A vectorial image soft segmentation method based on neighborhood weighted Gaussian mixture model.
Summary (1 min read)
1. Introduction
- The CT uroscan is the classical preoperative examintio for renal surgery.
- It consists of three to four time-spaced 3D acquisitions at several contrast medium diffusion stages, which give complementary information about the kidney anatomy.
- Getting the material probabilities by a soft segmentation method [2] instead of assigning a definite material to the voxels (especially the boundary voxels) will be more conformable to the reality.
- In order to integrate spatial information to the Gaussian mixture model based vectorial data segmentation method, the authors proposed to involve a neighborhood weight within the classification process.
2. Gaussian mixture model
- Each component density follows a Gaussian distribution.
- Based on statistical theory, the parameters are estimated by maximum likelihood (ML) and expectation maximization (EM) algorithm is used as an optimization method.
- Recall that the goal is to estimate the class probabilities on each voxel according to the intensity vectors.
3. Proposed neighborhood weighted method
- The iteration formula described in section 2 didn’t involve any spatial information about current voxel.
- The authors use Eq. (9) to just smooth the class decisions after classification with the classical Gaussian mixture model.
- The results are shown in Fig. 3. Fig. 3(a) illustrates the intensity distribution summation along three axes of the original image.
- Because of the inhomogeneity of the acquisitions and the partial volume effects, the result of the intensity-only method has some misclassification area, especially the renal cortex and the renal medulla because of their close intensity range, which is shown in Fig. 6(a).
- While taking the neighborhood information into the iteration process, the results are improved significantly, as shown in Fig. 7(b).
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Citations
140 citations
Cites methods from "A vectorial image soft segmentation..."
...The traditional Expectation-Maximization algorithm was slightly modified by introducing a context-sensitive penalty term (Tang et al. 2009): this way, at each iteration of the algorithm, the probability that a voxel belongs to a certain class depends not only on the voxel’s intensity, but also on…...
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52 citations
Cites background or methods from "A vectorial image soft segmentation..."
...We therefore apply a previously proposed [23] adaptation to the E-step....
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...Context-sensitive expectation-maximization In [23], the authors introduced contextual information into the traditional GMM-EM method as follows....
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...In reality, and intuitively, we can expect a certain voxel's value to be affected by those in its neighborhood [22,23]....
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...Because the traditional GMM-EM method is based only on intensity information, we use a modified GMM-EM method, initially proposed in [23], that considers additional contextual information....
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45 citations
Cites methods from "A vectorial image soft segmentation..."
..., incorporating spatial information [8–10], are introduced to make FCM and EM robust against noise to some extent....
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25 citations
Cites methods from "A vectorial image soft segmentation..."
...[10] H....
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...GMM parameters are estimated from training data using he iterative expectation-maximization (EM) [10]....
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14 citations
Cites background from "A vectorial image soft segmentation..."
...GMM-MT has later been extended by applying either a weighted arithmetic or a weighted geometric mean template to the conditional and the prior probability, called ACAP, ACGP, GCGP and GCAP [22, 23]....
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...Another approach incorporates local spatial information directly by using a mean template (GMM-MT) [21]....
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...The spatial information can be introduced in GMM as a weighted template for computing the conditional probability of xi by its neighbor probabilities [21, 23]....
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...This twostep approach allowed us to adapt the neighboring template of GMM-MT according to the image content....
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References
8 citations
"A vectorial image soft segmentation..." refers methods in this paper
...[14] proposed to use a multi-resolution Gaussian mixture...
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8 citations
"A vectorial image soft segmentation..." refers methods in this paper
...The first step in this integration process is to bring the different acquisitions into spatial alignment which has been done through a loc l mutual information maximization registration technique [1]....
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