In most cases, images generated by X-ray CT and MR are all-inclusive. That is, these two imaging modalities cannot directly produce the images of the selected tissue types or organ systems. For example, when the human abdomen is imaged by X-ray CT, the liver, kidney, stomach, pancreas, gallbladder, adrenal glands, spleen, etc., are all shown in the resultant image; when a cross section of the human brain is imaged by MRI, the scalp, bone, gray matter, white matter, and cerebrospinal fluid, etc., are all included in the resultant image. In order to obtain an image of the selected targets of interest, an image processing or image analysis method is often required. Generally, imaging refers to an operation or a process from the data to the
picture. X-ray CT represents an operation from photon measurements to a 2-D display of the spatial distribution of the relative linear attenuation coefficient (RLAC); MRI represents a process from free induction decay (FID) signal measurements to a 2-D display of the spatial distribution of the thermal equilibrium macroscopic magnetization (TEMM). Image processing refers to an operation or a process from the picture to the picture. The commonly used image processing approaches may include but are not limited to transform, enhancement, and restoration. Image analysis refers to an operation or a process from the picture to the “data.” Here, data may include some image primitives such as edges or regions as well as some quantities and labels related to these primitives. This chapter and the following chapters focus on image analysis. Various image analysis methods have been developed, and some of them are
applied to X-ray CT andMR images. The graph approach [1, 3, 5], the classical snakes and active contour approaches [5, 6, 8, 9], the Level set methods , and Active Shape model (ASM) and Active Appearance model (AAM) approaches  are edge-based approaches. Fuzzy connected object delineation [15-18, 20-22] and Markov random field (MRF) [24, 26, 28, 30, 32, 34, 36, 38] are the region-based approaches. This and the next chapter describe two statistical image analysis methods for X-ray CT and MR images based on the stochastic models I and II given in Chapter 9, respectively. In analyzing the so-called all-inclusive images as illustrated by the exam-
ples given in the beginning of this section, the first step is to determine how many image regions are presented in the image. After this number is detected, the second step is to estimate region parameters, for example, the mean and variance, etc. After these parameters are estimated, the third step is to classify each pixel to the corresponding image regions. By implementing these three steps, an all-inclusive image is partitioned into the separated image regions; each of them represents a tissue type or an organ system. The above detection-estimation-classification approach forms an unsupervised image analysis technique; it is a model-based, data driven approach.