แนวคิดหลัก
Understanding the geometric properties of curves under the square root velocity transformation is essential for efficient elastic analysis.
บทคัดย่อ
The content delves into the elastic analysis of augmented curves and constrained surfaces, focusing on fundamental geometric properties. It discusses the importance of Riemannian structures in metric comparison, especially in applications like morphology, image analysis, and signal processing. The use of Riemannian metrics for sequential data analysis has grown rapidly in recent years. The square root velocity (SRV) framework is highlighted as a convenient and numerically efficient approach for analyzing curves via elastic metrics. Extensions to manifold-valued data are also explored. The paper presents contributions related to plane curves' behavior under SRV transformation and applies the elastic approach to augmented curves, determining classes of surfaces like tubes, ruled surfaces, spherical strips, protein molecules, and hurricane tracks. The study is organized into sections covering Riemannian settings, applications to time series data, homogeneous spaces, tube surfaces, ruled surfaces, spherical strips, and hurricane tracks.
สถิติ
"arXiv:2402.04944v2 [math.DG] 22 Mar 2024"
"project ID 499571814"
คำพูด
"A Riemannian structure is highly desirable for metric comparison of curves in various application areas."
"The square root velocity framework provides a convenient and numerically efficient approach for analyzing curves via elastic metrics."
"Extensions of SRV framework from euclidean to general manifold-valued data can be found in [13,27,25,9,26]."