MRI brain extraction using a graph cut based active contour model

Brain extraction refers to stripping the skull and removing any non brain tissue such as fat, bone and eye balls from the MRI of the head. Brain extraction is an extremely important preliminary step before any brain analysis algorithm. This paper proposes a novel algorithm for the extracting the brain tissue using a graph cuts based active contour model. The model combines the implicit curve evolution techniques with graph cuts optimization tools to provide a fast and robust segmentation algorithm. A discrete version of the Mumford Shah functional will be presented and the optimization will be performed on a discrete lattice using the max-flow/min-cut algorithm. The implicit curve evolution is performed by iteratively minimizing the discrete function and is simply described as follows: we will construct a graph in which each pixel in the image has a corresponding vertex and we will add two auxiliary vertices (Source (S) and Target (T)) that will later represent the labeling and this will complete the vertex set of the graph. The edge set of the graph will consists of two subsets: Terminal links that connect each vertex to either the source or the target, the weights of these links represent the external energy of the active contour model and according to the Mumford-Shah functional will be calculated as the intensity deviation of the corresponding pixel around the mean value of the class of interest. Neighboring Links: these will connect the neighboring vertices with each other and, the weights of these links will represent the internal energy of the active contour and are calculated from the length of the evolving contour. A discrete approximation of the Euclidean length of the contour is presented using the Cauchy Crofton formula. After constructing the graph, a max-flow/min-cut algorithm will be applied to find the minimum cut. The minimum cut will subdivide the vertices of the class into two disjoint sets one of them contains the source and the other contains the sink, respectively. The pixels that correspond to all the vertices in the first set will be have a label 1 and all the other pixels will have a label zero and this terminates the labeling process. Applying the curve evolution model on the MRI slice, it will tend to group the more homogeneous tissue in one class and hence the white matter and gray matter tissues will be grouped with the fat and everything else in the other class. Fat is naturally far apart from the gray matter and white matter and hence, the curve evolution algorithm is followed by a connected component analysis that picks the most dominant component/s as the brain tissue. The advantages of our algorithm over the currently existing brain extraction algorithms are summarized as follows: 1) Graph cuts are considered as a global optimization tool and hence our model is less prone to error and not sensitive to initialization. 2) Graph cuts can obtain the global minimum of most functions in polynomial time, which makes our algorithm very fast when compared to most of the brain extraction techniques that mostly depend on level sets implementations. 3) The implicit curve representation makes the model very robust to topology changes.