^{1}

^{1}

^{2}

^{1}

^{1}

^{2}

Genetic algorithm (GA) is designed to search the optimal solution via weeding out the worse gene strings based on a fitness function. GA had demonstrated effectiveness in solving the problems of unsupervised image classification, one of the optimization problems in a large domain. Many indices or hybrid algorithms as a fitness function in a GA classifier are built to improve the classification accuracy. This paper proposes a new index, DBFCMI, by integrating two common indices, DBI and FCMI, in a GA classifier to improve the accuracy and robustness of classification. For the purpose of testing and verifying DBFCMI, well-known indices such as DBI, FCMI, and PASI are employed as well for comparison. A SPOT-5 satellite image in a partial watershed of Shihmen reservoir is adopted as the examined material for landuse classification. As a result, DBFCMI acquires higher overall accuracy and robustness than the rest indices in unsupervised classification.

Novel techniques of image classification, including supervised and unsupervised classifications, have been developed and widely applied to the problems of pattern recognition. Supervised classification requires prior knowledge for the training of the classification model. Taking satellite image classification, for example, the prior knowledge, means the average and standard deviation of spectrum of each landuse. Such a prior knowledge has been taken as criteria and then the examined image is classified to the distinct object of interest referring to the criteria [

On the contrast, unsupervised classification can be implemented automatically by analyst-defined clustering criteria as the basis for classification rather than the training data set collected beforehand. Unsupervised classification groups a set of test data in such a way that the data within a class (cluster) are more similar in some identities to one another than in other groups. Unsupervised classification starts with a specific number of classes either arbitrarily in accordance with the research objectives or based on the analyst’s expertise and then interprets all pixels within a data set into a correspondent class pixel by pixel. In accordance with such a merit, unsupervised classification is more suitable for the interpretation of environment with fragmentary land cover for areas or the image detection without prior statistics of the training data from the study field [

Inspired by the nature evolution process, GA has been extensively and successfully applied to many practical problems, such as urban landscape change analysis [

Bandyopadhyay and Maulik [

Accordingly, GA operations can start the evaluation by individuals (so-called GA strings or chromosomes) of population (initial generation) being substituted over a specified number of generations which are consisted of the strings from one initial individual that swapped some segments between two strings (so-called crossover), so as to find the optimal fitness piece by piece [

In this research, the new index was verified for its feasibility and stability via various initial sets (i.e., different lengths of chromosome and numbers of populations), selection ways, and crossover ways.

GA, based on mimicking the natural strategies of evolution, can preserve the fittest which is one of the useful optimization techniques. A genetic string, so-called an individual, is encoded of a particular solution to a problem. And the solution must be able to express characteristics of the sample space. Before an operation of GA, a number of individuals are produced for the population of initial generation. Each genetic string is usually encoded by the types of binary, integer, or real number. After the operations of crossover and mutation, the possible solutions within the solution space are obtained and calculated their fitness according to a fitness function. Repeating the operations of evolution and preserving the fittest by selection, the possible solutions could be evaluated generation by generation until the optimal solution is derived.

A genetic string is the foundation for establishing a genetic algorithm and could describe a possible solution to a problem. It is made of units what can represent the characters of the problem. An individual is a bit string of arbitrary units. Basically, the meaningful string length must consist of at least two and upper genes [

Once the initial generation is randomly selected from the universal set, some strings, even number usually, with superior fitness are partially selected into the crossover pool. Afterwards, new members of population based on the operations of crossover and mutation were generated for the next generation [

Two typical parameters, including crossover probability

The purpose of mutation is to prevent GA from being trapped into local optimal solutions. A low mutation probability, typically between 0.001 and 0.01, is given because a high mutation probability would change GA to random search. Sivanandam and Deepa [

In each generation, the priority of the genetic strings is ranked according to the fitness values calculated based on a fitness function. Through either maximizing or minimizing the fitness values generation by generation, the genetic string with the global optimum could be found to be the terminal clustering result.

