MR Image Monomodal Registration Using Structure Similarity Index

Olfa BEN SASSI1, Tijani DELLEJI1 , Abdelmalik TALEB-AHMED2, Imed FEKI1, 3, Ahmed BEN HAMIDA1

1 UR Technologie de l’Information & Electronique Médicale‘TIEM’ ENIS, Sfax University, Tunisia

2 Laboratoire LAMIH Université de Valenciennes et du Hainaut Cambrésis, France 3 Service de Neurologie, Hôpital Universitaire de Sfax, Tunisia

bensassi_olfa@yahoo.fr, Ahmed.Benhamida@enis.rnu.tn

Abstract Image Registration in medical imagery is one useful technique with an important role especially for pathology survey and control, medical treatment, or for post-operative control. It is based essentially on the similarity criterion measurement because it defines the objective criterion used to estimate registration quality between the homologous structures of images. This paper describes one application of the SSIM method as a similarity metric in the image registration technique. Usually the SSIM method is used in the images’ quality measurement, it consists in the combination of the comparison of luminance, the comparison of contrast, and the comparison of structure between two images. This property allowed us to adapt this approach in MR image monomodal registration and demonstrate its performance. Key Words- Registration, MR Image, Similarity criterion, Structure similarity index, Transformation. 1. Introduction

Brain imaging is extremely important as well for the comprehension of the functional and/or pathological processes, as for the development of adapted strategies of treatment. Thus, these last years, many researchers recognized the need to develop treatment tools in order to help the expert in his diagnosis choice, to announce the possible pathological risks to him, and to even guide its surgical gesture. Generally, it is a clinical aided system dedicated to make the decision.

However, although there is a diversity of brain imaging techniques, the traditional diagnostic protocols did not follow the same progression. Indeed, the doctor would have not only the images sources but also the tools to interpret and compare them. In particular, techniques

that allow the joint use of all the information are able to establish the most reliable, precise and exact diagnostic.

Nevertheless, as soon as we have at least two images representing the same physical reality, their joint analysis is relevant only in the condition of employing the same space reference frame to be able to carry out the comparison or the integration of all information in images. This task known under the name of registration constitutes an essential step in automated medical image analysis.

Image registration [1], [2], [3] is the process of spatial alignment of two or more images acquired from different sensors, viewpoints or time intervals. Registration is widely used in medical imaging applications for pathology survey and control, medical treatment, post-operative control, monomodal or multimodal image fusion [4], human brain mapping [5], study of pathology within a population, and statistics of the anatomical variability of a population.

Over the years, a large number of registration techniques have been developed for the various types of data and problems. The classification of these techniques is essentially based on the similarity criterion type.

In this work, we propose to apply the Structure SIMilarity technique ‘SSIM’ [6] that provides the estimation of the optimal transformation. In fact, SSIM method is habitually used in the images’ quality measurement, it consists in the combination of the comparison of luminance, the comparison of contrast, and the comparison of structure between two images. This property allowed us to adapt this approach in Magnetic Resonance Image ‘MR Image’ registration and demonstrate its performance.

This paper is organized as follows: first we will be interested in the presentation of the image registration by detailing its steps, next we will describe the development of the SSIM approach. An exploration of this algorithm will be hence presented and discussed with all the results obtained.

Image Processing Theory, Tools & Applications

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2. Image registration

The objective of registration process is to obtain a spatial transformation of a target image to a source image by which a similarity measure is optimized between the two images. Generally, we can describe the general principle of registration as shown in the following figure.

Figure 1. General principal of registration

To register two images Is (source image) and It (target

image), a geometric transformation must be estimated. This transformation associates at each point ‘s’ of the target image the coordinates T(s) = s + u(s) in the deformed image. The transformation applied to register the images can be categorized according to the degrees of freedom. So we find the rigid, affine, projective, and curved transformation.

We choose in our process to carry out a registration based on a rigid transformation [2] because this type of transformation is most usually employed in monomodal registration since it preserves distances, angles and parallelism.

Such transformation consists in the estimation of a translation and a rotation making it possible to transform the coordinates (x1, y1) of an image point into a point of coordinates (x2, y2) in the following way:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛

1

1

2

2

cossinsincos

yx

tytx

yx

θθθθ (1)

⎟⎟⎠

⎞⎜⎜⎝

⎛tytx represents the translation vector, and θ is the

angle rotation. Since the image It will undergo the transformation,

then we will obtain a second transformed image whose each pixel of coordinates (x2, y2) will have the same grey level as the pixel of coordinates (x1, y1).

