*因疫情關係，5/19(四)理學論壇暨數學系專題演講將改採線上方式辦理，webex鏈結如下

========演講資訊(以線上方式辦理)=========

【主講者】林文偉教授
國立陽明交通大學應用數學系/教育部國家講座
【演講題目】Computational Conformal Geometry with Optimal Mass Transportations and its Application on 3D Brain Tumor segmentations

【演講時間】2022年5月19日(四) 15:10-17:00

【會議鏈結】https://nckucc.webex.com/nckucc/j.php?MTID=md7b8928b1dca3f8922c5c64c288418fc

【會議號】2517 757 6638 (若無法從連結進入，可登入手機或電腦版webex軟體，於加入會議欄位輸入連結或號碼)

【密碼】n8UGpnGC4J3

*線上會議室將於演講開始前15分鐘開啟

【關鍵字】Optimal Mass Transportations (OMT), 3D Brain Tumor segmentations，Medical Image，Mathematical Identification Auxiliary

【演講摘要】In this talk, we would like to introduce the computational conformal geometry with optimal mass transportation techniques and its applications on 3D medical image detections and segmentations. The well-known uniformization theorem shows that a closed surface of genus-zero is equivalently conformal to a unit sphere. However, the numerical method and its convergence should be addressed. We will propose efficient algorithms on conformal energy minimization (CEM), stretch energy minimization (SEM) and volume stretch energy minimization (VSEM) for finding the conformal (angle-preserving) and equiareal (area-preserving) parametrizations, respectively, between a simply connected closed surface and a sphere, as well as, the volume-preserving parametrization between a 3-manifold with a genus-zero boundary and a unit ball. Based on the SEM and VSEM algorithms we further develop the reliable and robust algorithms for solving the optimal mass transportation (OMT) between an irregular 3D domain and a unit ball, while minimizing the deformation cost, and keeping the minimal distortion and the local mass ratios unchanged. Combining the proposed OMT with the U-net machine learning algorithm, we develop a novel two-phase OMT algorithm successfully applying for the detection and segmentation of 3D brain tumors with high training and validation Dice scores. For training, good Dice scores: 0.9538 for the WT (whole tumor), 0.9546 for the TC (tumor core) and 0.9093 for the ET (enhanced tumor) can be obtained. For validation, the Dice scores of WT, TC and ET with mesh refinement and ensemble voting postprocessing can reach 0.9371, 0.9062 and 0.8747. A significant accuracy improvement in brain tumor detection and segmentation is achieved. Furthermore, It takes within 200 seconds to complete the whole brain tumor segmentation process for each new brain sample.