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Journal ArticleDOI

A vectorial image soft segmentation method based on neighborhood weighted Gaussian mixture model.

01 Dec 2009-Computerized Medical Imaging and Graphics (Elsevier)-Vol. 33, Iss: 8, pp 644-650

TL;DR: A segmentation tool is presented in order to differentiate the anatomical structures within the vectorial volume of the CT uroscan to get a better classification result and is less affected by the noise.

AbstractThe CT uroscan consists of three to four time-spaced acquisitions of the same patient After registration of these acquisitions, the data forms a volume in which each voxel contains a vector of elements corresponding to the information of the CT uroscan acquisitions In this paper we will present a segmentation tool in order to differentiate the anatomical structures within the vectorial volume Because of the partial volume effect (PVE), soft segmentation is better suited because it allows regions or classes to overlap Gaussian mixture model is often used in statistical classifier to realize soft segmentation by getting classes probability distributions But this model relies only on the intensity distributions, which will lead a misclassification on the boundaries and on inhomogeneous regions with noise In order to solve this problem, a neighborhood weighted Gaussian mixture model is proposed in this paper Expectation maximization algorithm is used as optimization method The experiments demonstrate that the proposed method can get a better classification result and is less affected by the noise

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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A vectorial image soft segmentation method based on
neighborhood weighted Gaussian mixture model.
Hui Tang, Jean-Louis Dillenseger, Xu Dong Bao, Li Min Luo
To cite this version:
Hui Tang, Jean-Louis Dillenseger, Xu Dong Bao, Li Min Luo. A vectorial image soft segmentation
method based on neighborhood weighted Gaussian mixture model.. Computerized Medical Imaging
and Graphics, Elsevier, 2009, 33 (8), pp.644-50. �10.1016/j.compmedimag.2009.07.001�. �inserm-
00411983�

A vectorial image soft segmentation method based on neighborhood
weighted Gaussian mixture model
Hui Tang
1,3
, Jean-Louis Dillenseger
2,3
, Xu Dong Bao
1,3
and Li Min Luo
1,3
1
Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University,
210096, Nanjing, China
2
INSERM U642, Laboratoire Traitement du Signal et de l’Image, Université de Rennes I, 35042 Rennes, France
3
Centre
de Recherche en Information Biomédicale Sino-Français (CRIBs)

Abstract:
The CT uroscan consists of three to four time-spaced acquisitions of the same patient. After
registration of these acquisitions, the data forms a volume
in which each voxel contains a vector
of elements corresponding to the information of the CT uroscan acquisitions
. In this paper we
will present a segmentation tool in order to differentiate the anatomical structures within the
vectorial volume. Because of the partial volume effect (PVE), soft segmentation is better
suited because it allows regions or classes to overlap. Gaussian mixture model is often used in
statistical classifier to realize soft segmentation problems by getting classes probability
distributions. But this model relies only on the intensity distributions, which will lead a
misclassification on the boundaries and on inhomogeneous regions with noise. In order to
solve this problem, a neighborhood weighted Gaussian mixture model is proposed in this
paper. Expectation Maximization algorithm is used as optimization method. The experiments
demonstrate that the proposed method can get a better classification result and is less affected
by the noise.
Keywords: Gaussian mixture model, vectorial image segmentation, soft segmentation,
neighborhood, image classification, 3D/3D registration.

1. Introduction
The CT uroscan is the classical preoperative examination 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. The integration of this information
within a unique spatial volume gives the surgeon the knowledge of the patient specific renal
anatomy. The first step in this integration process is to bring the different acquisitions into
spatial alignment which has been done through a local mutual information maximization
registration technique [1]. After registration, the aligned data forms
a
vectorial volume
dataset
in which each voxel contains a vector of n elements corresponding to the information of the CT
uroscan acquisitions (n is equal to the number of acquisitions, three to four in our case). In
order
to get the material (tissue) distribution information of this vectorial volume, a
multi-dimensional segmentation or classification method should be performed.
Due to partial volume effects (PVE), the voxel intensities at the object boundaries are
usually the result of the combination of several materials. 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 the range of segmentation methods, clustering algorithms are termed unsupervised
classification methods which organize unlabeled feature vectors into clusters or “natural
groups” such that samples within a cluster are more similar to each other than samples
belonging to different clusters. The three most commonly used clustering methods are the
K-means [3], the fuzzy c-means (FCM) algorithm [4, 5] and the Gaussian mixture model
(GMM)
[6-8] solved by Expectation Maximization (EM) algorithm [9].
Among the three

methods, fuzzy c-means
and
Gaussian mixture model
have
the ability to perform soft
segmentation by getting class probability distributions.
The fuzzy c-means estimates the
parameters which minimize the distance from each voxel to the class centers. It uses only the
distance objective function without any other information about the intensity distributions. In
contrast, the method based on Gaussian mixture model uses the statistical theory to model
each voxel’s intensity, which is more reasonable to the real situation. In this paper, we choose
the Gaussian mixture model and estimate the Maximum Likelihood parameters by EM
algorithm.
Unfortunately, the intensity classification methods rely only on the intensity distributions
which will lead to misclassification at the object boundaries. In addition, the lack of
information during classification will lead to sensitiveness to noise in inhomogeneous regions.
In his tutorial [10] G. Kindlmann noted that for intensity-only classification problems
“histograms/scatter-plots entirely loose spatial information” and he asked if there would be
“any way to keep some of it?”. Many researchers have realized the importance of spatial
information for image
classification. As described by Roettger et al. [11], spatial information is
important, because a feature by definition is a spatially connected region in the volume domain
with a unique position and certain statistical properties. These authors indicated that only using the
statistical information of the scatter-plot will effectively ignore the most important part of a
features definition.
Zhang et al. [
12]
proposed a novel hidden Markov random field (HMRF)
model to integrate spatial information to Gaussian model based segmentation methods.
Instead of using Markov random field (MRF) as a general prior in Gaussian model based
approach as other researchers did [
13]
, the authors proposed a Gaussian hidden Markov

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