Elastic Functional Coding of Riemannian Trajectories.

Area of Science:

• Computer Vision
• Machine Learning
• Differential Geometry

Background:

• Human actions are dynamic phenomena often represented as feature sequences.
• Representing these as trajectories on Riemannian manifolds presents challenges due to non-linearity and high dimensionality.
• Existing manifold learning techniques are not directly applicable to Riemannian trajectories.

Purpose of the Study:

• To develop a method for learning low-dimensional embeddings of Riemannian trajectories representing human actions.
• To enable efficient search, retrieval, visualization, and recognition of dynamic visual phenomena.
• To address the limitations of traditional manifold learning for temporal data.

Main Methods:

• Utilized the transported square-root velocity fields (TSRVF) framework for trajectory representation.
• Developed a rate-invariant metric and vector space representations for Riemannian trajectories.
• Extended coding methods like PCA and KSVD to Riemannian trajectories and functions.

Main Results:

• Achieved state-of-the-art results in action recognition, visual speech recognition, and stroke rehabilitation.
• Reduced dimensionality and complexity by 100-250x.
• Demonstrated efficient trajectory capture, clustering, and diverse sequence sampling.

Conclusions:

• The TSRVF-based framework provides an effective way to learn low-dimensional embeddings for Riemannian trajectories.
• This approach enables significant improvements in various computer vision tasks involving dynamic phenomena.
• The invertible mappings allow for interactive visualization and action synthesis.