## 3 CAD Systems of Brain Disorders Based on Multimodal Fusion
### Critical Discussion about Multimodal Fusion Techniques  
Various multimodal fusion techniques have been exploited by several works related to brain imaging. We could break these techniques down into two types: Those that can be used in the frequency domain where the Fourier transform of the input image is first calculated, then the inverse Fourier transform is determined to provide the output image. Other fusion methods are of the spatial domain which are interested in the pixels of the input images whose modifications are made on the values of the pixels to provide the desired output image. In general, researchers have preferred to use pixel level fusion methods that have provided the best results such as IHS, PCA, independent component analysis. (ICA), guided filtering and Brovey transformation, etc. However, these techniques suffer from spectral degradation. Techniques using traditional fusion rules have also been used such as weighted average, absolute maximum, etc. Unfortunately, they provide a poor quality output image because the information from the low- and high-frequency coefficients is overlooked or used inefficiently. Since medical images are sensitive to the human visual system which exists on different scales, this type of technique is undesirable for performing the fusion. Pyramidal decomposition [250; 264; 265; 266; 267; 268; 269; 270; 271; 272; 273; 274] and multi-resolution [275; 276] techniques have solved this problem, citing fusion by the gradient pyramid, the Laplacian pyramid, the contrast pyramid, etc. On the other hand, the output image suffers from a reduced contrast with pyramidal fusion and slightly less with multi-resolution techniques. In addition, these techniques produce blocking effects, because in their decomposition process, no spatial orientation selectivity is taken into account. With the progression of multi-resolution fusion, wavelet (WT) transformation was widely used [250; 251; 252; 253; 254; 256; 257; 258] to merge medical images, particularly DWT, since it maintains spectral information. However, the spatial characteristics are poorly expressed. Added to this, the isotropic WT is devoid of shift invariance and multi-directionality. It also does not provide optimal expression of highly anisotropic edges and contours in brain images [183]. In the output image, it is difficult to surely preserve all of the salient features of the input images. This eventually causes an inconsistency in the results of the merger, and introduces artifacts. In addition, WT offers efficient fusion only for isolated discontinuities. Unfortunately, its performance deteriorates on edges and textured regions. On the other hand, it reserves limited directional information along the vertical, horizontal and diagonal directions [183]. Multi-scale geometric analysis (MSGA) [193] has overcome these limitations, thanks to its proposed techniques which allow multi-scale decomposition for high dimensional signals. Citing the ridgelet, curvelet, bandlet, brushlet and contourlet techniques [276; 277; 278; 279; 280; 281; 282; 283; 284; 285; 286; 287; 288; 289; 290; 291; 292; 293; 294; 295; 296; 297; 298; 299; 300; 301; 302; 303; 304; 305; 306; 307; 308; 309; 310; 311; 31  
the advantages of contourlet transformation by adding the characteristic of invariant decomposition by offset, which effectively suppresses pseudo-Gibbs phenomena. This increases performance thanks to the use of directive contrast which takes advantage of contrast and visibility. It also improves the quality of the output image, especially around the edges [183], by producing a more noticeable and more natural merged image. Some works have attempted to propose new approaches which go beyond the conventional context of fusion such as neural networks with pulse-coupled neural network (PCNN) [191; 281], fuzzy logic [282], genetic algorithms (GA) [283] and independent component analysis (ICA) [284].