David Pokrajac: Recursive partitioning simulation of breast tissue
Vir: Seminar za diskretno matematiko
Povzetek. Three dimensional breast models represent important tools used in a variety of tasks, from preclinical evaluation of imaging technique, to dosimetry and computer aided diagnostic. In collaboration with University of Pennsylvania, we have developed a breast simulation algorithm that can provide simulation of various breast structures and control of anthropometric parameters such as number of fat compartments, thickness of Cooper's ligaments and percentage of radiologically dense tissue. In this presentation, we discuss foundations of recursive partitioning algorithm and consider its experimental performance and asymptotic complexity. Then, we discuss various improvements of algorithm, aimed to simulate voxels with multiple materials (partial volume effect), improve control of ligament thickness and surface smoothness and achieve simulation of milk ducts. We emphasize solved and open mathematical problems arising from this application related to non-linear optimization, graph theory, three-dimensional signal processing and computational geometry.