Brain MR image segmentation algorithm Sigma-IFCM

Image segmentation is to put the image into non-intersecting area, so that each pixel in the region have some similar characteristics, in order for subsequent processing.

Image segmentation is one of the difficulties of image analysis, yet a common and effective image segmentation can meet different needs [1] [2]. In brain MR image analysis of the problem is particularly pronounced [3].

In a lot of image segmentation algorithms, fuzzy c-means (FCM) segmentation algorithm is the most widely segmentation.

Submitted by Dunn at the earliest, after Bezdek improvement [4]. Because fuzzy set theory on images of uncertainty a better description, FCM in medical image segmentation achieved good segmentation results. The earliest the FCM for medical image segmentation of brain is LiC L et al. [5]. As a result of medical image often have various unknown noise, therefore to segmentation brings great difficulties. Already have an improved FCM (IFCM) algorithm is used to resolve the problem, and achieved very good results in this [6]. On this basis, the paper presents a new algorithm, the FCM Sigma-IFCM (Sigma Improved Fuzzy C-Means) algorithm. This new algorithm used Sigma filter theory consider neighbor pixels and use the deburring and edge smoothing technique to correct segmentation of brain images. From experimental results, the segmentation algorithm than the IFCM has improved.

1 traditional FCM

Traditional FCM following the objective function for tuning:

Where x = {x1, x2 x3, ..., xn} as a DataSet; U = {uik} for fuzzy membership matrix, uik that KTH data belongs to a class of membership; V = {vi} collection for cluster centers; ||

xk-vi|| Indicates the distance of the xk and vi, measurement data points and cluster centers of similarity; m for fuzzy weighted index and 1 ≤ m < ∞, this article from m = 2; C number for clustering and 2 ≤ C < n.

Cluster centers calculation formula is:

Membership iteration formula is:

2 IFCM algorithm

To remove the effects of noise on segmentation, literature [7], modifying the FCM's objective function, but increased computational complexity.

While the literature [6] in each iteration process not only consider the pixel itself of gray values, also consider its neighboring pixel grayscale values, but only modified the d (t) calculated, on the other parts of the target function without modification. The following formula for literature, omit the superscript (t):

Other calculation process and some iteration formula is the same as the original FCM.

3 Sigma-IFCM algorithm

3.1 Sigma filter

The IFCM algorithm, consider neighbor points on the impact of the center point, regardless of the surrounding all eight neighbours.

Although this can eliminate the effects of noise on segmentation, but at the same time on each cluster edge causing effects that blur the edges of the cluster. Therefore, in the calculation of a pixel's neighbor, reference Sigma filters (i.e. Edge Preserve filter) theory. First calculate the mean value of all the neighbours and variance, and only consider grayscale values on the mean of a neighborhood in those places, so the number generally neighbor point is less than 8.

Mean μ is calculated as:

Where θ is a non-negative interval adjustment coefficient.

Other algorithm of calculation and IFCM is the same.

3.2 image smoothing

Due to the complexity of the brain image and segmentation, split the image always accompanied by Burr, spot, line edge concave inequality, through image smoothing, can remove orphaned Burr, black, smooth edge, fill area objective eyelet to improve image quality.

General use of smoothing n×n secondary matrix (n usually 3 to 5) for the template, line by line, column by column and image matching.

When the match is successful, then put in the template Center pixel point of segmentation results to and the neighboring pixel point of segmentation results. For a binary image, according to the secondary matrix 0, the distribution of 1 pixel, that is in the center of the pixel matrix from the "0" into "1", or "1" to "0".

3.2.1 deburring

Binary images are usually shown in Figure 1 of the 3 × 3 matrix deburring, including its three 90 ° rotation matrix formation.

