Agencias internacionales: NFIP, OMS y AEP

Pre-processing steps is required before applying any algorithm but the actual steps may vary significantly depending on image modalities, anatomy that is being studied, and obviously the application of interest. Here, we limit ourself to brain imaging modalities, which were introduced on the previous section and focus on applications directly related to the purpose of this these,i.e.,

image classification and group analysis. We only mention common pre-processing steps that might be necessary for understanding other section of the thesis. Discussing details of each step or any extra steps are beyond the scope of this chapter and will be mentioned in each chapter if it is necessary.

The diagram showed in Figure 2.4 represents a typical pre-processing pipeline used for group analysis and classification purposes in brain imaging. There are many other blocks that can be added to the diagram but we only mentioned the most general ones:

• Image Enhancement:A common step in a pre-processing pipeline is image enhancement. We use this step in a broad sense;i.e.,any step that improves image quality can be a part of this block. For example, denoising or bias field correction1_{, or histogram equalization}2_or

motion correction3 _{can be viewed as an image enhancement step. There might be several}

of such blocks in a typical pre-processing pipeline; it can be done before or after image registration.

• Tissue Segmentation: This step can be viewed as a part of feature extraction step. Since it is very common step particularly for brain image analysis, we introduce it as a separate step. The fundamental task in tissue segmentation is to classify the voxels in the volumetric MR data into subclasses of tissue types, e.g.,gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) tissue types [12], [234] (see Figure 2.5a for an example).

1_{Bias field signal is a low-frequency and very smooth signal that corrupts MRI images [210], [36].}

2_{Histogram equalization is a method in image processing to adjust contrast using the image’s histogram [103], [5].} 3_{One of the major sources of error in the analysis of functional Magnetic Resonance images is the presence of spurious}

activation arising due to patient head movement at the time of image acquisition. Motion correction algorithms are designed to remove this artifact [161].

Figure 2.4: The figure shows a general pre-Processing pipeline in medical imaging application for group- analysis and classification purpose: to establish voxel-wise correspondence, volumetric image of thei’th subject (Ii) should be aligned (warped) to a template (T). This normalization process is calledregistration

and produces a mapping (ϕi) for thei’th subject. The map (ϕi), the warped subject (Ii◦ϕi), the template

image (T), and the corresponding label image (L) are feed to a black-box for feature extraction. The warped image (Ii◦ϕi) can also be used by many other blocks two of the most common of which are shown here:

Image enhancement and Tissue segmentation. The image enhancement block may include histogram equal- ization, bias field correction, or any other procedure to enhance the quality of an input image. Enhanced image may be used for tissue segmentation (or any other block). This tissue segmentation block classifies voxels of the image into various tissue sub-types: White matter, Gray matter,etc.. All results areoptionally

provided to the feature extraction block that in turn produces the feature vectorxi.

• Registration: In order to compare images of different subjects, one may need to maintain voxel-wise correspondence. For example, to compare subjectiwith subjectj, we need to know which coordinate of, say thei’th subject, corresponds to, say coordinate(z1, z2, z3)

of thej’th subject. Therefore, a one-to-one mapping (ϕ) representing the correspondence is computed during the registration process. Instead of having pair-wise maps between all pairs of subjects, it is common to find a map to a common image called Templateor

(a) (b)

Figure 2.5:(a) shows an example of tissue segmentation (courtesy of [14]). (b) shows an example of structural segmentation; each color denotes a structure. Each segment can be used as a region of interest (ROI) for feature extraction step.

Atlas. Image registration is a topic of research on its own right and here we only give a brief introduction (see [192], [237], [149], [57], [129] and references therein for a survey on medical image registration methods).

A subject image (I) and the template (T) are viewed as a function that maps compact domains (i.e., Ω1 and Ω2 respectively) to a set of real values, namely: I : Ω1 → Rand

T : Ω2 →RwhereΩ1,Ω2⊂R3(assuming that the image is a volumetric image). A regis-

tration algorithm solves the following optimization problem:

min

θ∈ΘD(Ii◦ϕ(θ);T) (2.2.1)

whereϕ(θ) : Ω2 → Ω1 is the one-to-one mapping4 _{parametrized byθandΘis the set of}

all possible parameters and D(·;·) is a measure of distance (a divergence function); e.g., D(·;·) =R

Ω2kT(z)−(I◦ϕ(θ))(z)k2dz. I◦ϕ(θ)means composition (warping) the subject

image according to the mapping function. The idea is pictorially represented in Figure 2.6a.

4_{One-to-one mapping is usually not enough andϕneeds to be smooth too. Mathematically speaking,ϕshould be a}

(a) (b)

Figure 2.6: (a) show registration concept:ϕandϕ−1map the box to the circle and vice-versa respectively. Warped grids show local deformation. (b) shows the idea of determinant of Jacobian; the template objectT

is mapped to the three objects (I1,I2andI3). The color encodes logarithm of the determinant of the Jacobian

of the transformations. IfT is expanded, the determinant of the Jacobian is greater than one (its logarithm is positive), and it is less than one if the template object is shrunk.