A CHANGE DETECTION METHOD FOR REMOTE SENSING IMAGE BASED ON MULTI-FEATURE DIFFERENCING KERNEL SVM

Based on the support vector machine (SVM) tools and multiple kernel method, the combinations of kernel functions were mainly discussed. The construction method of image differencing kernel with multi-feature (spectral feature and textural feature) has been developed. Through this method and weighting of the categories’ samples, the improved SVM change detection model has been proposed, which could realize the direct extraction of spatial distribution information from several change classes. From the experiments we can draw the following conclusions: with the help of multiple kernel function integrating spectral features and texture information, the new change detection model can achieve higher detection accuracy than the traditional methods and is suitable for the small-sample experiment. Furthermore, it avoids the complex and uncertainty in determining change threshold required in the old detection methods.


Introduction
As for remote sensing image change detection, it is feasible in many application areas to construct the decision hyperplane based on single kernel function in feature space.But different feature space cannot be effectively described by single kernel function [1,2] .In addition, it will cause a large amount of computation if classification is handled with many combined types of feature space, or if the sample feature contains heterogeneous information.Meanwhile, single-core approach is unreasonable and circumscribed in the case of uneven data distribution on high-dimensional feature space.In recent years, a new hotspot in Kernel machine learning has been developed for the above problems, i.e., kernel combination method [3] .The advantage of combining kernel function of different features to form a multi-class kernel function has higher mapping performance and more flexibility [4,5] .
With the multiple kernel method, the integration of remote sensing image multi-feature such as spectral and textural feature, an improved support vector machine

Texture feature extraction based on gray level co-occurrence matrix (GLCM)
Gray Level Co-occurrence Matrix (GLCM) is a valid description of image texture, which is a tabulation of pixel brightness values (grey levels) occur in an image [6] .For an image I of size M×M whose gray value are i and j respectively, then the gray level co-occurrence matrix containing some certain spatial relationships is defined as the formula (1): Where = #{x}denotes the number of elements in the set, r 1 , c 1 ) and (r 2 , c 2 ) is a point pair on the image space, r 1 ,c 1 ,r 2 ,c 2 represents the pixel coordinates of the two points in the image respectively.
Let d represent the distance of the point-pair and α the direction of the two pixels, we will obtain the GLCM р i, j, d, α which varies with the distance d and the direction α.Usually, the direction α is assigned by 0°, 45°, 90°and 135° to construct 4 gray level co-occurrence matrixes while the value of pixel distance d should be decided by the nicety of the texture needed analysis.
Here in this article, five statistical quantities were chosen to realize the remote sensing image change detection [7,8] , whose formulas and physical mathematical properties are shown in the Table .1 as follows [9] .

Generation of the spectral dimension feature set
In this paper algebraic algorithms and transformation are applied to the generation of the spectral dimension feature set for the remote sensing image change detection including the following aspects:

2) Vegetation index (VI)
When we select the vegetation index to realize extraction, the vegetation types of different growth stages and varied densities should be taken into account [10] .NDVI: Normalized difference vegetation index, which is the best index factor to measure and monitor plant growth (vigor), vegetation cover and biomass production, is linear correlation to the vegetation distribution density.

GVI: Green vegetation index
GEMI: Global environment monitoring index, which varies regularly and orderly with the vegetation cycle of ups and downs in landscape environment [11] .

Construction of multi-feature differencing kernel SVM detection model
Based on the introduction and definitions about the multi-feature SVM above, with the multiple kernel method and the integration of remote sensing image multi-feature (spectral and textural feature), we could propose an improved support vector machine (SVM) change detection model, in which a multi-kernel function on multi-feature space was combined after applying an independent kernel function for different feature space respectively.
x , x , , x X n  , the element Proof: Let K 1 and K 2 be the Gram Matrixes of K The eigenvector x of the image were presumed to be made up of vector quantities represented by x (p) , p=1,2,…, p, from p different information source, then the eigenvector x of the image can be signed by In response to the theorem and lemma above, the compound mode of kernel function based on different information source can be divided into three categories as below [12][13][14] : 2) weighted accumulation kernel function 3) intersect information kernel function For multi-spectral remote sensing images, x i denotes the eigenvector of each pixel in s i x represents the vector of texture information (spatial information) and w i x is the vector of spectral information.The specific expression of immediate accumulation kernel function and intersect information kernel function applied to the fusion of two types of feature information whose feature dimensions must be the same are given in the formula (9)   and (10).
In addition, a new image differencing kernel is able to be constructed simultaneously for the purpose of change information extraction [15] ., where l is the number of the sample) which are as two datasets mapped into a high-dimensional feature space in a nonlinear mode, where linear learning is realized .The difference of the samples on two time phases as a new input sample is calculated as the formula (11).Then Sample i turns to be ( 1)  ( 2) ( ) ( ) ( ) At the same time, the corresponding dot product of the kernel function can be expressed as the formula (12) [16] .In that case, the difference kernel function is in the form of the formula (13).
On the understanding that the sample feature at different phases contains spectrum information as well as texture information [17][18][19][20] , it is necessary to apply intersect information kernel function into the multi-feature information in the first place and then a difference kernel at varied time phases can be constructed on this basis [21] .
As a result the difference kernel function of different time phases based on multi-feature space comes out as follows the formula ( 14): ( 1) ( ) { ( ), ( ), } ( 1) Confessedly, the general expression for the solution to SVM optimization in dual form can be described as: Thereupon, put the formula (14) into the one above and then we come at the multi-feature difference kernel SVM change detection model based on multi-feature difference kernel function in the form of the formula (15).
The combination of the multi-feature multi-kernel function and multi-phase difference kernel puts the immediate change information extraction into practice, bring the integration of a wide variety of information sources into effect and avoid the complexity and contingency of selecting threshold as well [23,24] .

