Towards Automatic Image Enhancement Using

Towards Automatic Image Enhancement Using Genetic Algorithms C. Munteanu

A. Rosa

LaSEEB-ISR-Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1- Torre Norte 6.21, 1049-001 Lisboa, Portugal, [email protected]

LaSEEB-ISR-Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1- Torre Norte 6.21, 1049-001, Lisboa, Portugal, [email protected]

Abstract- This paper introduces a new automatic image enhancement technique based on real-coded Genetic Algorithms (GAs). The task of the GA is to adapt the parameters of a novel extension to a local enhancement technique similar to statistical scaling, as to enhance the contrast and detail in the image according to an objective fitness criterion. We compared our method with other automatic enhancement techniques, like contrast stretching and histogram equalization methods. Results obtained, both in terms of subjective and objective evaluation, show the superiority of our method.

1 Introduction Producing digital images with good contrast and detail is a strong requirement in several areas like remote sensing, biomedical image analysis, fault detection. Methods that process the given image so that the result is visually more suitable than the original, are called image enhancement techniques. Automatic enhancement, that is a method to yield enhanced images without human (subjective) intervention, is a notoriously difficult task in image processing (Jain 1991). This is because automatic enhancement requires specifying an objective criterion for enhancement, while evaluating the quality of an image is done finally by the human interpreter. Most of the enhancement techniques existent to date, are empirical methods, dependent on the particular type of image (Gonzales 1987). More important, these techniques require interactive procedures to obtain satisfactory results, and therefore are not suitable for routine application (Ramponi 1996). Evolutionary algorithms have been applied to image enhancement by several authors like (Poli 1997, Munteanu 1999a, Saitoh 1999). In (Poli 1997), the authors apply a global contrast enhancement technique by using Genetic Programming (GP) to adapt the colour map in the image as to fit the demands of the human interpreter. The GP module was meant to partly reproduce the user behaviour in interpreting the quality of the image, but results reported indicated an unsuccessful behaviour. In (Munteanu 1999a), we applied a real-coded Genetic Algorithm (GA) to adapt

the gray-level intensity transformation in the image. The fitness of each image, taken as an individual in the population, was a subjective score given by the human interpreter. A similar global technique was adopted in (Saitoh 1999), this time the fitness being given by an objective criterion proportional to the number of edges in the image and to a clumping factor of the intensity transformation curve. Evolutionary techniques used so far for the image enhancement problem, have several shortcomings like: • making use of a global method for image enhancement, that is incapable of adapting to the local spatial content in the image (Poli 1997, Munteanu 1999a, Saitoh 1999). For some images, a global enhancement method, that is a method by which the pixels in the image are modified through a transformation function based on the gray-level distribution over an entire image, often doesn’t produce satisfying results (Gonzales 1987). In these cases a local procedure that enhances differently in different areas of the image is recommendable. • requirement for user interaction, as each image, treated as an individual in the population, should be rated subjectively by a human interpreter (Poli 1997, Munteanu 1999a). As in all cases of subjective fitness evaluation algorithms (Herdy 1996, Backer 1993), the major inconvenient is that the user has to spend too much time in evaluating each image, the whole process being tedious. • requirement for additional external parameters in the objective fitness criterion that make the automatic image enhancement technique parameter dependant (Saitoh 1999). In this case, the user applies an automatic enhancement technique, but he has to spend additional time in fine tuning the parameters in the fitness function, for each given image. In what follows we propose an evolutionary method for automatic contrast enhancement having the following advantages: a) it uses a local enhancement technique based on a variation of the statistical scaling method (Jain 1991). b) it uses no interaction with the user, during running stages of the algorithm, therefore the method is automatic. c) it uses an objective fitness criterion with no additional external

parameters. The remainder of the paper is organised as follows: Section 2 reviews the basic enhancement methods and presents our GA-based technique; Section 3 gives the experimental results obtained in comparison to contrast stretching and histogram equalization techniques, on a 8 image set, and Section 4 draws the conclusions of this paper.

method to the given image, as opposed to classical global enhancement methods; automation of the image enhancement process; robustness, that is producing good enhancement results on a large category of images. In what follows we describe in detail the GA-based image enhancement method.

