Intrinsic 3D Dynamic Surface Tracking based on Dynamic Ricci Flow and Teichmüller Map

Area of Science:

• Computer Vision
• Medical Imaging
• Computational Geometry

Background:

• 3D dynamic surface tracking is crucial for applications like computer vision and medical imaging.
• Existing methods struggle with large deformations and noise in surface registration.
• Efficiently registering non-rigid 3D surfaces remains a significant research challenge.

Purpose of the Study:

• To develop an automatic, robust method for non-rigid 3D dynamic surface tracking.
• To address challenges posed by large deformations and noise in surface registration.
• To improve the accuracy and efficiency of 3D dynamic surface tracking.

Main Methods:

• Utilizes surface Ricci flow and Teichmüller map methods for non-rigid 3D dynamic surface tracking.
• Employs quasi-conformal Teichmüller theory to minimize dilation and handle large deformations.
• Incorporates Delaunay triangulation and quadrilateral meshes for applicability to low-quality meshes.
• Identifies sparse surface features using machine learning and assigns landmark features with curvature settings.
• Computes Riemannian metric via dynamic Ricci flow, concentrating curvature on feature points.
• Performs registration using Teichmüller mappings to align feature points with minimal angular distortion.

Main Results:

• Successfully registered 3D facial surfaces with significant expression deformations.
• Demonstrated improved accuracy and efficiency compared to two state-of-the-art tracking methods.
• The method is effective even with low-quality meshes and noisy surface data.

Conclusions:

• The proposed method offers an effective solution for non-rigid 3D dynamic surface tracking.
• Surface Ricci flow and Teichmüller maps provide a robust framework for handling large deformations and noise.
• The technique shows significant potential for advancing computer vision and medical imaging applications requiring precise surface registration.