The review of a journal in IEEE transaction on medical imaging,

 vol.21, no.2, february 2002.

 

Title of Journal:

 

Computation of the Mid-Sagittal Plane

In 3-D Brain Images

 

By Sylvain Prima, Sébastien Ourselin, and Nicholas  Ayache

 

 

Abstract

The paper, which consists of 17 pages and devided into 5 chapters, offer a new method to compute, reorient, and recenter the mid-sagittal plane in anatomical and functional three-dimensional (3-D) brain images. The methods is an iterative process and the computation process is mainly using two steps. First is using  a block matching procedure to determine initial guess of mid-sagittal plane which performed and the second one is using a least trimmed squares estimation to define the parameters characterizing mid-sagittal plane. In order to get automatic computation the estimated plane is aligned with the center of the image grid, and the whole process is iterated until convergence.

The algorithms explored in this paper is fast and accurate, even for strongly tilt heads and even in presence of high accusition noise and bias field, as shown on a large set of real magnetic resonance (MR) images.

  

Index Terms -  Magnetic resonance imaging, symmetry, mid-sagittal plane.

 

1. Introduction

As noted above the paper presents a new method to automatically compute, reorient, and recenter the mid-sagittal plane in anatomical and functional three-dimencional (3-D) brain images. The method is very interesting and useful for enriching our knowledge, especially in medical image visualization field which is discussed in lectures. The method can be implemented not only in magnetic resonance (MR) but also other modalities like computed tomography (CT), positron emission tomography (PET) and single photon emission computed tomography (SPECT).

            The new technique oxplored in this paper is usefull to determine the mid-sagittal plane. This plane is used to split the tilt of the head into two roughly identical parts. And the knowledge about the plane can be a basis for further symmetry-analysis.

During the scanning process the information about anatomical or functional  symmetries and unsymmetries is usually hidden by the tilt of the patient’s head. So, it makes visual inspection or analysis harder. The correction of this tilt is important for many tasks, allowing normal as well as abnormal departures from symmety to appear more clearly.   This helps comparing the two sides of the brain by making manual or automatic measurements easiers.

Comparing the two sides of the brain is helpful for diagnosis in many casess  fractures in CT images, lesions or bleedings in MR images, defaults of perfusion in SPECT images. And further it can be helpful for diagnosing some disease like the variant Creutzfeldt-Jakob disease and the Alzheimer’s disease.

 

 

2. Previous Work and The Drawbacks

            There are some previous papers which consider the problem computing the mid-sagittal plane in head. They can be devided into two mainly classes, which can be either (1) the plane best matching the cerebral interhemispheric fissure, or (2) the plane maximizing a symmetry criterion. The previous methods can be seen in the following table :

           

 

            There are two severe drawbacks of previous symmetry-based methods, and the new methods offered in this paper deals with the drawbacks. First, the computation of local measures of symmetry and the use of a robust estimation technique allow to discriminate between symmetrical and asymmetrical parts of brain, the latter being naturally treated as outliers. Consequently, the computation of the mid-sagittal plane mainly relies on the underlying gross symmetry of the brain. Second, the regression step yields an analytical solution, computationally less expensive than maximization of the global similarity measures.

 

3. Description of the Method

            Mainly the computation composed of two steps. At first, given an initial guess of the mid-sagittal plane, the computation of local rather than global similarity measures between the two sides of the head allows to identify homologous anatomical structures or functional areas, using a block matching procedure.  Subsequently define the mid-sagittal plase as the one best superposing the on one side and their counterparts on the other side by reflective symmetry. Practically the computation or the parameters characterizing the plane is performed by a least trimmed squares estimation.

            The following explanation is about main principles of the methods. The details explanation can be seen in the paper pages 126-129.

            Given I, an MR image of the head, the mid-sagittal plane P is defined as the one best and superposing the points {a_i}and {S_p(bi)}, where a_i is a head voxel, bi its anatomical counterpart on the other side, and S_p the symmetry with respect to the searched plane P. Practically, P is obtained by minimization of the least squares (LS) criterion ∑_i ║ a_i - S_p(bi) ║², where ║∙║is the Euclidian norm. In Appendix I (refer to the main paper) desribed an analytical solution of the problem. The pairs {(a_i,bi)} are obtained as follows (see Figs. 1).

