Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

3D-2D image registration by nonlinear regression

We propose a 3D-2D image registration method that relates image features of 2D projection images to the transformation parameters of the 3D image by nonlinear regression. The method is compared with a conventional registration method based on iterative optimization. For evaluation, simulated X-ray images (DRRs) were generated from coronary artery tree models derived from 3D CTA scans. Registration of nine vessel trees was performed, and the alignment quality was measured by the mean target registration error (mTRE). The regression approach was shown to be slightly less accurate, but much more robust than the method based on an iterative optimization approach.

Registration-by-regression of coronary CTA and X-ray angiography

We evaluate the integration of 3D preoperative computed tomography angiography of the coronary arteries with intraoperative 2D X-ray angiographies by a recently proposed novel registration-by-regression method. The method relates image features of 2D projection images to the transformation parameters of the 3D image. We compared different sets of features and studied the influence of preprocessing the training set. For the registration evaluation, a gold standard was developed from eight X-ray angiography sequences from six different patients. The alignment quality was measured using the 3D mean target registration error (mTRE). The registration-by-regression method achieved moderate accuracy (median mTRE of 15 mm) on real images. It does therefore not provide yet a complete solution to the 3D–2D registration problem but it could be used as an initialisation method to eliminate the need for manual initialisation.