2 The GA enhancement algorithm – structure and motivations

2.1 Block processing algorithm and chromosome representation Local enhancement methods apply transformation functions that are based on the gray-level distribution, or other properties, in the neighborhood of every pixel in a given image (Gonzales 1987). An example of a local enhancement method is adaptive histogram equalization where each pixel is assigned a value according to a histogram equalization transform performed in the n×n neighbourhood of that pixel. Adaptive histogram equalization has shown good results in medical imaging (Zimmerman 1988). This approach is computationally expensive as histogram equalization is a time consuming strategy, and if it is applied to each pixel in the image it becomes even more time consuming. We have chosen to use a less time consuming method similar to statistical scaling presented in (Gonzales 1987). The method applies to each pixel at location (x, y) the following transformation:

Before proceeding with the description of our GA-based enhancement method, let use briefly review the basic strategies for image enhancement. Image enhancement techniques can be classified in four main categories as follows (Jain 1991): point operations, spatial operations, transform operations and pseudocolouring methods. Point operations which include contrast stretching, window slicing, histogram modeling, are zero-memory operations that remap a given input gray-level into an output gray-level, according to a global transformation. These methods have the disadvantage of treating the image globally, not being able to differentiate between several areas of the image that might require different levels of contrast enhancement. Of these techniques, linear contrast stretching and histogram equalization are the most widely used. Linear contrast stretching employs a linear transformation that remaps the gray-levels in a given image to fill the full range of values. Histogram equalization applies a transformation to the input image such that the output image will have a uniform histogram (that is, the gray-levels have a relative frequency that is uniformly distributed). Spatial operations include noise smoothing, median filtering, unsharp masking, lowpass, bandpass and high-pass filtering. In this category of methods, spatial operations are performed in local neighborhoods of input pixels, these operations being often convolutions with Finite Impulse Response filters (FIR), called spatial masks. Spatial operations might suffer from excessively enhancing the noise in the image or conversely by smoothing the image in areas that need sharp details (Ramponi 1996). Transform operations include linear filtering, root filtering, homomorphic filtering. These are techniques in which zero-memory operations are performed on a transformed image followed by the inverse transformation, the result being the enhancement of the image in particular spatial frequency domains. Pseudocolouring methods include false colouring and pseudocolouring, and are based on the fact that humans can distinguish many more colours than gray-levels, therefore gray scale images are artificially “coloured” using a proper colour map. The disadvantage of these methods comes from the non-uniqueness of the colour mappings, extensive interactive trials being required to determine an acceptable mapping. Our approach to image enhancement takes into account several factors: locality and adaptability of the

  M  ⋅ [ f (x, y) − c ⋅ m(x, y)] + m(x, y)a g( x, y) = κ (1)  σ (x, y) + b  0.5 < κ < 1.5; a ∈ Ψ1, b ∈ Ψ2 , c ∈ Ψ3 with Ψ1, Ψ2 , Ψ3 ⊂ R+ where m(x, y) and σ(x, y) are the gray-level mean and standard deviation computed in a neighbourhood centered at (x, y) and having n×n pixels. M is the global mean of the image, f(x, y) is the gray-level intensity of input image pixel at location (x, y), while g(x, y) is the pixel’s output gray-level intensity value, at the same location. The original method (Gonzales 1987) allowed only for a reduced range of possible output transformation, as constants in (1) where taken as b = 0, c = 1, while the last term was not present. (H _size-1 , V _size-1) Pixel (x, y) g(x, y) = T(f(x, y)) n n

N eighb orhood

(0 , 0)

Figure 1. Block processing – applying to each pixel in the image the operation T ( •) in the neighbourhood

We have broadened the spectrum of the transformation output range by modifying the original method as shown in equation (1). In our modified method b ≠ 0 allows for zero standard deviation in the neighbourhood, c ≠ 0 allows for only a fraction of the mean m(x, y) to be subtracted from the original pixel gray-level, while the last term may have a brightening and smoothing effect on the image. The quantities m(x, y) and σ(x, y) depend on the neighbourhood of the pixel, therefore they are dependent on the local information. The parameters of the method a, b, c and κ are the same for the whole image. The task for the GA is to find the best combination of the four parameters according to an objective criterion that describes the contrast of the image. The representation of the chromosomes is therefore a string of 4 real genes denoting the four parameters. This representation is given in figure 2, where T (•) designates the operation given in equation (1).