•  The original image I is flipped with respect to an arbitrary plane K, yielding the image S_k(I), which  S_k(I) is  the symmetry with respect to K.
• The “demons” algorithm (refer to [28] in main article) finds the anatomical counterpart bi’ in S_k(I) of each point a_i  in I, by way of a nonrigid registration between the two images.
• bi= {S_k(bi’)} is the anatomical counterpart of a_i on the other side of the head. For example, in I , the point a_i, located in the right temporal lobe (radiological conventions) is matched with the point bi, located in the left temporal lobe (see Fig. 1b.).

Experimentally, It is observed that the quality of registration between I and S_k(I) is equivalent for a large set of planes K , provided they are not “too far” from the search mid-sagittal plane P; this means that the set of points {bi} is independent of the chosen plane K. Practically, the most reasonable and simple choice for K is the plane located at the center of the image lattice, which is likely to be relatively close to P.

Once P is computed, the transformation R = S_k o S_p is a rotation if P and K are not parallel and a translation if P and K are parallel. The transformation R^1/2, when applied to the image I, automatically aligns the plane P with K, the latter being considered as fixed to the image grid (see Appendix II in main article).

 

 

Figure 1a.

 

 

 

Figure 1b.

 

Fig. 1. The nonrigid registration strategy :

Fig 1a.: coronal slice of the original image I, with K, the central plane of the grid, drawn in white.

Fig 1b : S_k(I) is the same image as I, but flipped with respect to K. The point a_i in I is matched

with the point b_i’ in S_k(I); b_i = S (b_i’ ) is a point of I, counterpart of a_i on the other side of the head.

 

 

           

4. The related work that has been published.

 

Author(s)	Year	Article	Description	The relation to the paper
M. E. Brummer	1991	Hough tranform detection of the longitudinal fissure in tomographic head images.	It covers  Hough tranform detection of the longitudinal fissure in tomographic head images based on fissure. The application is applied in MR.	Other method to find mid-sagittal plane based on  interhemispheric fissure of the brain .
P.C. Marais , R. Guillemaud, M. Sakuma, A. Zisserman, M. Brady	1996	Visualising cerebral asymmetry	It explain th visualising cerebral asymmetry based on fissure. The fissure is segmented in MR images and extract it slice by slice snake.	One of the some previous methods which based on the interhemispheric fissure of the brain .  It can be seen on pp.411-416 in Lecture notes in computer science,  Sept.1996, Hamburg, Germany.
B.A. Ardekani, J. Kershaw, M.Braun and I. Kanno	1997	Automatic detection of the mid-sagittal plane in 3D brain images	The papers show the method to detect automatically the mid-sagittal plane in 3D. The methods based on symmetry criterion.	The method is based on symmetry criterion which has drawbacks. And the main article deals with the symmetry drawbacks.
Y. liu , R.T. Collins, and W.E. Rothfus	1997	Automatical bilateral symmetry (midsagittal) plane extraction from pathological 3 D neuroradiological images	It explain the estimation a 2-D mid-sagittal axis for each coronal or axial slice and then reduce a 3-D plane from the set of these lines	One of the previous methods which are used in the methods Based on a Symmetry Criterion.
A.K Jain	1981	Image data compression.	Part of the paper explain the image data compression using block matching procedure.	It is an initial technique which then be used in the main article to compute robust estimation technique.
P.J. Rousseeuw and A.M Leroy	1987	Robust Regression and Outlier Detection.		It is the technique to gain the exact optimal value for h, the integer value in Least Trimmed Squares Estimation.

 

6. Conclusion

            The mid-sagittal plane of  brain in head is important plane in medical imaging and visualisation world. The knowledge of the plane ca be a basis for further symmetry-analysis, which is usefull for some tasks like diagnosis in many casess  fractures in CT images, lesions or bleedings in MR images, defaults of perfusion in SPECT images. And further it can be helpful for diagnosing some disease like the variant Creutzfeldt-Jakob disease and the Alzheimer’s disease.

            So many methods made by researcher to find the mid-sagittal plane and the previous methods still have the drawbacks, and the main article deals with the drawback. The new methods offer in the main article consist of two step, as explained above, and the algorithms is fast and accurate.

 

 

References

 

[1]          Sylvain Prima, Sébastien Ourselin, and Nicholas Ayache, “Computation of the Mid-Sagittal Plane In 3-D Brain Images,” IEEE transaction on medical imaging, vol.21, no.2, february 2002.

[2]