proposed segmentation is an unsupervised approach that does not require prior knowledge about the number of textures classes, texture parameters and spectrum distribution of the images. The approach consists of two processes. Only based on the spectral information, an SSF-based histogram thresholding is taken as the ®rst process to get coarse segmented results and the major clusters of the multi-spectral data that form the principal multi-spectrum set. The histogram thresholding provides an initial segmented result to signi®cantly reduce the amount of time needed in the following MRF-based iterative process. In the second process, a texture segmentation method based on the MAP-MRF framework is used to re®ne the coarse segmented result. A second-order GMRF is used to model the spatial interactions within and between spectrum bands of the image, and then the global GMRF parameters are estimated by using the pseudolikelihood method (Panjwani and Healey, 1995). Based on the principal multi-spectrum set and the global GMRF parameters to maximize posteriori distribution probability, every pixel is labeled with the proposed hybrid GA-ICM method. The segmented image consists of a number of homogeneous regions; each region contains only one spectral texture and this spectral texture is di€erent from the ones of its adjacent regions. The remaining sections of this paper are organized as follows. Section 2 presents the proposed

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approach. The experiments and discussions are given in Section 3. The conclusions are summarized in Section 4.

2. The proposed segmentation approach The proposed unsupervised texture segmentation approach consists of two processes: (i) SSF-based histogram thresholding and (ii) GMRFbased global segmentation. 2.1. SSF-based histogram thresholding The locations of peaks and valleys of a histogram indicate the clusters of similar-spectral pixels in an image. The histogram thresholding exploits the information embedded in the histogram to segment the image. However, most histograms contain too many rugged peaks to e€ectively analyze. Witkin (1984) proposed the scale space ®lter (SSF) that uses di€erent Gaussian functions to smooth the histogram and then detects the locations of peaks and valleys to ®nd the pixel clusters. For a p-band spectral image, p 1-D histogram thresholdings are individually performed for all spectrum bands. Then the thresholded results are combined together to partition the p-dimensional spectrum space (Celenk, 1990). Assume that the p spectrum bands are named b1 ; b2 ; . . . ; bp ; then the spectrum space is partitioned into C…Cb1 ; Cb2 ; . . . ; Cbp † ˆ Cb1 Cb2


Cbp , where Cbi denotes clusters in bi band and denotes the cross-product operator (Liu and Yang, 1994). Major multi-spectral clusters composing the majority of the multi-spectral image are determined from C…Cb1 ; Cb2 ; . . . ; Cbp †. The centers of all major clusters form the principal multi-spectrum set that will be utilized in the following segmentation. 2.2. GMRF-based global segmentation In this study, a GMRF is used to model multispectral textured images. Then the GMRF parameters are estimated from the statistical results of the whole image by using the pseudolikelihood

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method (Panjwani and Healey, 1995) and a MAP criterion is used for labeling every image pixel. 2.2.1. GMRF model representation An MRF is a contextual model that speci®es the local dependence of image regions by de®ning a neighborhood system on the pixels of an image and a probability density function on the spectrum distribution of the pixels. For multi-spectral images, the GMRF model should consider not only the spatial interactions within each spectrum band, but also the interactions between di€erent spectrum bands. We extend the model proposed by Panjwani and Healey (1995) to describe a p-band spectral image. Let X …s† ˆ ‰x1 …s† x2 …s† . . . xp …s†Š represent the multi-spectral Gaussian random vector of a pixel s in a textured region R. Then the GMRF for modeling the textured region is de®ned by the following conditional probability density function: P …X …s† j R† ˆ

1 p

1=2

……2p† j R j†  ÿ1  exp ‰e1 …s† e2 …s†


ep …s†Š 2  T Rÿ1 ‰e1 …s† e2 …s†


ep …s†Š ;

…1†

where ‰e1 …s† e2 …s†


ep …s†Š is a zero-mean Gaussian noise vector. The spatial interactions of the multispectral pixels are given by ej …s† ˆ …xj …s† ÿ lj † ÿ

p X X hji;t …xi …s ‡ t† ÿ li †; iˆ1 t2gji

j ˆ 1; 2; . . . ; p;

…2†

where lk is the mean of variable xk ; hji;t s are model parameters and the subscribed gji sets represent di€erent neighborhood systems. We use a p  p neighborhood matrix to completely de®ne the interactions between each pair of spectrum bands. The correlation matrix is denoted as 2 3 v11 v12


v1p 6 v21 v22


v2p 7 6 7 Rˆ6 . …3† 7; 4 .. 5 vp1

vp2






vpp

Fig. 1. Partial parameters of spatial interaction between different spectrum bands.

