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It is a well-known problem of remotely sensed images classification due to its complexity. This paper proposes a remotely sensed image classification method based on weighted complex network clustering using the traditional

Remote sensing is an all-round detective technology rose and rapidly developed from 1960s, which shows its superiority in urban planning, resources exploration, environment protection, land monitoring, agriculture, forestry, military and so on, and still develops its applications in breadth and depth.

Remotely sensed image classification is an important issue in remote sensing technique applications, whose goal is to classify the pixels in the remotely sensed images by ground-object categories. For example, the images are divided into many districts which represent forest, grass, lake, town, and other ground-object categories. Remotely sensed image classification can be carried on according to the following steps. First, feature parameters are analyzed and chosen according to the spectral characteristics of each ground-object. Second, feature space is divided into nonoverlapping subspaces. Then, each pixel vector in the images is assigned to each sub-space.

The classification of remotely sensed image is divided into supervised classification and unsupervised classification. The basic principle of supervised classification is to determine discriminant functions and corresponding criterion according to prior knowledge of classification, and the progress is to determine undetermined parameters in discriminant functions by taking advantage of a certain amount of samples’ observed values in known classifications, which is called learning, then, the samples’ observed values of unknown classification are put into discriminant functions, and the sample’s classification is determined according to the criterion. There are several kinds of commonly used supervised classification approaches. Minimum range classification is to use the distance in feature space to express element data and the similar degree of classified category characteristic. After each category characteristic parameter by the training data is obtained, the distance between the unknown element and each eigenvector or eigenvector represented is first calculated, and then the unknown element is assigned to the category with the least distance. Maximum likelihood classification is to calculate the likelihood of each pixel point by point and this pixel is assigned to the category corresponding to the maximum likelihood. This classification precision is high, but the assorting process is complex and the computing time is long. Parallelepiped classification carries on the classification with a simple decision rule to the remotely sensed data. Decision boundary in the image data space forms an

The nonsupervised classification [

The

The

The above classification approaches have been used for the mid- and low-resolution satellite remotely sensed image, which processes high spectrum in the universal applications, while the high-resolution remotely sensed image actually has many insufficiencies now.

This paper proposes one kind of new remotely sensed image classification method by the combination of the complex network architecture characteristic and the

In this paper, the first section is the introduction. The main principle of the complex network is briefly outlined in the second section, the remotely sensed image classification method based on complex network is proposed in the third section, and the fourth section shows simulated experiments and results analysis. Finally, the fifth section gives the conclusion and prospect.

Since the end of 20th century, complex network [

The statistical properties of the complex network architecture mainly have the average path length, the clustering coefficient, degree distribution, and betweenness.

In the network, the distance

The average path length

Generally, assume the node

Degree is a simple and important concept in the independent node attribute. Node

In the complex network, there are some nodes which are not very large, but they are actually significant like a bridge in the entire structure [

Let

Node accumulation coefficient [

At present the research for complex network mainly aims at the unweighted complex network. But in the realistic network, the weights of the edges are often dissimilar and will affect the performance of the entire network. The weighted complex network can better express the structure of the complex network than unweighted complex network. Comparing to the definition of the degree and the accumulation coefficients above, the definition of the nodes’ weighted degree, the weighted accumulation, and the weighted accumulation, coefficient below in the weighted complex network are given [

A node’s degree may be defined as the sum of the weights of this node and its all neighboring nodes, which is also called weighted degree, namely, the weighted degree

The node’s weighted degree reflects the joint strength between this node and other nodes. The larger the node’s weighted degree, the more this node is suitable to be the cluster center.

The clustering coefficient

The node’s weighted clustering coefficient manifests local interconnection density and the intensity of this node. The larger the node’s weighted clustering coefficient is, the more the node is suitable to be the cluster center.

The weighted network synthesis characteristic value of the node

The connection

For better cluster realization to remotely sensed image classification, overcoming sensitive shortcoming of the

In this paper, a vector which is composed of the pixels from the same location of each band is considered as a node. The similarity between nodes is taken as the weighted degree, which represents the connected degree of these two nodes. In addition, the weak connected edge that the value of weighted degree is smaller than the threshold is deleted.