Currently, many indices, such as K-means index (KMI), separation index (SI), partition separation index (PASI), Davies-Bouldin index (DBI), and fuzzy C-means index (FCMI), have been presented to be the fitness functions of GA. Among the previous indices, DBI considers the inner differences within a cluster as well as the differences among the clusters so that the better clustering results could be acquired. However, rather than considering the influence between the other clusters, the specified pixel DBI considers only the influence between the specified pixel and the cluster it belonged to. FCM basically integrated fuzzy membership function with C-means clustering and then further integrating into GA as a fitness function, so-called FCMI, can be a complementary to DBI. Therefore, in this paper, DBFCMI, integrated FCMI with DBI, is built to attempt to obtain the better clustering accuracy.

Dunn [

The dissimilarity between classic set and fuzzy set.

Classic set

Fuzzy set

Unlike DBI, FCMI considers the influence between each pixel and all cluster centers. That is, the distance between a pixel and the pixels in the same cluster will be considerably less than the distance between a pixel and the pixels in different clusters. Of course the reciprocal influence of the former one is considered larger than the latter one. Also the membership grade is considered based on the same distance measurement. The objective function of FCMI is shown as (

In order to demonstrate the performance of DBFCMI, this research referred to the literature of Yang and Wu [

DBFCMI is mainly based on DBI. Furthermore, it evaluates distance between a pixel and the cluster centers based on fuzzy membership rather than the distance between the pixel and the cluster center which the pixel belonged to (see (

Fuzzy C-means index (FCMI)

Davies-Bouldin index (DBI)

Partition separation index (PASI)

Davies-Bouldin and fuzzy C-means index (DBFCMI)

There are two termination criteria for the GA operation, including the convergence of optimal solution searching or the specified number of generations that have evolved. Even though the latter termination criterion is adopted by most researchers [

The study site is a hillside within the watershed of Shihmen reservoir located in Northern Taiwan (see Figure

Spectral centers of landuse.

Landuse | Band | |||
---|---|---|---|---|

Spectral center | ||||

B1 (NIR) | B2 (G) | B3 (R) | B4 (SWIR) | |

Vegetation | 134.5 | 99.5 | 72.0 | 66.9 |

Water | 58.8 | 52.4 | 55.9 | 57.1 |

Forest | 112.1 | 98.3 | 57.3 | 58.4 |

Bare land | 128.9 | 93.9 | 72.9 | 65.9 |

Structure | 133.2 | 88.1 | 90.5 | 77.3 |

Standard deviations of the spectrum.

Landuse | Band | |||||
---|---|---|---|---|---|---|

Standard deviation | |
Threshold | ||||

B1 | B2 | B3 | B4 | |||

Vegetation |
27.2 | 22.1 | 7.2 | 4.0 | 27.2 | 22.1 |

Water | 13.5 | 12.8 | 11.5 | 6.6 | 13.5 | 12.8 |

Forest | 13.4 | 11.2 | 7.4 | 4.2 | 13.4 | 11.2 |

Bare land | 17.7 | 14.4 | 12.4 | 5.5 | 17.7 | 14.4 |

Structure | 27.3 | 16.6 | 32.3 | 22.1 | 27.3 | 16.6 |

(a) Location of the Shihmen reservoir; (b) location of the study site; (c) the subset satellite image of the study site; (d) subset aerial photograph with the same studied range; (e) distributions of ground truth.

Most indices whenever are integrated into GA might probably cause the excessive classifying. Therefore, expect the 5 categories of landuse in accordance with the surface; the other categories determined here by GA are all defined as the 6th landuse, so-called others.

We implemented different GA operations settings in order to verify the stable optimum of DBFCMI. In this research, the different populations consisting of 30, 60, 75, and 90 string numbers coupled with the given GA parameters, including maximal string length of 8 genes [

Overall accuracy of each index varying with populations.

