COMPUTER INTEGRATED SURGERY IICRITICAL REVIEW OF PAPERSIn recent years, medical imaging has become very common in the hospital setting but westill lack many resources necessary in analyzing this data. The set of papers that I have selectedfor this review focus on algorithms designed to segment MR images and then use thesesegmentations to generate cortical surfaces. Being able to view cortical surfaces is veryimportant because it helps understand the physiology of the brain and can ultimately be used inearly detection of depression disorders.The first step of the generation of the cortical surfaces, is the segmentation of the brainimage data into multiple compartments including white matter, gray matter, and cerebral spinalfluid. This is done by parametrically fitting known density functions to the histogram of theimage using the expectation maximization (EM) algorithm. There are a couple of key problemsin accurately segmenting brain volumes which have to do with characteristics of the MRmachine. MR signals have a temporal drift in the signal received so that as time goes on there isa decay in the signal which causes images to appear more dull. The way to get around thisproblem is to obtain alternate MR slices (1,3,5,7… 2,4,6,8…). After MR slices are acquired inthis way, the brain volume goes under some image processing to eliminate this temporal drift insignal. The second problem has to do with spatial inhomogeneity and is a significantly harderproblem to solve. However, the EM algorithm which is employed in these papers gets aroundthis difficult in a very convincing fashion.First of all, we must define what we mean by spatial inhomogeneity. When an MR scan isbeing taken different parts of the brain are different distances away from the antenna and thiscauses some parts of the brain to show up brighter than others. As one can imagine, this can1cause a lot of problems for a Bayesian segmentation algorithm which relies solely on theintensity of the voxels. However, what is instead done in the EM algorithm is to first break upthe MR volume into small sections where the difference in intensity due to spatialinhomogeneities is negligible in each section. Following this, each section is then locallysegmented and then the volume is merged back together. The paper by Joshi et al shows throughtheir sample set of brains that for brains with small intensity inhomogeneity, the EM algorithm isonly marginally better than other algorithms but for other brains with a ‘marked variation inillumination’ the accuracy improves very significantly. This was a key result in the paper becauseit moved scientists one step closer to obtaining accurate segmentations.The way the actual sections are segmented is quite interesting. One of the most importantconcepts in segmentation is the idea of thresholding. Basically, if different objects show up asvery different intensities, we can set a threshold where things within a certain intensity intervalwill belong to a certain object. A specific type of MR scan called an MPRAGE scan was used inthe papers. MPRAGE scans have a very good signal to noise ratio, have an excellent dynamicrange and are very good to look at the anatomical features of the brain. In these scans, whitematter has the highest intensity, gray matter has moderate intensity and cerebral spinal fluidshows up dark. The following is an example of the histogram:2IntensitiesThe images acquired were 8 bit images which mean that the intensities of the voxels can havevalues between 0 and 255. Once the histogram is obtained, three Gaussians are forced upon thehistogram and the Gaussians are selected such that they most accurately fit the histogram. ThreeGaussians are chosen rather than two or four because of the knowledge that in the brain, themajor regions of volume are CSF, GM, and WM. The intersections of the Gaussians signifyintensities where the probability of CSF is equal to the probability of GM (intersection 1), andwhere the probability of GM is equal to the probability of WM (intersection 2). The optimalthreshold is the point of these intersections because this minimizes the probability of error. Animplicit assumption made here is that the costs of all mistakes are equal and that there is zerocost for correct predictions. After the thresholds are picked, all that is left to obtain thesegmentation is to go through each voxel and decide which compartment it belongs to,depending on our decided thresholds.Now that we have an accurate segmentation, the next step is to generate a corticalsurface. An isosurface generation algorithm by Gueziec and Hummel [4] that uses tetrahedraldecomposition is employed. This algorithm is very similar in nature to the ‘Marching Cubes’algorithm first designed in 1987 but the MC algorithm had some inherent ambiguities thatresulted in holes in the surface. The tetrahedral decomposition algorithm does not suffer thosedrawbacks. Basically, the TD algorithm generates a tessellation of triangles for an isosurface of agiven intensity. It decomposes each voxel into five tetrahedral. The resulting surface is a closedand valid triangulation made up of the triangles that bound these tetrahedra. To generate thecortical surface, we use the gray-matter / white-matter threshold obtained from the segmentation.It turns out that the TD algorithm produces triangulations that tend to be overparameterized and this makes the rendering of the surfaces to be computationally intensive. The3way this problem is solved in the series of papers is to employ some basic decimation techniquesthat reduce the number of polygons without dramatically changing the shape or geometry of thesurface. Two techniques are basically used to achieve this. First, vertices that lie on a lowcurvature region of the surface can be removed and the hole formed due to its removal is thenretriangulated. Second, edges that are very short result in narrow triangles that have small areas.What is done here is merge the two vertices and get rid of that edge which also directlyeliminates all triangles that shared that edge. By using these two techniques the number ofpolygons in the surface was reduced by