Differential Evolution and Covariance Ellipsoid for non-rigid transformation tracking of internal organs
Carlos Villaseñor, Nancy Arana‐Daniel, Alma Y. Alanís, Carlos López-Franco · 2018
In nowadays research, tools that help to visualize physical phenomena are helpful to address a great variety of modeling problems. In particular, tools that offer a three-dimensional representation of internal organs represent a huge advantage to understand their functions and anomalies, which could lead to better diagnosis and treatments of diseases. In this paper, we propose a novel internal organs modeling algorithm, based on Differential Evolution algorithm and Covariance Ellipsoid computation. The proposed algorithm uses k-means++ clustering over the registration of a 4D-Magnetic Resonance Imaging of an internal organ and calculates the representative covariance ellipsoid, then we track the non-rigid transformation using the spectral decomposition of the covariance matrix and Differential Evolution to optimize the geometric representation. The proposal offers a compact 4D map with local optimized non-rigid transformations, and the algorithm scheme is simple to implement with low computational cost with good accuracy. It avoids calculating the covariance matrices every time. We show the experimental results of a liver's right lobe movement during the respiratory cycle.