g(x, y)=T(f(x,y); a, b, c, κ)

Chromosome x:

approach the uniform distribution, as in the case of histogram equalization techniques. We have found that the following fitness (to be maximised) is a good choice for an objective criterion:

F (x ) = log(log(E (I (x )))) ⋅

(2)

In equation (2) function F(x) denotes the fitness function applied to chromosome x, I(x) denotes the original image I with the transformation T applied according to equation (1), where the respective parameters a, b, c, κ, are given by the chromosome x = (a b c κ). E(I(x)) is the intensity of the edges detected with a Sobel edge detector (DaPonte 1988), 1 where the detector is applied to the transformed image I(x) . n_edgels denotes the number of edgel pixels as detected with the Sobel edge detector. The term H(I(x)) is a measure of the entropy in the image I(x). H_size, V_size are the horizontal and vertical sizes (number of pixels in each direction) of the image. The Sobel detector used, is an automatic threshold detector (Rosin 1997). The sum of intensities of edges E(I) included in the enhanced image is calculated by the following expression (DaPonte 1988):

E (I ) =

∑∑ x

Figure 2: Chromosome representation

2.2 Objective enhancement criterion and fitness function In order to apply an automatic image enhancement technique, which does not require human intervention, and no objective parameters given by the user, a criterion for enhancement method should be chosen. This criterion will be directly related to the fitness function of the GA. Let us proceed by noting that a good contrast and enhanced image has a high number of edgels (that are pixels belonging to an edge). Also, an enhanced image has a high intensity of the edges compared to a non-enhanced variant of the same image (Saitoh 1999). The number and intensity of edgels are not enough to describe a valid fitness criterion for a more naturally enhanced image. The problem is that an image can have an extreme contrast with sharp transitions from white to black (or conversely, from black to white), and a relatively small number of gray levels (histogram of the image with two peaks: each one placed at the extremities of the gray-level intensity interval). In this case the image will have a relatively high number of edges and a very high intensity of edges. A criterion that is proportional to number and intensities of edgels might give an oversized credit to an image that doesn’t have a natural contrast. What is needed is a quantification of the number of gray-levels present in the image, or equivalently the histogram of the image should

n _ edgels(I (x )) ⋅ H (I (x )) H_size × V_size

δh I ( x, y ) 2 + δv I ( x, y ) 2

(3)

y

δh I (x, y ) = g I (x + 1, y − 1) + 2 g I (x + 1, y ) + g I (x + 1, y + 1) − g I (x − 1, y − 1) − 2 g I ( x − 1, y ) − g I ( x − 1, y + 1) δv I ( x, y ) = g I ( x − 1, y + 1) + 2 g I ( x, y + 1) + g I ( x + 1, y + 1) − g I (x − 1, y − 1) − 2 g I ( x, y − 1) − g I ( x + 1, y − 1) As the GA tries to find the solution x_sol that maximizes the fitness, it means that we perform the operation described in equation (1), as to: a) increase the relative number of edgels in the image; b) increase the overall intensity of edges, and c) increase the entropic measure in the image. Increasing the measure of entropy means, equivalently, transforming the histogram of the image to one that aproximates a uniform distribution. According to the definition of histogram equalization (Jain 1991), this means that we actually perform histogram equalization by maximizing the measure of entropy. We have chosen the entropic measure because it is easy to integrate into the fitness function.

1

Note that we used a log-log measure of the edge intensity not to over emphasize this parameter when compared to the others in the fitness function. Large values for edge intensity might produced extreme contrast, and un-natural images.