The "X" can be any value that represents the pixel point here is not considered, when matrix template on the image, as long as the image moves and template match, put the template Center of "1" to "0". In the algorithm, while the image is not a binary image, but the same principle. That is, if the template Center "1" at the pixels into a cluster a, and the surrounding "0" at the pixel point into another type of cluster b, it becomes the center pixel is also included in cluster b, to remove the split after the brain image edges of burrs. At this point do not consider the "X" at the pixel's segmentation. 、

3.2.2 line smoothing and void fill, Department of

P > line Ministry smooth and holes filled method and deburring are the same, just different templates. Usually takes 2-3 × 3 matrix of smooth line, including its three 90 ° rotation matrix formation. Similarly, when a matrix template on the image, as long as the image moves and template match, change the template Center pixel's segmentation.

3.3 calculation steps

Sigma-IFCM algorithm for the objective function and the same as the original, FCM, such as the formula (1), calculated as follows:

(1) determine the number of cluster C, fuzzy weighted index m and iteration stops threshold ε;

(2) initialize cluster centers, General random generated C a cluster centers;

(3) initializes the membership matrix U (0);

(4) using the formula (4) calculation of d, note the neighbor's formula is (5);

(5) using the formula (2) the calculation of the various cluster centers V (t);

(6) using the formula (3) update U (t + 1);

(7) select a convenient comparison matrix norm to U (t) and U (t + 1), if ||

U(t+1)-U(t)|| ¡Ü ε, stop iteration, otherwise order t = t + 1 return (4);

(8) on the segmentation of images for deburring and edge smoothing.

At last.

Each pixel on each cluster centers have a membership, like cable point segmentation to membership largest cluster centers.

4 experimental results

The original of the IFCM segmentation and improved segmentation algorithm for Sigma-IFCM medical image segmentation.

The choice of brain MR image from Mcgill University simulation of MR simulation brain image database. Download brain image is an image of MR Tl-weighted. Download this study is the noise of 7 per cent and 9 per cent of the brain images, respectively IFCM algorithm and SigmaIFCM algorithm comparison, as well as evaluation of segmentation results as shown in table 1, figure data are 30 image segmentation based on the average of the results.

You can use three parameters to assess the performance of the algorithm: Under Segmentation (UnS), Over Segmentation (OvS) and Incorrect SegmentRate (InC) [6].

This three-parameter value smaller, better segmentation algorithm. All images into the brain white matter, gray matter, cerebrospinal fluid, and background. Formula (4) in the parameter value λ ξ and 0.47 and O.53 respectively. Formula (5) parameter θ of 1.2.

As can be seen from table 1, for the noise is 9 percent of the brain images, Sigma-IFCM algorithm three evaluation parameters in a different way than the original IFCM algorithm parameter value to small, especially the brain white matter and cerebral gray matter of segmentation is more prominent.

The description in this case the improved Sigma-IFCM algorithm than the original IFCM algorithm achieved better segmentation results. For 7% of the noise of the image, the IFCM algorithm Sigma-IFCM and segmentation than the overall effect is a slight advantage on the former, but the effect is not as good as the noise of 9 per cent is obvious. From these data, the more noise, image segmentation SigmaIFCM algorithm better. Figure 3 is the segmentation of brain image before, (a) is original and no noise simulation MR Brain images; (b) is a 9 per cent of the noise of analog brain images. Figure 4 is the segmentation criteria and after two algorithms for segmentation of brain images.

The article presents an improved IFCM brain MRI image segmentation algorithm.

As a result of medical image generally have various unknown noise, using ordinary segmentation algorithm will have a significant impact on results. This article by SigmaIFCM algorithm improved pixel neighbor of choice programme, on the basis of eliminating noise remains split after the smooth edges of the image properties, and then reference the deburring edge smoothing techniques to modify partition image. Statistics show that on segmentation results improved significantly. Future work on the initial place point selection to do some research. The initial point in this article as the surrounding neighborhood of 8 pixels, you can consider the larger as the surrounding neighborhood of 24 points. In addition, deburring and edge smooth way to further research and discussion.