the entry vkl is the expected value of ek el and represented by vkl ˆ E‰ek el Š ˆ

1 X ek …s†el …s†; MR s2R

…4†

where MR is the total number of pixels in region R. One example of the spatial interactions between a site (i, j) in the b1 band and three neighbors in the b1 and b2 bands is shown in Fig. 1. 2.2.2. GMRF parameter estimation In a multi-spectral image, the spectral vector of a pixel depends on its neighbors and the neighboring spectral vectors are statistically dependent according to Eq. (2). Thus, a pseudolikelihood method (Panjwani and Healey, 1995) is used to estimate the global GMRF parameters. For a given image region R modeled by a GMRF, the function Lˆ

Y

1

……2p† j RR j†1=2  ÿ1 ‰e1 …s†e2 …s†


ep …s†Š  exp 2  T ‰e …s†e …s†


e …s†Š Rÿ1 1 2 p R s2R

p

…5†

is the product of conditional probability densities of all pixels in region R. Since the spectral vectors of a pixel and its neighbors are not independent, the function L is not a true likelihood function and often called the pseudolikelihood. The parameters

D.-C. Tseng, C.-C. Lai / Pattern Recognition Letters 20 (1999) 1499±1510

can be estimated with a set of linear equations. Maximizing the pseudolikelihood function L by di€erentiating with respect to each of the GMRF parameters results in sets of linear equations for all parameters (Panjwani and Healey, 1995). For example, let di …s† ˆ xi …s† ÿ li and di;t …s† ˆ xi …s ‡ t† ÿli , for i ˆ 1; 2; . . . ; p; t 2 g1i , the parameters h1i;t ; i ˆ 1; 2; . . . ; p; t 2 g1i , can be estimated by the equation 2

2 d1;t …s†

6 d …s†d1;t …s† X6 6 2;t 6 .. 6 s2R 4 . dp;t …s†d1;t …s† 2

h11;tjt2g11 6h 6 12;tjt2g12 6 6 .. 6 . 4 h1p;tjt2g1p

d1;t …s†d2;t …s†






2 d2;t …s†






.. . dp;t …s†d2;t …s†






d1;t …s†dp;t …s†

3

7 d2;t …s†dp;t …s† 7 7 7 .. 7 . 5 2 dp;t …s†

3

2 3 d1 …s†d1;t …s† 7 7 7 X6 6 d1 …s†d2;t …s† 7 7 6 7: 7ˆ .. 6 7 7 4 5 s2R . 5 d1 …s†dp;t …s†

…6†

Note that any entry is a list of values not just a value since t 2 g1i is a set of neighboring pixels. 2.2.3. Pixel labeling We label each pixel according to the principal multi-spectrum set and the GMRF parameters to maximize a posteriori distribution probability (MAP). The principal multi-spectrum set is substituted into the posteriori spectral distribution probability, and one component of the principal multi-spectrum set that maximizes the posteriori spectral distribution probability is used to label pixels. Such a GMRF-based global segmentation corrects the mislabeling problem in the preceding coarse segmentation. In our segmentation procedure, we use the iterated conditional modes (ICM) algorithm (Besag, 1986) to label the image pixels. The ICM algorithm is a deterministic relaxation algorithm using the greedy strategy to ®nd the best estimation based on the MAP criterion. However, the result obtained from the ICM algorithm is heavily dependent on the initialization (Li, 1995). Always, the ICM algorithm ends up in a local

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optimum. Currently, it is not known how to properly set a better initialization to obtain a better solution, and it is critical to resolve the problem of setting initialization before using the ICM algorithm. Here we use a genetic algorithm (GA) to provide a better initialization for the ICM algorithm. In general, a GA contains a ®xed-size population of potential solutions over the search space. These solutions are encoded as binary or realnumber strings called individuals or chromosomes. The initial population can be created randomly or based on the problem-speci®c knowledge. In each iteration, called a generation, a new population is created based on a preceding one through the following three steps: 1. evaluation: each individual of the old population is evaluated using a ®tness function and given a value to denote its merit, 2. selection: individuals with better ®tness are selected to generate next population, and 3. mating: genetic operators such as crossover and mutation are applied to the selected individuals to produce new individuals for the next generation. The above three steps are iterated for many generations until a satisfactory solution is found or a terminated criterion is met. Thus, using a GA to solve a problem, we must specify the following components: (i) a genetic representation of solutions to the problems, (ii) one way to create an initial population of solutions, (iii) an evaluation function that rates all candidate solutions according to their ``®tness'', (iv) genetic operators that alter genetic composition of children during reproduction, and (v) control parameters (e.g., population size, crossover, mutation rates, etc.) 2.2.3.1. Solution representation. A real-coded GA is a GA that uses ¯oat-point (or real) numbers to represent genes (Michalewicz, 1992). An individual in a real-coded GA is a vector of real numbers. In our utilization of a GA, a spectral vector X …s† ˆ ‰x1 …s†x2 …s†


