Data-Driven Metric Learning for Image Databases Represented as Riemannian Manifolds Embedded into Image Spaces

• Paulo A. Braz LNCC / UFS
• Gastão F. Junior LNCC / UFS
• Gilson A. Giraldi LNCC / UFS

DOI: https://doi.org/10.5753/eniac.2026.29794

Resumo

We present a data-driven pipeline for learning a smooth Riemannian metric over reduced image representations and computing geodesic trajectories. The method estimates local tangent structure with medoid-based clustering and cluster-wise PCA, aligns local coordinate systems, and blends metric tensors using radial basis function weights. Geodesics are solved as boundary value problem initialized from discrete manifold paths, with checkpointed continuation for difficult transitions. Results show that BVP refines graph-based paths, while linear interpolation, although short, crosses regions less supported by the empirical data distribution. The proposed framework provides a practical tool for probing intrinsic geometric structure in learned image representations.

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