2.3 Selection and crossover Both the selection and crossover of the real-coded GA have been used to insure a steady convergent behaviour of the GA. The trade-off we had to make is the well known trade-off between exploration and exploitation present in any search method including GA. The convergent exploitation assured by selection and crossover should well-balance the wide exploration effect achieved by our mutation operator. The selection method was chosen as a combination between binary tournament which has a constant and relatively high selection pressure (Miller 1996), with a K – elitist scheme (Bäck 1991) that assures the preservation of the K best individuals in the population. The crossover operation was chosen such that the correlation between the parents and the children would be high, again to assure an exploitative behaviour of the search algorithm. We chose arithmetic crossover (Michalewicz 1996), between several choices of real-coded GA crossover operators like α-BLX (Eschelman 1993), SBX (Deb 1999), and UNDX (Ono 1997), because in the case of arithmetic crossover, offspring genes are close to the parents’ genes as they are produced inside the line connecting both parental 2 genes . Arithmetic crossover is defined as follows:

x1o = ax1p + (1 − a )x 2p , x 2o = (1 − a )x1p + ax 2p

(4)

where x{p1, 2} are the parents chromosomes, x{o1, 2} are the offspring and a is a randomly generated number drawn from a uniform distribution: U([0, 1]). 2.4 PCA-mutation Mutation operator has been chosen to insure high levels of diversity in the population. We introduced PCA-mutation in (Munteanu 1999b), and shown that it has very good capabilities in maintaining higher levels of diversity in the population. We briefly summarize the PCA-mutation operator, as follows: The population X of the GA can be viewed as a cloud of N points in a l-dimensional space, where N is the size of the population and l is the length of the chromosome. It can be shown (Munteanu 1999b) that a GA converging has the effect of decreasing the number of Principal Components (PCs) as calculated with the Principal Components Analysis (PCA) method on data cloud X. This comes as a result of the loss of diversity in the population as the GA moves on. In order to combat the loss of diversity we designed a method of mutation that tends to homogenize the components, preventing the population from having a small number of PCs while the other components are close Other possible crossover operators like SBX, UNDX, αBLX allow for the children to cover a wider space, but in our application what is needed is more“focused”exploitative crossover operator.

2

to zero. A detailed description of PCA method can be found, for example, in the textbook (Fukunaga 1967). It suffices here to say that after calculating the orthogonal basis of eigenvectors V = (v i )i =1...l and the corresponding eigenvalues λi , i = 1...l (arranged in decreasing order of magnitude), from the data cloud X, we project the data cloud X onto the basis V. Then, we take some random numbers c ij in a predefined interval [0, c max ] and pre-sort them in increasing order of magnitude: c ij , such that:

K

K

c ij−1 ≤ c ij ,∀i = 1 l , j = 1 N

. The mutation does the following

operation to the projected population:

∀i

( ) 2 = Prv (x j ) + c ij−1 j = 1KN 2 2 Prvmutated (x j ) = Prv (x j ) + c ij

Prvmutated xj i −1 i

2

i −1

(5)

i

( )

where Prv x j i

is the projection of X onto eigenvector

mutated

v i and Pr is the projected population after applying the operation in (5). The final operation is the inverse projection mutated to the initial coordinate system, after taking care of Pr that negative and positive projected coordinates will be remapped back into negative and positive coordinates, respectively. A detailed presentation of PCA-mutation can be found in (Munteanu 1999b). As shown both theoretically and empirically in (Munteanu 1999b), PCA-mutation can attain very high levels of population diversity, and when counterbalanced with an exploitative selection and crossover scheme, the strategy can be quite effective in preventing genetic drift and premature convergence. One potential disadvantage of PCA-mutation is the fact that it is computationally expensive when the length of the chromosome l increases. However, in our application this is hardly the case, as l is quite small (l = 4).

3 Experimental results In order to evaluate our GA-based enhancement method, we compared, on 8 images, our method with other two automatic enhancement methods: linear contrast stretching and histogram equalization. Both subjective evaluation of results and objective evaluation criterion were employed to rank the methods. Results for the GA-based method were given for typical runs of the GA. We found that suitable intervals in equation (1) are Ψ1 = [0, 1.5], Ψ2 = [0, 0.5], Ψ3 = [0, 1]. The GA employed has the following parameters: population size N = 40 individuals, chromosome length l = 4, binary tournament and K-elitism with K = 5, generational type replacement, arithmetic crossover with Pc = 0.8, PCAmutation with Pm = 0.3 and cmax = 1. In table 1 the names of

the images are given along with parameters specific to the respective image.

brightness/contrast appears good for these images (see figure 3), the fact that our method adds an averaging effect on the image seems to have biased the human evaluators into not favouring the GA-based method.