),(),( 111222 yxIyxI tt = (2)

However, before transformation, a preliminary step consisting in the extraction of pertinent information of the images is required allowing to guide registration. These information, constructed from Is and It using the functions Fs and Ft, are based on characteristics of image data. Various characteristics are exploited to drive image registration algorithms and they include geometric methods and iconic methods.

Geometric methods consist in the extraction of the geometric feature, such as points, contours, or surfaces, manually or automatically. On the other hand, iconic methods present the low level information in the image such as pixel intensities, and pixel positions.

Once information is extracted, it become necessary to define a similarity criterion to quantify the resemblance between the two images. Several criterions are usually employed and which are divided into two categories: feature-based techniques [7], [8], [9], [10], [11] and intensity-based techniques [12], [13], [14].

Finally, a phase of optimization consists in finding the

optimal transformation∧T which minimizes or maximizes

the similarity criterion. Optimization task can be presented in the following way:

))(,(minarg TIIET recarefT Φ∈

∧= (3)

Ф: field of transformation

3. Structure similarity index ‘SSIM’

The main property of this approach is the local comparison of structure, brightness, and contrast of images. In fact, structural information in an image is defined as being the attributes which represent the object’s structures. And since brightness and contrast can vary in an image, we use them in the definition of the SSIM method [6]. So the measurement similarity system, showed in the figure 2, comprises three modules of comparison which can be gathered to obtain the best decision.

3.1. Brightness comparison

Brightness is estimated by the average intensity

measurement x of each image.

∑=

=n

iix

nx

1

1 (4)

xi is the grey level of each pixel in the image x So, brightness comparison function ))(,( TIIl ts

depends on average intensities sI and ))(TIt .

Is

It

Update of T

T(s) = s + u(s)

E (ts, It (T)) Fs

Ft

Similarity criterion

Transformation

Preprocessing

Optimization It (T)

Is

It

1)(

1)(.2))(,( 22

CTII

CTIITIIl

ts

tsts

++

+= (5)

C1 is a constant included to avoid the instability when

))((22

TII ts + tends towards zero. With 2).1(1 LKC = ; K1<<1;

L represents de dynamic range of the pixel’s value. The value’s range of this measurement l is [0, 1], and

the best value is equal to 1 only if )(TII ts = 3.2. Contrast comparison

Image contrast is evaluated by the standard deviation xσ .

)(xVarx =σ (6)

With Var(x) is the variance defined by:

2

1)(1)( ∑

=

−=n

ii xx

nxVar (7)

Therefore, contrast comparison is considered as a comparison between Isσ and )(TItσ , it is given by the following function:

22.2

),( 2)(

2)(

)( CC

IIcTItIs

TItIsTts ++

+=

σσσσ

(8)

With 2).2(2 LKC = ;

K2<<1 The value’s range of this measurement l is [0, 1], and

the best value is equal to 1 only if ))(()( TIVarIVar ts = .

3.3. Structure comparison

Comparison structure is based on the calculation of the covariance Cov(x,y); it is determined by this equation:

3.3))(,(

))(,()( C

CTIICovTIIs

TItIs

tsts +

+=

σσ (9)

Covariance function is calculated as the following way:

))((1),(1

yyxxn

yxCov i

n

ii −−= ∑

=

(10)

Figure 2. SSIM diagram

3.4. Structure similarity index Structure similarity function S is given by the

combination of the three functions quoted previously.

[ ] [ ] [ ]γβα ))(,(.))(,(.))(,())(,( TIIsTIIcTIIlTIIS tstststs =

(11)

Similarity measurement must satisfy the following conditions:

- Symmetry: )),(())(,( IsTISTIIS tts = . - Overestimation: 1))(,( ≤TIIS ts . - Unique maximum: 1))(,( =TIIS ts if and only

if )(TII ts = . α , β , andγ are positive coefficients that translate the

importance of each one of these parameters l, c and s. To simplify the expression of structure similarity

function, we fixed 1=== γβα and223 CC = . So, we

obtain the final expression of the SSIM(Is, It(T)):

Brightness Measurement

Contrast Comparison

Is

Contrast Measurement

+

_

÷

Brightness Comparison

Structure Comparison

Brightness Measurement

It

Contrast Measurement

+

_

÷

Combination

Similarity Measurement

)2)(1)((

)2))(,(.2)(1)(.2(2

)(222

CCTII

CTIICovCTIISSIM

TItIsts

tsts

++++

++=

σσ

(12)

To estimate the quality of registration, it is useful to apply the SSIM index locally. That is due to the following causes:

- Space statistical properties are no stationary. - For a typical distance tested, only one particular area

in the image can be perceived with a high resolution by the human observer at only one time given.

