## 2 Cad Systems of Brain Disorders Based on MRI Technology
### Segmentation of Brain Regions
#### 2.2.2 Segmentation Techniques Proposed in Literature: Description, Advantages and Disadvantages
In the Markov random field (MRF), the local conditional probabilities are calculated by the Hammersley--Clifford theorem, which allows to pass from a probabilistic representation to the energy representation via the Gibbs field. MRF [80; 81; 82; 83] is characterized by their statistical properties; non-directed graphs can succinctly express certain dependencies that Bayesian networks cannot easily describe. It is effectively applied for the segmentation of MRI images, for which there is no natural directionality associated with variable dependencies. In MRF, the computation of the normalization constant Z requires a sum over a number of potentially exponential assignments generally; it is an NP-difficult. In addition, many non-directed models are difficult to interpret or intractable which require approximation techniques. * **Hidden Markov models:** similar to the MRF, it's non parametric probabilistic method. It is possible to express a posterior probability of a label field from an observation in hidden Markov models (HMM), thanks to the [PERSON] theorem. HMMs [84; 85; 86; 87] make it possible to model arbitrary characteristics of observations, making it possible to inject knowledge specific to the problem encountered into the model, in order to produce an ever finer resolution of spectral, spatial and temporal data. In the case of HMMs, the types of previous distributions that can be placed on masked states are severely limited; it is not possible to predict the probability of seeing an arbitrary observation. In practice, this limitation is often not a problem, as many common uses of HMMs do not require such probabilities. * **Support vector machines:** SVMs [89; 90; 21; 91; 92] are a non-parametric probabilistic method whose objective is to find an optimal decision border (hyperplane) which separates the data into groups. The formation process depends on various factors such as the penalty parameter C or the kernel used, such as the linear, polynomial kernel, the radial-based function (RBF) and in its particular case the Gaussian kernel. The generalization performance of this method is high, especially when the dimension of the function space is very large. It makes it possible to train non-linearly generalizable classifiers in large spaces using a small learning set. It minimizes the number of classification errors for any set of samples. However, it requires a high learning time and memory space for data storage. Moreover, the optimality of the solution can depend on the kernel used unfortunately, there is no theory allowing to determine a priori which will be the best kernel for a concrete task. Also, SVMs assume that the data is distributed independently and identically, which is not appropriate for the segmentation of noisy medical images. The Contour Approach  
The primitives to be extracted are lines of contrast between regions of different gray levels and relatively homogeneous. We could cite the derived models and the scale-space models. * **Gaussian Scale-Space representation:** this concept [93; 94; 95; 96] makes it possible to manage image structures at different scales by generally smoothing. This representation is obtained by solving a linear diffusion equation. Its transparent and natural way of handling scales at the data level makes this concept popular. However, it is sensitive to signal noise since smoothing is applied without an average filter. In addition, parasitic characteristics are to be considered because of the high-frequency noises which introduce local extrema into the signal. * **Derived models:** they make it possible to model image zones (contours) assuming that the digital image comes from a sample of a scalar function developed with a narrow and differentiable support. In this case, the variations in intensity of the image are characterized by a 3D variable which represents the light intensity corresponding to the illuminations (shadows), changes in orientation or distance, changes in surface reflectance, changes in absorption of rays, etc.