Robust unsupervised segmentation of infarct lesion from diffusion tensor MR images using multiscale statistical classification and partial volume voxel reclassification
机构：[a]Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China[b]Department of Neuroradiology, Beijing Tiantan Hospital, Beijing 100050, China重点科室医技科室放射科放射科首都医科大学附属天坛医院[c]Medical Imaging Processing Group, Institute of Automation, Chinese Academy of Sciences, No. 95 Zhongguancun East Road, Beijing 100080, China
This paper is supported by the National Science Fund for Distinguished Young Scholars of China under Grant No. 60225008, the Special Project of National Grand Fundamental Research 973 Program of China under Grant No. 2002CCA03900, the National Natural Science Foundation of China under Grant Nos. 90209008, 60172057, 30270403, 30370418, 60302016, and the National High Technology Development Program of China under Grant No. 2002AA234051. Appendix A Rajapakse et al. (1997) introduced the segmentation method of adaptive MAP estimation in details as described below. The process of segmentation is to find x that represents the correct tissue class at each voxel site given by image y . We attempt to find the MAP estimation from the image data. Here p ( x ∣ y ) is the posterior density of the segmentation x given the image y . Because the prior probability of image p ( y ) is independent of the segmentation x , from Bayesian theorem (19) p ( x | y ) α p ( x , y ) = p ( y | x ) p ( x ) The image data at a particular site i represents a noise-corrupted version of the signature of the tissue class at that voxel. We assume that the noise is additive, white, Gaussian, tissue dependent, and space variant. Here μ k , i , n k , I , and σ k , i , respectively, represent the mean image intensity of class k at site i , the noise signal at site i for tissue class k , and the standard deviation of the noise for the tissue class k at site i . The measurement model is characterized by the parameter set θ = { θ i , i ∈ I }, where θ i = { θ k,i = ( μ k , i , σ k , i ), k ∈ Λ }. If R k denotes the region or the set of all voxel sites belonging to tissue class k , then the conditional density p ( y ∣ x) can be written as (20) p ( y | x ) = ∏ k ∏ i ∈ R k p k ( y i | θ k , i ) = ∏ k ∏ i ∈ R k 1 ( 2 π ) σ k , i exp { − 1 2 ( y i − μ k , i σ k , i ) 2 } The probability density of x is given by a Gibbs distribution ( German and Geman, 1984; Pappas, 1992 ), having the form (21) p ( x ) = exp { − β ∑ c ∈ C V c ( x ) } where β is a normalizing constant and the summation is taken over all the cliques C over the image. A clique is a set of points that are neighbors of one another. By substituting Eqs. (20) and (21) in Eq. (19) and omitting the constant factors, the posterior probability is (22) p ( x | y ) α exp { − U ( x ) } where the energy function U ( x ) (23) U ( x ) = 1 2 ∑ k ∑ i ∈ R k ( y i − μ k , i σ k , i ) 2 + ∑ k ∑ i ∈ R k log ( σ k , i ) + β ∑ c ∈ C V c ( x ) The problem of finding the MAP estimate of the segmentation is same as the minimization problem of the energy function U ( x ).
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大类|2 区医学
小类|1 区神经成像2 区神经科学2 区核医学
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推荐引用方式(GB/T 7714)：
Li W,Tian J,Li E,et al.Robust unsupervised segmentation of infarct lesion from diffusion tensor MR images using multiscale statistical classification and partial volume voxel reclassification[J].NEUROIMAGE.2004,23(4):doi:10.1016/j.neuroimage.2004.08.009.
APA：
Li, W,Tian, J,Li, E&Dai, J.(2004).Robust unsupervised segmentation of infarct lesion from diffusion tensor MR images using multiscale statistical classification and partial volume voxel reclassification.NEUROIMAGE,23,(4)
MLA：
Li, W,et al."Robust unsupervised segmentation of infarct lesion from diffusion tensor MR images using multiscale statistical classification and partial volume voxel reclassification".NEUROIMAGE 23..4(2004)
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