Population | Index | ||||
---|---|---|---|---|---|

Overall accuracy (%) | |||||

DBI | FCMI | PASI | DBFCMI | Average | |

30 | 71.6 | 73.2 | 64.9 | 75.5 | 71.3 |

60 | 74.7 | 69.3 | 68.6 | 72.9 | 71.4 |

75 | 70.3 | 73.7 | 70.8 | 72.1 | 71.7 |

90 | 73.8 | 65.7 | 70.7 | 73.9 | 71.0 |

Standard deviation | 2.0 | 3.7 | 2.8 | 1.4 | — |

K-HAT of each index varying with populations.

Population | Index | ||||
---|---|---|---|---|---|

K-HAT | |||||

DBI | FCMI | PASI | DBFCMI | Average | |

30 | 0.36 | 0.34 | 0.24 | 0.48 | 0.34 |

60 | 0.35 | 0.24 | 0.07 | 0.33 | 0.25 |

75 | 0.37 | 0.31 | 0.29 | 0.39 | 0.34 |

90 | 0.32 | 0.21 | 0.16 | 0.36 | 0.26 |

Standard deviation | 0.02 | 0.06 | 0.10 | 0.04 | — |

Overall accuracy of each index varying with selection ways.

Selection way | Index | ||||
---|---|---|---|---|---|

Overall accuracy (%) | |||||

DBI | FCMI | PASI | DBFCMI | Average | |

Roulette wheel selection | 71.6 | 73.2 | 64.9 | 75.5 | 71.3 |

Rank selection | 68.3 | 47.7 | 69.1 | 75.1 | 65.0 |

Standard deviation | 2.3 | 18.0 | 3.0 | 0.3 | — |

K-HAT of each index varying with selection ways.

Selection way | Index | ||||
---|---|---|---|---|---|

K-HAT | |||||

DBI | FCMI | PASI | DBFCMI | Average | |

Roulette wheel Selection | 0.36 | 0.34 | 0.24 | 0.48 | 0.34 |

Rank selection | 0.19 | 0.06 | 0.10 | 0.39 | 0.19 |

Standard deviation | 0.12 | 0.20 | 0.10 | 0.02 | — |

The image classification results corresponding to overall accuracy and K-HAT values in Tables

The best result interpreted by the different indices varying with populations.

Optimal solution by elite selection in GA operations includes many ways. Two of them are adopted widely, that is, roulette wheel selection and rank selection. Thus, the two selection ways applied to the four indices were evaluated based on overall accuracy and K-HAT as well. The testing results presented in Tables

Figure

The best result interpreted by the different indices varying with selection ways.

In the way of crossover approaches, including single-point crossover (P1), two-point crossover (P2), multipoint crossover (P3), three-parent crossover (P4), ordered crossover (P5), and shuffle crossover (P6), related to the different indices, they were also tested in this research (see Tables

Overall accuracy value of each model varying with crossover ways.

Crossover way | Index | ||||
---|---|---|---|---|---|

Overall accuracy (%) | |||||

DBI | FCMI | PASI | DBFCMI | Average | |

P1 | 74.3 | 71.6 | 72.9 | 74.6 | 73.3 |

P2 | 71.6 | 73.2 | 64.9 | 75.5 | 71.3 |

P3 | 70.8 | 72.5 | 71.5 | 72.5 | 71.8 |

P4 | 68.8 | 74.5 | 68.9 | 74.7 | 71.7 |

P5 | 70.5 | 70.2 | 70.9 | 75.0 | 71.6 |

P6 | 68.7 | 64.2 | 56.0 | 75.0 | 73.3 |

Standard deviation | 1.2 | 3.0 | 1.4 | 0.2 | — |

K-HAT value of each model varying with crossover ways.