Table 1. Image sizes and number of maximum generations for the GA run

Image a) abdomen b) airplane c) cameraman d) eight e) head f) house g) pout h) tire

Size (pixels) 256 × 256 512 × 512 256 × 256 242 × 308 256 × 256 256 × 256 291 × 240 205 × 232

GA max no. of generations 40 50 40 40 40 40 50 40

In table 2 the fitness, calculated with equation (2) is given for each image and each method employed. From this table it is clear that the fitness criterion defined in (2) gives much better scoring to our proposed method. The other techniques (linear contrast stretching) and histogram equalization receive much less scores. Histogram equalization scored better than contrast stretching only on the pout image.

Table 2. Results in terms of fitness score

Image / fitness a) abdomen b) airplane c) cameraman d) eight e) head f) house g) pout h) tire

Linear Stretching 1.5391 69.797 33.070 26.210 25.578 47.037 13.525 0.899

Histogram equalization 0.801 29.991 8.917 7.007 10.666 19.271 13.566 0.380

GAbased 11.296 257.364 100.975 159.947 140.837 230.031 124.001 2.394

3.1 Subjective evaluation In order to evaluate the performances of the image enhancement techniques, subjective evaluation of images produced by the three methods involved in comparison (GAbased, histogram equalization and linear contrast stretching), was done by 6 human interpreters. Each image had to be ranked by giving a score ranging 1 to 3, the best score being 1, with no ties allowed. The subjective criterion for ranking was natural brightness/contrast for the enhanced images. Results are given in table 3. From this table it can be seen that our GA-based method ranks best when globally ranked (see the “Total rank” row in the table), and ranks best for each image, but the airplane and tire images. Even if the

Table 3. Subjective evaluation results (lower rank value is better) Method

Rank a) b) c) d) e) f) g) h) Total rank

Linear Stretching 1 2 1 2 3 3 2 3 1 4 1 3 1 3 3 1

3 3 0 1 1 2 2 2

Avg

2.3 1.5 1.8 2.0 2.1 2.1 1.8

Histogram equalization 1 2 3 0 3 3 3 1 2 0 2 4 0 1 5 0 2 4 1 1 4 1 2 3

4

2

0

1

5

21

11

1.3 1.9

0

16

5

13

30

GA-based method Avg

2.5 1.8 2.6 2.8 2.6 2.5 2.3

1 5 0 4 5 5 4 2

2.8 2.5

2 27

3 0 4 1 0 0 0 1

Avg

3

1

14

7

1.8 1.6

2 1 2 1 1 1 2 3

1.1 2.6 1.5 1.1 1.1 1.3 1.8

The subjective fitness evaluation gives credit to our GAbased method in favour of the other methods. However, an objective criterion should also be employed to rank the methods. The objective evaluation results are given in the next subsection. 3.2 Objective evaluation The objective evaluation criterion was taken to be the Detail Variance (DV) and Background Variance (BV) described in (Ramponi 1996). DV and BV values are obtained as follows: firstly, the variance of the gray levels in the neighbouring pixels is calculated at each pixel in the image. Next, the pixel is classified to the foreground when the variance of the gray levels is more than a threshold, and the pixel is classified to the background when the variance of the gray levels is lower than the threshold. The averaged variance of all pixels included in the foreground class is DV, and the averaged variance of all pixels included in the background class is BV. When the DV value of the resulted image increases and BV is not changed compared to the original gray image, then it is supposed that efficient contrast enhancement has been achieved (Ramponi 1996). The DVBV criterion is far from being a perfect objective criterion, but merely gives an indication of how to evaluate the images in a more systematic way. In table 4 the obtained DV and BV values, are given, where the threshold was chosen to be 0.01 and the n × n neighbourhood: n = 3. From table 3, the results indicate a good behaviour of our GA-based method, better than the other methods for most images, however for the plane and pout images results might indicate otherwise.

