Brain mid-sagittal surface extraction based on fractal analysis

In a normal human brain, inter-hemispheric fissure separates the brain into the left and the right hemispheres. In this paper, we model IF as a mid-sagittal surface on the input 3D brain MR image. For this purpose, we introduce a new method to extract MSS. In the proposed method, lacunarity is used to extract an initial symmetry plane, and then, fractal dimension is calculated in order to measure similarity degree between two brain hemispheres. Inside of each axial slice, a thin-plate spline surface is constructed based on the FD and intensity values, and a local optimization is applied to fit this TPS surface to the brain data using a robust least-median-of-squares estimator. Finally, MSS is modelled as a stack of the fitted TPSs, and the optimization is applied again in order to smooth the final MSS. MSS is the output of our method. The efficiency of the proposed method is evaluated using both simulated and real MR images and is compared to the state of the art. Our studies show that the proposed method discovers significant mid-sagittal surface with respect to the increased noise level and INU existence, in clinical images and pathological samples. This superiority is reasonable because of using FD and lacunarity being noise and INU independent and optimizing by TPS working locally.