# MRI and CT Fusion in Stereotactic Electroencephalography: A Literature Review
## 3 Results
### Methods of Image Fusion
#### 3.1.1 Image Registration  
Image registration consists of finding a transformation \(T\) such that it aligns a moving image \(I_{M}\) with a fixed image \(I_{F}\), by minimizing a cost function \(C\), where the vector \(\mu\) contains the parameters for the transform (Equation (1)) [31; 32]. \[\mu=arg\min_{\mu}C(T_{\mu};I_{F},I_{M}). \tag{1}\]  
Figure 3 summarizes the procedure where a transformation was applied to \(I_{M}\). Then, a similarity metric between \(I_{M}\) and \(I_{F}\) was optimized by updating the transform. The registration procedure could be classified based on two criteria: (i) the transformation (Figure 3b), where the procedure was sub-classified into rigid and non-rigid; (ii) the optimization metric, where the registration was sub-classified according to the similarity metric (Figure 3c). Considering these criteria, first, the concept of transformation and similarity metrics is presented, and then, the results are summarized. Registration: Transformation  
The first type of method is the rigid registration, which applies a single transformation to the entire \(I_{M}\). This method can be categorized, depending on the transformation type and degrees of freedom, into [31]:  
1. translation: translation only (three degrees of freedom in 3D);
2. Euler: rotation and translation (six degrees of freedom in 3D);
3. similarity: rotation, scaling, and translation (nine degrees of freedom in 3D);
4. affine: translation, rotation, scaling, and shearing (12 degrees of freedom in 3D). These transformations define the degrees of freedom of the deformation model. The affine transformation has the most degrees of freedom in comparison. The second type of method is the non-rigid registration, which are computationally more complex than rigid registration, since this requires finding local deformations of the moving image. Non-rigid methods are sub-classified into two main categories based on the deformation model: transformations derived from physical models and transformation derived from interpolation and approximation models [33]. Figure 3: Registration procedure. (**a**) Input images for the registration. (**b**) Optimization of the transformation for \(I_{M}\). (**c**) Measurement of the similarity metric to compare the transformed \(I_{M}\) with \(I_{F}\). Registration: Metrics  
The metric or cost function is an essential part of the registration procedure, which also determines the type of transformation and optimization [32; 34]. The most common metrics are:  
1. Mean-Squared Difference (MSD): measures the average gray difference between the \(I_{F}\) and \(I_{M}\) voxels;
2. Correlation Coefficient (CC): measures the gray-level similarities between the \(I_{F}\) and \(I_{M}\) voxels [35];
3. Normalized Correlation Coefficient (NCC): is the CC after normalizing the images;
4. Mutual Information (MI): measures the dependency between two variables (moving and fixed image) and is calculated using the entropy, the probability joint histogram distribution, and the Parzen window estimation [35];
5. Normalized Mutual Information (NMI): an alternative to the MI metric that solves the drawbacks such as misregistration in small overlapping regions [10]. The most common metrics in multi-modal brain registration are the MI and the NMI, which rely on the probability distribution between the images [10; 11]. Registration Methods Literature  
Among the 15 selected original research articles, seven proposed methods for rigid registration (Table 3). [PERSON]'s method is an example of a non-rigid registration method with the use of the MI to localize deep electrodes in SEEG [17]. This method uses the Insight ToolKit (ITK), an open-source toolkit for medical image registration and segmentation [36]. Finally, the method was validated using images of ten patients, five males and five females, aged between eight and seventeen years. For the accuracy measurement, a photograph of the electrodes was taken from a digital camera, and then, the electrodes of the resulting MRI were projected in the 2D photograph.