xp …s†Š representing the spectral components of a pixel s is encoded as an individual. Each component xi …s† is assigned a real number sampled from the uniform interval [0, 1] to denote the judge outcome. We create a population

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of individuals and evaluate each individual, and then select the better individuals to construct the next population. Finally, the spectral vector with the highest ®tness value is found. Based on the individual representation, one pixel is repeatedly processed after the previous one was completely processed. 2.2.3.2. Initial population. In general, a GA creates its starting population randomly, however, we can heuristically rather than randomly generate the individuals in the initial population to improve the search performance. Here we use the result of the SSF-based histogram thresholding as an individual, and the remaining individuals are randomly generated. 2.2.3.3. Fitness function. A ®tness function is the survival arbiter for individuals. Since the objective is to ®nd the spectral vector of a pixel that maximizes the conditional probability density function, the ®tness function is just de®ned as the same as Eq. (1), F ˆ P …X …s† j R† ˆ 

1 p

……2p† j R j†1=2

 ÿ1  e1 …s†e2 …s†


ep …s† 2   T ÿ1 R e1 …s†e2 …s†


ep …s† ;  exp

…7†

with the same de®nitions of ei …s†'s and R. The spatial interactions between a pixel and its neighbours are embedded in the ®tness function; thus, a better spectral vector of a pixel can be obtained via a GA search. 2.2.3.4. Genetic operators. Three primary genetic operators: selection, crossover and mutation are generally used in GAs. Selection: The selection operator determines the surviving individuals. Each surviving individual is reproduced into several copies according to its relative responsibility. Two reproductive strategies were commonly used. Generational reproduction replaces the whole population in each generation, but steady-state reproduction only replaces the less-®tted members in a generation.

Baker (1987) compared various selection methods comprehensively, and presented an improved version called stochastic universal sampling (SUS) method. We use the steady-state reproduction and the SUS method in the proposed segmentation approach. Crossover: The crossover operator for a realcoded GA is analogous to that of binary-coded GA. The crossover operator randomly pairs individuals with a probability pc , and swaps parts of their genetic information to produce new individuals. Several kinds of crossover operators such as one-point, two-point and multi-point splitting have been proposed (Goldberg, 1989). For simplicity, the one-point crossover is adopted in the current segmentation approach. In the onepoint crossover, two parents are selected and two children are produced. One of the selected parents is with the best ®tness and the other is randomly selected. A randomly selected point is generated and used to cut each parent into two parts. Two children are formed by swapping the parts of parents demarcated by the crossover point. Mutation: For a binary-coded GA, the mutation operator creates a new individual by inverting one or more genes of an individual with a probability pm to increase the variability of the population. In contrast, two mutation operators have been proposed for real-coded GA (Michalewicz, 1992). A random mutation replaces a gene with a random number from the corresponding solution domain and a dynamic mutation stochastically changes a gene over time by adding or subtracting a random number. In the proposed segmentation approach, random mutation is adopted in which a gene in the crossover child is completely replaced with a random number sampled from the uniform interval [0, 1]. 2.2.3.5. Control parameters. The population size in¯uences the performance of GAs. A small-sized population reduces the evaluation cost but results in premature convergence, because the population provides insucient samples in the search space. For a large-sized population, the GA can gain more information to search better solutions because the population contains more representative

D.-C. Tseng, C.-C. Lai / Pattern Recognition Letters 20 (1999) 1499±1510

solutions over the search space. However, more computations are needed in a large-sized population, and this situation possibly results in an unacceptably slow rate of convergence. Both crossover and mutation probabilities may in¯uence the performance of GAs. A GA may stagnate to search new solutions if the crossover probability is low. However, if the crossover probability is too high, unstable solutions may be quickly substituted into the population for individuals with better ®tness. On the other hand, if the mutation probability is too high, the search of GA becomes a random-like process. In the proposed segmentation approach, we try a few samples to ®nd appropriate values for the used parameters. After using a GA to ®nd a good initialization for the ICM algorithm, the pixel labeling is done by the ICM algorithm. In each iteration, every