The Kappa coefficient here is used to measure the agreement between two raters who each classify

Input: remotely sensed image.

Output: image classification, classified precision, Kappa coefficient.

The hyperspectral image file is read and pretreated. These include radiation adjustment processing, geometry correction processing, mosaic processing, and cutting out processing [

The band data is chosen to do the experiment according to the standard deviation and corresponding coefficients.

The weighted degree WD based on the formula (

The

The connected degree between pixel nodes is calculated based on the formula (

The threshold

The connected degree between

For the new cluster center, the distance between the sample and each new cluster center is computed and compared, and the sample is assigned to the class with the smallest distance.

For the new class, the cluster center is recalculated. If the results are completely the same with the previous results, then the assorting process ends. Otherwise, turn to Step

The proposed algorithm can be depicted by the following flow chart (Figure

Flow chart of the proposed algorithm.

These experiments are used to validate the accuracy of remotely sensed image classification method based on the eigenvalue and connected degree of complex network and compare the classification accuracy with

The experiment designs simulated experimental images of three bands with Gaussian noise. Suppose the noise of each band is independent identically distributed Gaussian random noise, with zero mean and variance 0.01. The size of simulated experimental image is

Classification results of simulated experimental images and different algorithms of three bands with added Gaussian noise.

Simulated noised experimental images

Classification results by

Classification results by ISODATA method

Classification results by the new method

The classification accuracy percentage is firstly calculated, and the statistical results are shown in Table

Classification accuracy percentage of simulated images by three classification methods.

Project | Class 1 | Class 2 | Class 3 | Classification |

accuracy | ||||

Ground truth | 4402 | 5482 | 6500 | 100% |

4359 | 5461 | 6474 | 99.5% | |

ISODATA classification method | 4359 | 5455 | 6478 | 99.4% |

New method based on complex network | 4387 | 5467 | 6477 | 99.6% |

From Table

The Kappa coefficient of classified result by the new method is computed below.

Confusion matrix is firstly calculated, and the results are shown in Table

Confusion matrix of classified results by proposed method based on complex network.

Project | Class 1 | Class 2 | Class 3 |
---|---|---|---|

Class 1 | 4387 | 7 | 8 |

Class 2 | 15 | 5467 | 0 |

Class 3 | 23 | 0 | 6477 |

Kappa coefficient | 0.9951 | ||

Kappa error | 0.0007 | ||

Maximum Possible Kappa | 0.9979 |

From the relationship between Kappa coefficient and classified accuracy in Table

The classification accuracy of algorithms is very important. In order to obtain more accurate classification precision, the parts of AVIRIS hyperspectral data are selected in the experiments, which is photographed in a remote sensing experimental plot of the northeast of the US Indiana in June 12, 1992 [

In the high spectrum remotely sensed image selected by the experiments, we should select the bands that are less polluted by the moisture noise because some bands are polluted seriously by the moisture noise. Band selection [

First the standard deviation of each band is calculated and arranged in descent order, as shown in Table

First 30 bands and standard deviation descending according to the standard deviation.

Band | Standard deviation | Band | Standard deviation | Band | Standard deviation |
---|---|---|---|---|---|

Band 29 | 1012.186414 | Band 33 | 866.810154 | Band 50 | 771.726478 |

Band 28 | 995.72999 | Band 23 | 864.978506 | Band 20 | 764.574815 |

Band 27 | 932.214293 | Band 31 | 856.363198 | Band 45 | 757.351603 |

Band 26 | 932.1544 | Band 43 | 853.999667 | Band 51 | 755.848178 |

Band 25 | 910.697106 | Band 22 | 839.800843 | Band 52 | 754.248011 |

Band 30 | 908.840288 | Band 44 | 837.885813 | Band 34 | 742.718947 |

Band 42 | 907.544127 | Band 39 | 807.049573 | Band 19 | 731.861102 |

Band 32 | 898.713883 | Band 21 | 797.873879 | Band 53 | 727.076556 |

Band 41 | 884.337735 | Band 48 | 788.812468 | Band 38 | 720.686685 |

Band 24 | 875.553739 | Band 49 | 775.506589 | Band 47 | 719.547723 |

Calculate the correlation coefficients (CCs) between two bands, as shown in Table

The correlation matrix of partial band.