Crossover way | Index | ||||
---|---|---|---|---|---|

K-HAT | |||||

DBI | FCMI | PASI | DBFCMI | Average | |

P1 | 0.32 | 0.31 | 0.33 | 0.36 | 0.33 |

P2 | 0.36 | 0.34 | 0.24 | 0.48 | 0.34 |

P3 | 0.26 | 0.33 | 0.30 | 0.32 | 0.30 |

P4 | 0.29 | 0.35 | 0.34 | 0.36 | 0.34 |

P5 | 0.35 | 0.25 | 0.26 | 0.37 | 0.31 |

P6 | 0.23 | 0.20 | 0.10 | 0.39 | 0.23 |

Standard deviation | 0.05 | 0.06 | 0.09 | 0.03 | — |

Figure

The best result interpreted by the different indices varying with crossover ways.

Curve comparison of spectral centers between ground truth and landuse classified based on optimal solution of four indices.

Figure

According to the foregoing analysis, it is worth to notice that rather than classifying the number of landuses accurately but inconformity with the distribution, the ability of distribution determination possesses the crucial influence upon the optimal solution.

Figures

Curve comparison of overall accuracy based on four indices varying with different GA operations.

Curve comparison of K-HAT based on four indices varying with different GA operation.

Figure

Standard deviation comparisons of overall accuracy and K-HAT between the four indices varying with different GA operations.

This paper presented a novel fitness index, DBFCMI, in GA process for the unsupervised classification of SPOT-5 satellite image. For comparison, three indices, including Davies-Bouldin index (DBI), fuzzy C-means index (FCMI), and partition separation index (PASI), were also adopted in GA classification. The conclusion is drawn as follows.

Spectra of bare land and vegetation are as similar as forest in the tested image, so that it is difficult to discriminate the three landuses from each other with GA classifier. Therefore, in most conditions the best associated model of GA can only distinguish bare land and vegetation into forest.

Overall accuracy and K-HAT are stronger related to distribution of classified landuse than the number of classifications. Besides, except distribution, another critical influence is depending upon the area of landuse especially the landuse with a large area. The best overall accuracy of 75.5% and the best K-HAT of 0.48 were acquired by DBFCMI, with merely three landuses, including forest, water, and structure. However, except the distribution of water and structure which can be determined more identical than the other indices, the largest region of forest can be determined appropriately by DBFCMI as well. Therefore, the influence is not so critical even though the spectra of bare land and vegetation are too similar to forest to be distinguished.

Comparing with the three indices including DBI, FCMI, and PASI, FCMI and PASI are both based on fuzzy theory so that all the other cluster centers will be considered to influence each independent pixel more or less according to the distance between the pixel and the centers. On the contrary, DBI index based on the classic set theory identifies each pixel in the training data into only one cluster that reduces computation time but results in moderate accuracy. Basically, the physical phenomenon of the spectrum reflection resulted from the neighborhood objects is inevitable. However, sometimes the ideal performances of image classification are obtained by GA coupled with DBI rather than FCMI or PASI. DBFCMI has possessed both advantages of DBI and fuzzy theory and all the examination of this research had been demonstrated that it is effective in the unsupervised image classification. As a result, the best overall accuracy of DBFCMI, DBI, FCMI, and PASI is 75.5%, 75.0%, 74.9%, and 74.2% separately. DBFCMI presents 0.75% increment in the average of the other indices. Overall accuracy is promoted about 1.01% in average. On the other hand, the best K-HAT of DBFCMI, DBI, FCMI, and PASI is 0.48, 0.37, 0.39, and 0.39 separately. DBFCMI presents 0.1 increments in the average of the other indices. Accordingly, DBFCMI can almost promote K-HAT value to 26.13% in average.

Pixel

Total number of pixels

Total number of clusters

The membership value of

The centroid of

The number of pixels belonging to the

Standard deviation of the pixels in the

Minkowski distance of order

The

Total chromosomes of each generation

Membership function of pixel

Total pixels of

The mean of all of the cluster centers.

The authors declare that there is no conflict of interests regarding the publication of this paper.

^{N}