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pixel is sequentially updated according to the principal multi-spectrum set and the GMRF parameters by maximizing a posteriori distribution probability. After each iteration, the GMRF parameters are re-estimated with the currently updated labels. The labeling process is repeated for a ®xed number of iterations. Given an image I, the estimated GMRF parameter set H and the principal multi-spectrum set W, the estimated label X^ …s† for a pixel s is written as X^ …s† ˆ arg max P …X …s†jI; H; W†: X …s†

…8†

Dubes et al. (1990) showed that the ICM algorithm converges in ®ve or six iterations for a graylevel image. Huang et al. (1992) suggested that about 10 iterations are sucient to converge for a color image.

Fig. 2. Segmented results of the noisy image ST-1: (a) the original image; (b) the SSF-based thresholded result; (c) the GMRF-based global-segmented result without GA; (d) the GMRF-based global-segmented result with GA. A color version of this ®gure is available as an Electronic Annex. See www.elsevier.nl/locate/patrec.

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3. Experiments In this section, we present four experiments with two synthesized color (3-band) images and two SPOT satellite (3-band) images to demonstrate the performance of the proposed segmentation approach. The experimental results include SSF-based coarse-segmented images, GMRFbased global-segmented images without GA in the pixel labeling, and GMRF-based global-seg-

mented images with GA in the pixel labeling. In order to speed up the coarse segmentation, a simple version of SSF thresholding is employed to replace the original-proposed SSF thresholding (Witkin, 1984). In the simple version of SSF thresholding, we just de®ne a criterion to select a proper scale function to smooth the histogram for thresholding. The experiments were performed on a Pentium Pro-200 PC with Windows NT v4.0 operating system. The algorithm was im-

Fig. 3. Segmented results of the textured image ST-2: (a) the original image; (b) the SSF-based thresholded result; (c) the GMRF-based global-segmented result without GA; (d) the GMRF-based global-segmented result with GA. A color version of this ®gure is available as an Electronic Annex. See www.elsevier.nl/locate/patrec.

Table 1 The error rates for two synthesized images Images Approaches

Noisy image ST-1 (%)

Textured image ST-2 (%)

The SSF-based histogram thresholding image The GMRF-based global-segmented image without GA in the pixel labeling The GMRF-based global-segmented image with GA in the pixel labeling

17.00 3.48 0.24

15.40 7.38 0.11

D.-C. Tseng, C.-C. Lai / Pattern Recognition Letters 20 (1999) 1499±1510

plemented with MS Visual C++ development tool. It should be noted that though the values of parameters in GAs, such as maximum generation number and probabilities of genetic operators, always in¯uence the performance of the algorithms, GAs are always robust with respect to these parameters. Thus, only a few tries are needed to specify the parameter values. Certainly, reasonable parameters ensure good results and give rise to quick convergence. The parameters used in the experiments: (i) the generation number is 500, (ii) the population size is 50, (iii) the probabilities of crossover and mutation are 0.8 and 0.1, respectively, and (iv) 10 iterations of the ICM algorithm are performed in all pixel labeling.

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Two synthesized color noisy or textured images were used to evaluate the performance of the proposed approach as shown in Figs. 2(a) and 3(a). The sizes of the images are all 200  200 pixels. The ®rst synthesized image, ST-1, is a noise image corrupted by additive Gaussian noisy with a standard deviation 70. The second synthesized image, ST-2, is a textured image containing four di€erent textures: brick, burlap, canvas and sandstone. In the segmented images, pseudocolors are used to indicate the segmented results. The segmentation results are shown in Figs. 2 and 3, respectively. The segmentation results can be evaluated by visual inspection and by computing the error rate. Since the regions of the synthesized images are known, the error rate is easily calculated to

Fig. 4. Segmented results of the 430430-pixel. SPOT image SP-1: (a) the original image; (b) the SSF-based thresholded result; (c) the GMRF-based global-segmented result without GA; (d) the GMRF-based global segmented result with GA. A color version of this ®gure is available as an Electronic Annex. See www.elsevier.nl/locate/patrec.