- The quality measurement can provide a space chart of the local image quality, which provides more information on registration quality, which is useful in the applications of the medical imagery.

The local statistics sI , )(TIt , sIσ , )(TItσ , and ))(,( TIICov ts are calculated in a local window of size

BB × which moves pixel by pixel on the entire image. In each step, the local statistics and SSIM index are calculated in the local window. In our work we are interested in only one total quality measurement of the mapping. We use for that an average index called MSSIM(Is, It(T)). Indeed, the more the value of this index is close to 1 the more the registration process is perfect.

∑=

=M

iTts iIiISSIM

MMSSIM

1)( ))(),((1 (13)

)(iI s and )()( iI Tt are the contents of images in the ith local window. And the parameter M represents the number of the local window in the image.

4. Experimental results

MR images involved in this study present a longitudinal section acquired from different time intervals. The first exam, that showed a cerebral pathology, was carried out in August 2006. The second exam was passed in February 2007 in order to exanimate the pathology evolution and if the treatment led to good results. Figure 3.a corresponds to the first exam, and figure 3.b corresponds to the second exam. Knowing that the two images were extracted from the same section.

Accuracy in this field is very interesting. For that the mental comparison between these two images is not effective in certain cases, especially if the doctor wants to determine precisely the anomaly evolution to identify his decision. From where, we should recourse to automatic techniques and more specifically to the registration technique in this case. So, we applied our algorithm that includes the rigid transformation and the SSIM approach as a similarity criterion. We considered the figure 3.a as the source image, and the figure 3.b as the target image.

Figure 3. MR Images studied (a) Source image, (b) Target image

After simulation, we found the required optimal transformation among a set of transformation defining the field deformation of the image. The optimal rotation angle is 5=θ degree, and the optimal vector translation

is⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛03

tytx pixel. This transformation is obtained in

such a way that the SSIM index is closest to one. The table below contains the SSIM index value before

and after transformation. These values were calculated using a 33× widow size that is selected arbitrarily. In fact, it is more interesting to work with a small size window to reach more precision. We notice that SSIM index value was improved after transformation. Indeed, it increased comparing with the initial value.

Table 1. SSIM index value

Before transformation After transformation

0.7325 0.7504

In order to be convinced by these results, we illustrate in the figure 5 the superposition of the segmented target image on the source image before transformation (figure 5.a) and after transformation (figure5.b).

Figure 4. Target image segmentation

We have used the Estimation-Maximization ‘EM’ algorithm [15] for segmentation (figure 4) in order to extract the geometric pertinent information.

We can see clearly the registration accuracy from the brain contour, in particular in the zones surrounded by circles. This figure and the improved SSIM value after

(a)

(b)

transformation prove that the obtained transformation is the optimal. And in this way, doctor becomes able to understand the pathology evolution, and take the best decision.

Figure 5. Superposition of the segmented target image on the source image

(a) Superposition before transformation (b) Superposition after transformation

Registration accuracy is of crucial importance because

it represents the principal source of uncertainty. So, one registration method must have a good spatial accuracy (in the order of 2 or 3 mm). It must be also stable and its accuracy should not depend on the user. If it isn’t the case, many registration errors appear and are translated by a homogeneous displacement of anatomical data.

For that raison, we tried to evaluate our algorithm by comparing it with a well known method which is the mutual information criterion ‘MI’ [14].

The optimal rotation angle obtained by this technique is 5=θ degree, and the optimal vector translation

is⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛13

tytx pixel. We can note that the only difference

between MI approach and SSIM approach is the value of the term ty. This difference is equal to one pixel. Consequently we can conclude that SSIM technique could be used in medical registration as the other methods since it allowed a satisfactory accuracy.

5. Conclusion

Image registration process is a crucial step in all image analysis tasks. The objective is to find a spatial transformation of a target image to a source image by which a similarity measure is optimized between the two images. In this paper we are interested in the MR Image monomodal registration. We tried to adapt the SSIM method, which is habitually used in the images’ quality measurement, as a similarity criterion. Obtained results showed that this approach can be applied in registration technique.

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(a) (b)