勷勤数学•专家报告

题      目：A Novel Highway Network for Surface Reconstruction in Computer Graphics

报  告  人：韩耀宗 教授  (邀请人：叶颀)

                                    香港中文大学

时      间： 1月21日  11：30-12:30

地     点：数科院西楼111

报告人简介:

        韩耀宗教授现任香港中文大学数学系及中国科学技术大学心理学系客座教授。已经发表SCI论文173余篇，被斯坦福大学John Loannidis教授团队列为世界上被引用次数最多的前2％科学家。他的研究主要集中在计算数学领域及涉及从观测数据中推导出未知参的数反问题，其应用涵盖工程、医学成像和地球物理学、无损检测、环境监测和诊断的关键领域。他的研究工作通常结合偏微分方程数值方法、优化技术和统计建模，以应对复杂的现实挑战。2024年，他担任《边界元工程分析》期刊人工智能驱动技术特刊的客座主编，并同时在香港中文大学教授人工智能的数学基础硕士课程。在研究课程中，指导学生选择研究主题并应用课程中教授的人工智能和数值计算技术进行文献调查、收集和分析数据，并为现实生活中的问题提出解决方案。研究结果发表在高引用的Medical Health学术雜誌上。

摘      要：

        Surface reconstruction from point clouds is a fundamental challenge in computer graphics and medical imaging. In this talk, we introduce a novel Square-Highway (SqrHw) Network to explore the application of advanced neural network architectures for an accurate and efficient reconstruction of surfaces from data points. Its performance alongside plain neural networks and a simplified highway network is illustrated through various numerical examples including the reconstruction of simple and complex surfaces, such as spheres, human hands, and intricate models like the Stanford Bunny. We also analyze the impact of factors such as the number of hidden layers, interior and exterior points, and data distribution on surface reconstruction quality. Our results show that the proposed SqrHw architecture outperforms most existing neural network configurations, achieving faster convergence and higher-quality surface reconstructions. Additionally, we demonstrate the SqrHw’s ability to predict surfaces over missing data, a valuable feature for challenging applications like medical imaging. Furthermore, our study demonstrates that the proposed SqrHw network yields more stable weight norms and backpropagation gradients compared to the Plain Network architecture. This research not only advances the field of computer graphics but also holds utility for other purposes such as function interpolation and physics-informed neural networks, which integrate multilayer perceptrons into their algorithms.

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