## 1 Introduction  
A number of institutions perform special medical checks for brain, known as \"Brain Dock\" in Japan, by using advanced imaging techniques like computed tomography (CT), magnetic resonance imaging (MRI) and positron emission CT (PET), because the Japanese are also keen in preventing various neurological conditions including stroke, dementia, _etc._ The purpose of the Brain Dock is to detect asymptomatic brain diseases in their early stages, _e.g._, asymptomatic lacunar infarction, unruptured intracranial aneurysms, dementia, and to prevent such cerebral disorders [1]. As for stroke, for instance, the asymptomatic lacunar infarction and unruptured intracranial aneurysms should be detected for the prevention of cerebral infarction and subarachnoid hemorrhage (SAH), respectively. Furthermore, dementing disorders such as Alzheimer's disease (AD) and vascular dementia are major public health problems in countries with greater longevity, such as in Japan, where the average life expectancy was 82 years in 2004 [2]. For the detection of the AD, neuroradiologists attempt to evaluate the degree of cerebral atrophy subjectively based on cortical thicknesses in the temporal lobe or parietal lobe, sizes of hippocampus and entorhinal cortex, and expansion of lateral ventricles. On the other hand, multiple sclerosis (MS) is one of the most serious neurological disorders, which develops in young adults. Multiple sclerosis is a progressive neurological disorder, which is caused by the structural damage of axons and their myelin sheathes in the central nervous system. The progression of the MS lesions shows considerable variability and MS lesions present temporal changes in shape, location, and area between patients and even in the same patient [3-6]. However, it would be very difficult to detect the lesions among a great number of images or a small number of patients out of many healthy people. It is possible for radiologists to miss the lesions of patients, because of their heavy workloads. Therefore, radiologists would need to experience a number of training sessions to detect the lesions of patients correctly and efficiently. In addition, the number of images, which neuroradiologists have to diagnose, has increased rapidly, because MRI has shifted from two-dimensional (2D) imaging to 3D imaging, and the resolution as well as signal-to-noise ratio has become higher. Consequently, neuroradiologists have been demanding the new approach of \"computer-aided diagnosis (CAD)\" due to their heavy workloads in the field of neuroradiology. CAD has become one of the major research subjects in medical imaging and diagnostic radiology. The basic concept of CAD was proposed by The University of Chicago, in the mid-1980s, whose idea it was to provide a computer output as a \"second opinion\" to assist radiologists in interpreting images, so that the accuracy and consistency of radiological diagnosis could be improved, and also the image reading time could be reduced [7-9]. Since then, a number of researchers have developed computer-aided diagnostic CAD schemes for detection and classification of various kinds of abnormalities such as microcalcifications and masses in mammograms [10-13], pulmonary nodules and diffuse lung diseases in CT [14-18], and colonic polyps in CT colonography [19-22]. Besides, the clinical usefulness of CAD schemes has been studied by performing the receiver operating characteristic (ROC) analysis in experiments similar to clinical situations [10,16,23,24]. However, it has been said that it would be arduous to develop CAD systems using MRI, because the image quality of MR images including specific artifacts and image noise could vary with imaging sequences and patients. In recent years, various kinds of CAD methods have been developed in the neuroradiology using MR images [25-31]. Radiologists expect that CAD systems can improve their diagnostic abilities based on synergistic effects between the computer's and radiologist's high abilities by using the information analysis including the medical images.