Constrained optimization of nonparametric entropy-based segmentation of brain structures

We propose a constrained, three-dimensional, nonparametric, entropy-based, coupled, multi-shape approach to segment subcortical brain structures from magnetic resonance images (MRI). The proposed method uses PCA to develop shape models that capture structural variability. It integrates geometrical relationship between different structures into the algorithm by coupling them (limiting their independent deformations). On the other hand, to allow variations among coupled structures, it registers each structure separately when building the shape models. It defines an entropy-based energy function, which is minimized using quasi-Newton algorithm. To this end, probability density functions (pdf) are estimated iteratively using nonparametric Parzen window method. In the optimization algorithm, constraints are used to improve segmentation quality. These constraints are extracted from training data. Sample results are given for the segmentation of caudate, hippocampus, and putamen, illustrating highly superior performance of the proposed method compared to the most similar methods in the literature.