2024/03/31 by Tongtong Zhang, Xian Wei, Zhang, Tongtong +3
Computer Science · #Advanced Image and Video Retrieval Techniques #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Image Retrieval and Classification Techniques
paper · pdf · doi:10.48550/arxiv.2404.00544
openalex publication_date 2024/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick named Deep Extrinsic Manifold Representation (DEMR) for visual tasks in this context. DEMR incorporates extrinsic manifold embedding into deep neural networks, which helps generate manifold representations. The DEMR approach does not directly optimize the complex geodesic loss. Instead, it focuses on optimizing the computation graph within the embedded Euclidean space, allowing for adaptability to various architectural requirements. We provide empirical evidence supporting the proposed concept on two types of manifolds, SE(3) and its associated quotient manifolds. This evidence offers theoretical assurances regarding feasibility, asymptotic properties, and generalization capability. The experimental results show that DEMR effectively adapts to point cloud alignment, producing outputs in SE(3) , as well as in illumination subspace learning with outputs on the Grassmann manifold.