Computational Geometry in Medical Applications

This doctoral thesis develops novel techniques in Computational Geometry and applies them to Medical Imaging, Image-Guided Surgery and Motor Neurorehabilitation. 

In Medical Imaging, this Thesis contributes with: (a) optimization of parametric forms applicable to image segmentation and organic shape synthesis, and (b) simplification of topology and geometry of porous materials, which enables   mechanical computations (previously intractable) while faithfully representing local pore geometry.

In Image-Guided Surgery, this Thesis addresses surgical patient registration, including: (c) a robotic research platform for the controlled acquisition of intraoperative medical images, (d) intraoperative registration of Computer Tomography and Ultrasound medical images of the patient spine, and (e) homologated and public Ultrasound Image dataset with ground-truth to test 2D-3D or 3D-3D image registration algorithms.

In Motor Neurorehabilitation this Thesis addresses the patient posture estimation in exoskeleton-based therapy. Its contributions include: (f) enhanced estimation of upper limb joint angles, significantly improving exoskeleton - based estimations, and (g) enhanced estimation of shoulder angles using low-cost marker-based optical systems along with the rehabilitation exoskeleton.

All the aforementioned contributions have been submitted to the screening and critique of the international relevant scientific communities, achieving publication, homologation and/or favorable appraisal by experts. The developed systems, data sets and algorithms are currently applied in the National Hospital for Spinal Cord Injury (Toledo, Spain) and Surgical Robotics Project ORXXI (Basque Country, Spain).