Medical image segmentation method and apparatus
View Patent ↗A medical image segmentation method includes: step 1 , initialize of the number of clusters and determine the initial values of the cluster centroids; step 2 , calculate a Hausdorff distance between each cluster centroid and each pixel in the image; step 3 , calculate a membership function of each pixel based on the Hausdorff distance and a Euclid distance between the cluster centroids and each pixel; step 4 , calculate an objective function, cluster the pixels of the image based on the updated membership function, and update the centroid value; and repeating step 2 - 4 , until a difference between two objective function values is less than a threshold value. Then the membership function from the last iteration is a final segmentation.
1. A medical image segmentation method, which comprises the following processing steps:
step 1 , initialize the number of clusters and determine the initial values of cluster centroids;
step 2 , calculate a Pseudo-Hausdorff distance between each cluster centroid and each pixel in an image;
step 3 , calculate a membership function of each pixel being a member of a cluster based on the Pseudo-Hausdorff distance and an Euclid distance between each cluster centroid and said each pixel;
step 4 , calculate an objective function, cluster the pixels of the image based on the membership function, and update the values of the cluster centroids; and
repeat step 2 - 4 , until a difference between the objective function values of two consecutive iterations is less than a threshold value, and then the membership function from the last iteration is a final segmentation.
2. The medical image segmentation method as claimed in claim 1 , wherein the initial values of the cluster centroids are calculated by an image histogram where differences between each centroid are the same.
3. The medical image segmentation method as claimed in claim 1 , wherein the step of calculating the Pseudo-Hausdorff distance between each cluster centroid and each image pixel comprises:
choose several neighbor regions with said each image pixel at the center, calculate a mutual information between each chosen neighbor region and the centroids;
select the neighbor region that has the maximum mutual information value; and
calculate the Hausdorff distance between said each centroid and the selected neighbor region as the Pseudo-Hausdorff distance between said each cluster centroid and said each image pixel.
4. The medical image segmentation method as claimed in claim 3 , wherein the several neighbor regions are defined by rectangular regions with a width and height of 3, 5, and 7 pixels.
5. The medical image segmentation method as claimed in claim 3 , wherein mutual information between sets A and B are determined by
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where p(i,j) is the joint distribution function of sets A and B, p(i) and p(j) are the distribution functions for sets A and B, respectively.
6. The medical image segmentation method as claimed in claim 5 , wherein the Hausdorff distance between sets A and B is calculated by
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and wherein the Pseudo-Hausdorff distance between a centroid v k and a pixel i with value x i , ∥x i −v k ∥ H , is d H (A,B), with A being a set consisting of the centroid v k and B being a set consisting of values of the pixels belonging to the selected neighbor region centered at pixel i.
7. The medical image segmentation method as claimed in claim 6 , wherein the membership function of each pixel is determined by the Pseudo-Hausdorff distance and Euclid distance between the pixel and the centroids, the equation for calculating the membership function is
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where x i is the gray scale value of pixel i, v k is the centroid, c is the amount of centroids, α is determined by the image resolution and contrast, ∥x i −v k ∥ is the Euclid distance between x i and v i .
8. The medical image segmentation method as claimed in claim 7 , wherein the objective function is J=Σ i=1 n Σ k=1 c u ik m ∥x i −v k ∥ 2 +αΣ i=1 n Σ k=1 c u ik m ∥x i −v k ∥ H 2 where n is the number of the image pixels, c is the amount of centroids, x i is the gray scale value of pixel i, v k is the centroid, α is the empirical parameter and m is 2.
9. The medical image segmentation method as claimed in claim 7 , wherein the equation to calculate the updated centroids is
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where x i is the gray scale value of pixel i v k ′ is the updated centroid of v k , n is the number of the image pixels, and m is 2.