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evaluate the segmentation performance. The error rate is de®ned as the ratio of the total misclassi®ed pixel number to the total pixel number in the image. The error rates for these two synthesized images are shown in Table 1. The proposed approach has the least error rate. By visually examining these segmented results, we can ®nd the SSF-based histogram thresholded results are still quite noisy. The reason is that the SSF-based histogram thresholding only takes spectral information into account and su€ers from the lack of spatial information. Comparing the results of SSF-based thresholding to those of GMRF-based segmentation without GA, considerable improvements are obtained. It shows that the GMRF-based approach considering the spa-

tial information can e€ectively correct the misclassi®ed problem in the coarse-segmented images. If we apply the GA to the GMRF-based segmentation, we can ®nd that the majority of misclassi®ed pixels are signi®cantly eliminated in the noisy or textured images. This improvement comes from that the GA fully utilizes the spatial correlations among the pixels in a neighborhood and provides a better initialization for the ICM pixel labeling, therefore the proposed approach yields better segmentation results as shown in Figs. 2(d) and 3(d). Two SPOT satellite images were processed to illustrate the performance of the proposed approach as shown in Figs. 4(a) and 5(a). The image sizes are 430  430 and 390  390 pixels, respec-

Fig. 5. Segmented results of the 390390-pixel SPOT image SP-2: (a) the original image; (b) the SSF-based thresholded result; (c) the GMRF-based global-segmented result without GA; (d) the GMRF-based global segmented result with GA. A color version of this ®gure is available as an Electronic Annex. See www.elsevier.nl/locate/patrec.

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tively. The results of SSF-based coarse-segmented images, GMRF-based global-segmented images without GA in the pixel labeling and GMRFbased global-segmented images with GA in the pixel labeling are shown in Figs. 4(b)±(d) and 5(b)± (d), respectively. The segmented results cannot be evaluated by the above error rate since we do not have their true labels. Although a quantitative evaluation function has been proposed for image segmentation (Liu and Yang, 1994), the declarative segmentation criteria: (i) segmented regions should be uniform and homogeneous, (ii) region interiors should be simple and without many small holes, (iii) adjacent regions should have signi®cantly di€erence, and (iv) boundaries of each region should be simple and spatially accurate (Haralick and Shapiro, 1985) still give us more con®dence to evaluate the segmented results of high-complexity remote-sensing images. Due to the texture property of remote-sensing images, only spectral information is not enough for the segmentation. We can ®nd many pimple regions which should be grouped into one region are separated in Fig. 4(b) and the majority of image regions are apparently not segmented well in Fig. 5(b). Applying GMRF segmentation to include the spatial interactions within and between the spectra of the multi-spectral images reduces the mislabeling and simpli®es the texture distribution of the original images as shown in Figs. 4(c) and 5(c). Comparing the results obtained from GMRF-based segmentation without and with GA, we ®nd that the initialization of the ICM algorithm plays an important role and has signi®cant in¯uence on the ®nal segmented results. When we combine the GA and ICM algorithm in the pixel labeling, many small regions disappear and the regions with the same texture are grouped more correctly as shown in Fig. 4(d). The proposed approach not only eliminates the tiny regions in the images, but also makes the boundaries of dim regions clear. The substantial improvement can be found in the upper-right corner of Fig. 5(d). Hence, the proposed approach actually produces more satis®ed segmented results based on the above segmentation criteria.

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4. Conclusions An unsupervised hybrid approach that combines a GA with the ICM algorithm in a MAPMRF framework for multi-spectral textured image segmentation was proposed. The GA was used to provide a good initialization for the ICM algorithm and the ICM algorithm was then used to label pixels. The ICM algorithm is a deterministic relaxation algorithm and tends to trap into a local optimum near the initial solution after a few iterations. Even if the iterations of the ICM algorithm are increased, the solution is still not signi®cantly improved. Thus in the proposed hybrid GA-ICM approach, GA can ®nd a more proper initial solution for the ICM algorithm to ®nd a better solution. In the proposed approach, the generation number of the GA is far larger than the iteration number of the ICM algorithm; thus, the GA always dominates the computational performance. The computation time of a SA algorithm has been veri®ed to be much more than that of a GA (Lin et al., 1993; Gunnels et al., 1994), thus the proposed approach is still far more ecient than an SA-based approach. The proposed segmentation approach has been applied to the synthesized color textured images and multi-spectral remote-sensing images. From the experimental results, we address several conclusions: 1. The SSF-based histogram thresholding produces coarse segmented results and provides accurate principal multi-spectral data for further segmentation. 2. The GMRF-based global segmentation reduces the mislabeling problem in the coarse segmentation and simpli®es the texture distribution of the original image. 3. The proposed hybrid unsupervised segmentation provides a better segmented results. Though the ability of the ICM algorithm is limited, better results are obtained from better initialization. A GA actually provides the ICM algorithm a good improvement for further exploration. The hybrid GA-ICM approach possessing both the fast convergence of ICM algorithm and the powerful global exploration

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