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Medical image segmentation based on non-parametric mixture models with spatial information

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Abstract

Because of too much dependence on prior assumptions, parametric estimation methods using finite mixture models are sensitive to noise in image segmentation. In this study, we developed a new medical image segmentation method based on non-parametric mixture models with spatial information. First, we designed the non-parametric image mixture models based on the cosine orthogonal sequence and defined the spatial information functions to obtain the spatial neighborhood information. Second, we calculated the orthogonal polynomial coefficients and the mixing ratio of the models using expectation-maximization (EM) algorithm, to classify the images by Bayesian Principle. This method can effectively overcome the problem of model mismatch, restrain noise, and keep the edge property well. In comparison with other methods, our method appears to have a better performance in the segmentation of simulated brain images and computed tomography (CT) images.

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Abbreviations

f :

Probability distribution function

X 1, . . . , X N :

Independent and identically distributed samples

e i :

The orthogonal basis

L 2([a, b]):

Hilbert orthogonal base of space

1/s :

The smoothing parameter

\({(a_{0,j},a_{1,j},\ldots,a_{K_{N_{j}},j})}\) :

The estimate of Fourier coefficients of condition probability density function

\({K_{N_j}}\) :

The point of cutoff in the expansion of cosine

N j :

The number of pixels of the jth class

g(1/s):

The Mean Integrated Squared Error (MISE)

N:

Sample number

h ij :

A spatial function

\({P(j|\bar{{x}}_i )}\) :

The probability of the neighboring pixels of x i labeled as \({\bar{x}_{i}}\) belonging to the jth class

NB(x i ):

A square window centered on pixel x i in the spatial domain

n :

The size of neighborhood

P NB(j|x i ):

The weighted posterior probability of current pixel x i with neighboring information

w j :

The weight of the jth component of mixture models

f j (x|θ j ):

The density function of the jth component

K :

The number of classes

j(x i ):

Represents the label of the class of the pixel x i

F(I):

Image segmentation quality criterion

I :

The image to be segmented

R :

The number of regions in the segmented image

A i :

The area or the number of pixels of the ith region

e i :

The average number of wrongly classified pixels of region i

C 1, C 2 :

The original image and segmented image of each pixel in the region

x :

The gray level of the pixel

α :

Threshold

P, R :

The quantities precision and recall

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Authors and Affiliations

  1. School of Computer Science and Telecommunication Engineering, Jiangsu University, Room 522, Zhenjiang, Jiangsu Province, People’s Republic of China

    Yu-Qing Song, Zhe Liu, Jian-Mei Chen, Feng Zhu & Cong-Hua Xie

  2. School of Computer Science, Jilin Nomal University, Sipin, Jilin Province, People’s Republic of China

    Zhe Liu

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  1. Yu-Qing Song
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  2. Zhe Liu
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  3. Jian-Mei Chen
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  4. Feng Zhu
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  5. Cong-Hua Xie
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Correspondence to Zhe Liu.

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Song, YQ., Liu, Z., Chen, JM. et al. Medical image segmentation based on non-parametric mixture models with spatial information. SIViP 6, 569–578 (2012). https://doi.org/10.1007/s11760-010-0185-5

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