Image Set Classification Using a Distance-Based Kernel Over Affine Grassmann Manifold.

Area of Science:

• Computer Vision
• Machine Learning
• Manifold Geometry

Background:

• Linear subspace modeling is common for image set classification.
• Affine subspace modeling, though less explored, offers potential for improved classification.
• The affine Grassmann manifold (AGM) presents unique geometric challenges for classification.

Purpose of the Study:

• To develop a novel kernel method for image set classification using affine subspaces.
• To address the difficulties posed by the non-Euclidean geometry of the AGM.
• To map points in the AGM to a finite-dimensional Hilbert space for easier analysis.

Main Methods:

• Modeling image sets as affine subspaces within the AGM.
• Embedding the AGM into a higher-dimensional Grassmann manifold (GM).
• Utilizing a novel affine subspace-based kernel derived from projection distances.
• Employing kernel-gram matrix diagonalization for feature extraction.
• Applying distance-preserving and sparsity constraints for classification.

Main Results:

• The proposed kernel successfully maps AGM points to a Hilbert space.
• Diagonalization of the kernel-gram matrix yields low-dimensional Euclidean features.
• Classification using distance-preserving and sparsity constraints achieves minimum residual error.
• Experiments on gait, object, hand, and body gesture datasets show competitive performance.

Conclusions:

• The novel affine subspace-based kernel provides an effective approach for image set classification.
• The method successfully navigates the complexities of the AGM.
• Promising results demonstrate the technique's potential compared to existing methods.