# MRI and CT Fusion in Stereotactic Electroencephalography: A Literature Review
## 3 Results
### Methods of Image Fusion
#### 3.1.2 Image Merging Methods  
Merging is the process of combining the aligned images. These methods are classified into three categories: Multi-Scale (MSD), non-Multi-Scale (non-MSD), and hybrids [39]. This section presents an overview of these methods. Table 4 shows the found articles about emerging methods. Multi-Scale Decomposition Methods  
These are methods that transform an input image \(I_{k},k\in\{1,2,...,K\}\) into a multi-scale representation \(y_{j}^{k},l\in\{1,2,...,L\}\)[30]. The most common techniques are the pyramidal and transform domain methods [39]. The first method decomposes the image into an array of different scales, then combines decomposed images using fusion rules. The Laplacian Pyramid Transform (LPT) and the local Laplacian Filter (LLF) are examples of pyramidal methods. In contrast, the domain transform methods decompose an image into lower approximations, then fuses every approximation into a single image. Examples of these techniques are: (i) the Discrete Wavelet Transform (DWT); (ii) the Discrete Ripple Transform (DRT); and (iii) the Non-Subsampled Shearlet Transform (NSST). An example of a Multi-Scale Decomposition (MSD) is the proposed technique by [PERSON] et al., which combines the DWT and the DRT, which is robust to discontinuities in edges and contours [24]. This method consists of the following steps:  
1. Taking input images, specifically CT and MRI, and aligning them to the same magnitude;
2. Applying the DWT to align images;
3. Obtaining the wavelet coefficient map from the aligned images;
4. Applying the DRT to the wavelet coefficient maps and obtaining an initial fused image;
5. Applying the inverse DWT and obtaining the fused image. [PERSON] validated the algorithm against DWT methods using two pairs of MRI and CT images. This validation uses the metric of the Root-Mean-Squared Error (RMSE) and Peak-Signal-to-Noise-Ratio (PSNR), where [PERSON]'s method exhibited the best performance with a PSNR of 20.56 and an RMSE of 572.23. In contrast, the DWT obtained a PSNR and RMSE of 17.27 and 1219.30, respectively [24]. The method proposed by [PERSON] requires further validation with more images, from any public multi-modal dataset. Extensions to the DWT are used to reduce some problems of the DWT, such as discontinuities in the edge and contours presented in two-dimensional signals [40]. One example of these extensions is the NSST, which improves the preservation of multi-dimensional signal features [40]. Based on this, [PERSON] and [PERSON] developed a framework for multi-modal medical image fusion in 2014 [25]. This framework uses the NSST to obtain the high and low frequency components of an image, to combine them separately, and then reconstruct the fused image using the inverse NSST. [PERSON] and [PERSON] tested their method using nine pairs of MRI and CT images, from patients with a severe cardiovascular accident. This method was compared against four different fusion algorithms: (i) image fusion in the Intensity-Hue-Saturation (IHS) space; (ii) Non-Subsampled Contourlet Transform Fusion (NSCT); (iii) image fusion using the NSST in the IHS color space; and (iv) image fusion based on NSCT in the IHS color space. The result showed that the method of [PERSON] and [PERSON] achieved the best performance in the MI, with a score of 2.99. In comparison, the closest method in performance was the NSCT technique in the IHS color space with an MI of 84.28. Another example of the NSST for image fusion is the method proposed by [PERSON] et al. in 2021 [29]. [PERSON] et al. used a non-rigid registration with B-splines to align the input images