CCs | Band | |||||||||

Band 29 | Band 30 | Band 31 | Band 32 | Band 33 | Band 34 | Band 35 | Band 36 | Band 37 | ||

Band | Band 29 | 1 | 0.99 | 0.99 | 0.99 | 0.99 | 0.96 | 0.87 | 0.47 | −0.16 |

Band 30 | 0.99 | 1 | 0.99 | 0.99 | 0.99 | 0.97 | 0.88 | 0.47 | −0.15 | |

Band 31 | 0.99 | 0.99 | 1 | 0.99 | 0.99 | 0.98 | 0.91 | 0.51 | −0.12 | |

Band 32 | 0.99 | 0.99 | 0.99 | 1 | 0.99 | 0.97 | 0.88 | 0.47 | −0.15 | |

Band 33 | 0.99 | 0.99 | 0.99 | 0.99 | 1 | 0.98 | 0.91 | 0.52 | −0.11 | |

Band 34 | 0.96 | 0.97 | 0.98 | 0.97 | 0.98 | 1 | 0.96 | 0.63 | 0.01 | |

Band 35 | 0.87 | 0.88 | 0.91 | 0.88 | 0.91 | 0.96 | 1 | 0.81 | 0.26 | |

Band 36 | 0.47 | 0.47 | 0.51 | 0.47 | 0.52 | 0.63 | 0.81 | 1 | 0.77 | |

Band 37 | −0.16 | −0.15 | −0.12 | −0.15 | −0.11 | 0.01 | 0.26 | 0.77 | 1 |

For the band having quite great similarity, we only need to choose one of the bands, between two essential factors the standard deviation and the correlation coefficient of the bands influenced, and we should choose bands with the larger standard deviation and smaller correlation coefficient between each other.

According to the standard deviation in Step

In order to compare the classification precision, the new algorithm, which is a nonsupervised classification approach, is compared with other two nonsupervised classification approaches, the

Figure

Raw remotely sensed data and classified results by different algorithms.

Real data of ground-object category

False color image synthesized by bands 42, 29, 120

Output result of

Output result of ISODATA algorithm

Output result of new algorithm

The classification accuracy of simulated experimental image by each classified method is counted below. In this experiment the image pixels are chosen as size of

Classification statistics of partial data.

Item | Category 1 | Category 2 | Category 3 | Classified |

precision | ||||

Ground data | 966 | 3446 | 1678 | 100% |

423 | 3525 | 2142 | 82% | |

ISODATA | 418 | 3487 | 2185 | 82% |

New algorithm based on complex network | 1251 | 3153 | 1684 | 90.4% |

The Kappa coefficient of the new algorithm based on complex network is calculated as follows: first the confusion matrix is calculated, which is shown as Table

Confusion matrix of classification results by new algorithm based on complex network.

Item | Category 1 | Category 2 | Category 3 |
---|---|---|---|

Category 1 | 883 | 315 | 139 |

Category 2 | 192 | 2377 | 121 |

Category 3 | 176 | 461 | 1424 |

Kappa Coefficient | 0.6353 | ||

Kappa error | 0.0085 | ||

Maximum possible Kappa | 0.8797 |

The merits of this algorithm are illustrated as follows. This paper chooses well the initial cluster center according to the connection among nodes and the nodes’ weighted network synthesis characteristic value and overcomes sensitive shortcoming of the

It overcomes the sensitive shortcoming of the

According to the connection of the node, cluster center is selected, which reduces the probability of selecting different nodes of the same kind as the cluster center, reduced the iterative times of the algorithm, and raised the algorithm efficiency.

This paper proposes a remotely sensed image classification approach based on the complex network eigenvalue and connected-degree combining weighted complex network synthesis characteristic value with