a) abdomen

b) plane

e) head

f) house

c) cameraman g) pout

d) eight

h) tire

Figure 3. Enhancement results: upper left – original image; upper right – GA based method; lower left – histogram equalization; lower right – linear contrast stretch

Table 4. The DV and BV values for enhancement methods

Image

a) b) c) d) e) f) g) h)

Original DV

BV

Linear stretch DV BV

Histogram equalized DV BV

GA-based DV

BV

0.12

0.02

0.13

0.02

0.20

0.02

0.22

0.01

0.13

0.02

0.18

0.02

0.21

0.03

0.18

0.04

0.15

0.02

0.18

0.02

0.21

0.03

0.17

0.02

0.17

0.01

0.19

0.02

0.16

0.04

0.20

0.04

0.13

0.03

0.12

0.03

0.13

0.06

0.13

0.04

0.17

0.02

0.18

0.02

0.18

0.04

0.19

0.04

0.18

0.01

0.15

0.02

0.15

0.04

0.14

0.01

0.14

0.01

0.16

0.01

0.38

0.00

0.17

0.01

However, DV is not always reflecting precisely the detail content level in the image because one can note from figure 3 that airplane image and pout image have more detail in the GA-based method’s case. A more objective explanation can be found by calculating the number of edgels as detected with the Sobel automatic edge detector. The image that contains the highest number of edgels can be rated as having high detail content. Table 5 gives these results for images airplane and pout. It is clear from this table that the GAbased method achieves the best detail content in images airplane and pout. One should note also, that in the case of the tire image, the histogram equalization method achieves high DV but at the cost of a very low BV, so this image (see figure 3), appears with good detail, but also very whitish.

increasing the number of generations the GA is let to run, compared to the maximum number of generations that was chosen (see table 1).

a)

b)

c)

d)

e)

f)

g)

h)

Table 5. The number of edgels in airplane and pout images

Image

Original

b) plane g) pout

3067 1492

Linear stretch 3067 1492

Histogram equalized 3008 1937

GAbased 3261 2039

3.3 Robustness Robustenss of the GA-based method is related with the repeatability of the results. To evaluate the robustness of the GA-based method 10 independent runs were performed for each image. Figure 4 gives the equivalent gray-level transformation between the input image and the output image for each run. In order to evaluate the repeatability of the experiments we should see that all the curves, for each image, have the same shape and be clustered together. The plots in figure 4 indicate a good behaviour of our GA-based method, also in terms of the repeatability of this method. Note that two outlier curves have been obtained for the house and pout images. The shape of these curves with abrupt slant, suggest that the images obtained for the respective curves were almost black and white (extreme contrast). Improvement of robustness may be achieved by

Figure 4. Input-output gray-level transformation for GAbased method

Summarizing the results obtained, our GA-based method proved to be efficient in image enhancement. Both human subjective evaluation and objective criterions like DV-BV and “number of edgels”, point out that our method produces better images than the classical linear contrast stretching and histogram equalization techniques, for a diverse set of images. On several images like the biomedical images: abdomen and head, the eight and tire images, our GA-based method achieved spectacular results, compared to results obtained by the other methods.

4 Conclusions In this paper we propose a new approach to automatic image enhancement using real-coded GA. Results obtained indicate that our method outperforms the classical point operations (linear contrast stretching and histogram equalization), which are also automatic methods, in terms of high effectiveness on a large category of images. The method applies a real-coded GA with significant modifications like PCA-mutation, in order to attain better explorative behaviour. To profit from this behaviour the GA uses high pressure selection scheme and a more exploitative scheme of recombination, that balance the exploratory effect of the mutation used. The search is therefore well-balanced, and robust (the same good results are achieved when experiments are repeated). Automatic behaviour was achieved by specifying a suitable fitness function proportional to the number and intensity of edgels in the image and to the entropic measure of the image. The fitness function is fully objective, no human subjective term being required. The GA evolves the parameters of a local enhancement method that better adapts to the local features in the image, in comparison to linear contrast stretching and histogram equalization that treat the image globally. Summarizing, our method applies a local enhancement technique driven by GA evolution, to achieve both automatic behaviour, i.e. method doesn’t require user interaction, and robustness, i.e. applicability to a large category of images, a combined goal that is not attained by other existent enhancement methods. Our method may be extended in several ways such as: fine tuning of the GA parameters in order to reduce the population size and maximum number of generations required. A more substantial extension is to be researched, in which the chromosome will code local parameters of the method that applies to each neighbourhood. Also, the trade-off between efficiency and computational cost will be investigated.