Experimental results and analysis
We choose TM multispectral images on band 1~5 and band 6 of some certain islands in Yangtze River Delta Area taken on April, 25 of 2008 and July, 17 of 2009, in which the square measure of the experimental area is 5625 hectares.Compared with the land-use map, the main surface features in this experimental area are divided into five categories, signed water as C1, structures C2, buildings C3, vegetation C4 and bare ground C5 [25] .The original remote seining images at the band543-RGB from 2008 and 2009 are presented in Fig. 2.These experiments will be analyzed in detail as follows.2) Multi-feature information of images on every time phase including 6 dimension spectral feature and 6 dimension texture feature is extracted in method discussed in section 1 and 2. Fig. 3 shows the texture images on band 3, 4 and 5, in which the image from 2009 is taken as example.3) The intersect information kernel on and between different time phases can be acquired according to the combination model of the formula (10).3) The change results can be direct detected by multi-feature differencing kernel based on SVM, without the procedure for setting a threshold accompanied with redundant artificial interference.This leaves out the complexity and uncertainty in searching optimal threshold.

(Fig. 1
Fig.1 Flow chart of Multi-Feature Differencing Kernel SVM change detection model represent the gray level or reflection (radiation) rate in band m and n respectively in pixel (x, y) of the image.

3 )
Other index models SBI: Soil brightness index NDBI: Normalized difference building index NWI: New water index NDWI: Normalized difference water index

Fig. 2
Fig. 2 Remote sensing images of the experimental area

4 ) 4 (
According to formula (13), we begin with the construction of multi-feature difference kernel, where the kernel functions of each part were obtained through the intersect information kernel achieved from the processes above and then we set up the optimal separating hyperplane on the basis of the algorithm of multi-feature difference kernel based SVM.After the treatment above, we gained the change detection results of the experimental areas from 2008 to 2009 as shown in Fig.d) .In order to certificate the change detection model of multi-feature difference kernel based on SVM, three representative kinds of change detection methods, the change detection method in difference image on a single band with the highest precision (band 2), the first principal components change detection method and the method of simultaneous classification on multi-phases, were applied into the same test samples.Fig.4 (a), (b), (c) show the change detection results of the experimental areas as follows.In Fig.4,(a) shows the result of the change detection method in difference image on a single band with the highest precision (band 2); (b) shows the result of the first principal components change detection method; (c) shows the result of the method of simultaneous classification on multi-phases; (d) shows the result of the multi-feature difference kernel change detection based on SVM.It can be seen from Fig.4 that in image (a) and (b), there exist dramatic noise and a loss of edge information, which is obviously shown in the change area of ditch on upper side of the image.From image (c), we can find the method applied here better avoided the effect of noise, but mistook some vegetation area influenced by the radiation difference for change area because of the radiation difference of varied phase images.The comparison result of quantitative analysis was listed in the Table.

Fig. 4 1 )
Fig. 4 The change detection results of the experimental area.
also be seen as a combination of multi-kernel functions, it is just a simple summation of the different features and different phase.While the method of Multi-feature differencing kernel based on SVM a) applies the combined kernel functions, in which the data from different feature space is mapped through inputting into the corresponding kernel function, and then b) construct the multi-feature differencing kernel.These made the data in a new feature space be better expressed with effective fusion of information on different time phase, which are supported by higher level of the four accuracy indexes (i.e.overall detection accuracy, probability of detection, probability of miss and probability of false positive).

Definition 2 (The Equivalent Definition of Mercer kernel
column j is the matrix named K with l rows and l columns, which is also named Gram Matrix of K and is related to12x , x , , x n .):If(x,x ) K  is a continuously symmetric function of XX  , where X represents a compact set in R N and (x, x ) K  is semi-positive definite about any Gram Matrix of 12 x , x , , x X n  , (x, x ) K is the kernel function to meet the needs of Mercer.