A Novel Histogram-Based Fuzzy Clustering Method for Multispectral Image Segmentation

Fuzzy C-Means (FCM) clustering has been widely used in remote sensing and computer vision. However, when dealing with multispectral images, the conventional FCM regards spectral responses of all bands on each pixel as a feature vector and conducts image clustering by searching cluster centers in a multi-dimensional space. It is rather time-consuming due to the fact that it has to visit each pixel many rounds during the iteration procedure. Besides, it is sensitive to noise, which mainly results from its ignorance spatial information. In order to overcome these problems, a novel histogram-based fuzzy clustering method is presented in this paper. The proposed method clusters each band independently and fuses the results to form the final segmentation map. On each band, a spatial-spectral image is computed previously, and then the histogram of this image is exploited to find the initial clusters, which is followed by a clustering procedure directly performed on the histogram instead of image pixels. The experimental results over remote sensing images show that the proposed method can achieve more accurate results but uses less time.


Introduction
Fuzzy C-Means (FCM) is one of the most widely used techniques for image segmentation.It was first proposed by Dunn [1] and later extended by Bezdek [2].FCM has robust characteristics for ambiguity and is able to retain more original image information than hard or crisp methods [3].However, it is rather time-consuming when dealing with multispectral images, because it has to visit each pixel multiple rounds during the iteration procedure.Besides, it is also sensitive to noise because of its ignorance spatial information.
A variety of improved approaches were proposed to incorporate the spatial information into the original FCM, such as fuzzy local information C-Means (FLICM) [3], Enhanced Fuzzy C-Means Clustering (EnFCM) [4], HMRF-FCM [5], Zhang's method [6], and our proposed methods [7][8][9].All of them tried to improve the traditional FCM by introducing spatial information in different ways and achieved some excellent results in their intended realms.Among them, EnFCM has the best time efficiency because it performs the clustering procedure on the gray-level histogram of a newly generated image, which is a linearly-weighted sum image formed from the original image and its local neighbor average image.Due to the fact that the number of gray levels is generally much smaller than the size of the image, the execution time is significantly reduced.Unfortunately, this method is only suitable for segmenting gray-level image.For multispectral image, it has to convert it into a gray-level one previously, which may results much losses of important information.In this equation, represents the wavelength of the sinusoidal factor, is the orientation of the normal to the parallel of the Gabor function, represents the sigma of the Gaussian envelope, and is the spatial aspect ratio which specifies the ellipticity of the support of the Gabor function.For each pixel, the magnitude over all orientations is considered.In this paper, the parameters are set ∈ 2,4,6,8 , ∈ 0,45,90,135 , and 0.25 .This generates 4 4 1 1 16 different configurations of Gabor filters.After applying to the gray-level image on each band, 16 Gabor images are generated.We pick out the first component of the principles of the Gabor features to form the spatial image ζ .Then, the gray-spatial image is obtained by (2) where is used to control the effect of the spatial image, and the term is the band of the original image .

Let
, , ⋯ , be the histogram of .We determine the initial clusters by seeking the local peaks of .First of all, the discrete difference of is calculated in advance, which is denoted as .Then, a point 1 256 is a peak point if it satisfies: All peak points are employed as the initial cluster centers of the following fuzzy clustering procedure.In this paper, we perform a smooth filter on before calculating its difference to reduce the impact of image noise.Besides, two points with a distance smaller than a predefined threshold will be merged.

Histogram-based FCM
The objective function of the histogram-based FCM is defined as where is the prototype of the cluster, ( ∑ 1 ) represents the fuzzy membership of gray value with respect to cluster .By minimizing (4), and can be estimated: The iterative procedure of the histogram-based FCM is summarizes as follows: (a) Set values of , and ; (b) Initialize the cluster centers by using method described in 2.

Experimental Results
Many images are tested to evaluate the performance of the proposed MsHFCM algorithm.We demonstrate its effectiveness using only one remote sensing image, which was acquired by an unmanned aerial vehicle of Phantom 4 Advanced over an area of South Anyang, China, on Nov. 15,

The
The test road, and textures, w the difficul  Besides, we evaluate these algorithms with respect to two indicators: random index (RI) [12] and time consumed.RI takes a value between 0 and 1, with the values close to 0 indicating a bad segmentation result, and the values close to 1 indicating a good result.All indicators are recorded in Table 1.As can be seen from the table, the proposed method used less time but achieved the best accuracy.It is due to the fact that the histogram-based method greatly accelerates the clustering procedure.Such a result clearly illustrates the success of the basic idea of proposed method to combine the merits of EnFCM and AHFCM.

Conclusions
This paper presents a novel histogram-based FCM algorithm.It inherits the merits of AHFCM to independently cluster each spectral band and fuse the labels to form the final result.It also inherits the merits of EnFCM to incorporate spatial information by a newly precomputed gray-spatial image and execute histogram-based clustering for the sake of time efficiency.Experimental results have shown the superiority of the proposed method.

2 . 1 ;
(c) Set the loop counter 0; (d) Calculate the membership matrix and cluster centers by (5); (e) If max then stop, otherwise, set 1 and go to Step (d).

Figure 2
Figure 2 R