References Bäck T. and Hoffmeister F. (1991) “Extended Selection Mechanisms in Genetic Algorithms”, Proceedings of Fourth International Conference on Genetic Algorithms, San Mateo: CA,

Morgan Kaufmann, pp. 92-99. Backer E. (1993) “Evolving Line Drawings”, Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo: CA, Morgan Kaufmann, pp. 627. DaPonte J. S. and Fox M. D. (1988) “Enhancement of Chest Radiographs with Gradient Operators”, IEEE Transactions on Medical Imaging, vol. 7(2), pp. 109-117. Deb K. and H.-G. Beyer (1999) “Self-Adaptation in RealParameter Gentic Algorithms with Simulated Binary Crossover”, Proceedings of GECOO’99, Morgan Kaufmann, San Francisco: CA, pp. 172-179. Eshelman L. J. and Schaffer J. D. (1993) “Real-coded genetic algorithms and interval schemata”, Foundations of Genetic Algorithms II, pp. 187-202. Fukunaga K. (1972) “Introduction Recognition”, Academic Press.

to

Statistical

Pattern

Gonzales R. and Winter P. (1987) “Digital Image Processing”, Addison Wesley. Herdy M. (1996) “Evolution Strategies with Subjective Selection”, Parallel Problem Solving from Nature – PPSN IV, LNCS 1141, pp. 22-31. Jain A. K. (1991) “Fundamentals of Digital Image Processing”, Prentice Hall. Michalewicz Z. (1996) “Genetic Algorithms + Data Structures = Evolution Programs”, Springer Verlag. Miller, B. L. and Goldberg, D. E. (1996) “Genetic Algorithms, Tournament Selection and the Effects of Noise”, Complex Systems 9, pp. 193 - 212. Munteanu C. and Lazarescu V. (1999) “Evolutionary Contrast Stretching and Detail Enhancement of Satellite Images”, Proceedings of Mendel’99, Brno, Czech Rep., pp 94-99. Munteanu C. and Lazarescu C. (1999) “Improving mutation capabilities in a real-coded GA”, Proceedings of EvoIASP'99, LNCS, vol. 1596, Springer-Verlag, pp. 138-149. Ono I. and Kobayashi S. (1997) “A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover”, Proceedings of Seventh International Conference on Genetic Algorithms, San Francisco: CA, Morgan Kaufmann, pp. 246 – 253. Poli R. and Cagnoni S. (1997) “Evolution of Pseudo-colouring Algorithms for Image Enhancement”. Technical Report: CSRP-975, Univ. of Birmingham. Ramponi G., Strobel N., S. K. Mitra and T.-H. Yu (1996) "Nonlinear Unsharp Masking Methods for Image Contrast Enhancement " Journal of Electronic Imaging, vol.5(3), pp. 353366. Rosin P. L. (1997) “Edges: saliency measures and automatic thresholding”, Machine Vision and Applications, Springer Verlag, vol 9, pp. 139 – 159. Saitoh F. (1999) “Image Contrast Enhancement Using Genetic Algorithm”, Proceedings of IEEE SMC’99, Tokyo, Japan, pp. 899904. Zimmerman J. B., Pizer S. M., Staab E. V., Perry J. R., McCartney W. and Brenton B. C. (1988) “An Evaluation of the Effectiveness of Adaptive Histogram Equalization for Contrast Enhancement”, IEEE Transactions of Medical Imaging, vol 7(4), pp. 304-312.