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Deep Extrinsic Manifold Representation for Vision Tasks
Mar 31, 2024
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.
rpcPRF: Generalizable MPI Neural Radiance Field for Satellite Camera
Oct 11, 2023Novel view synthesis of satellite images holds a wide range of practical applications. While recent advances in the Neural Radiance Field have predominantly targeted pin-hole cameras, and models for satellite cameras often demand sufficient input views. This paper presents rpcPRF, a Multiplane Images (MPI) based Planar neural Radiance Field for Rational Polynomial Camera (RPC). Unlike coordinate-based neural radiance fields in need of sufficient views of one scene, our model is applicable to single or few inputs and performs well on images from unseen scenes. To enable generalization across scenes, we propose to use reprojection supervision to induce the predicted MPI to learn the correct geometry between the 3D coordinates and the images. Moreover, we remove the stringent requirement of dense depth supervision from deep multiview-stereo-based methods by introducing rendering techniques of radiance fields. rpcPRF combines the superiority of implicit representations and the advantages of the RPC model, to capture the continuous altitude space while learning the 3D structure. Given an RGB image and its corresponding RPC, the end-to-end model learns to synthesize the novel view with a new RPC and reconstruct the altitude of the scene. When multiple views are provided as inputs, rpcPRF exerts extra supervision provided by the extra views. On the TLC dataset from ZY-3, and the SatMVS3D dataset with urban scenes from WV-3, rpcPRF outperforms state-of-the-art nerf-based methods by a significant margin in terms of image fidelity, reconstruction accuracy, and efficiency, for both single-view and multiview task.
Fast Satellite Tensorial Radiance Field for Multi-date Satellite Imagery of Large Size
Sep 21, 2023
Existing NeRF models for satellite images suffer from slow speeds, mandatory solar information as input, and limitations in handling large satellite images. In response, we present SatensoRF, which significantly accelerates the entire process while employing fewer parameters for satellite imagery of large size. Besides, we observed that the prevalent assumption of Lambertian surfaces in neural radiance fields falls short for vegetative and aquatic elements. In contrast to the traditional hierarchical MLP-based scene representation, we have chosen a multiscale tensor decomposition approach for color, volume density, and auxiliary variables to model the lightfield with specular color. Additionally, to rectify inconsistencies in multi-date imagery, we incorporate total variation loss to restore the density tensor field and treat the problem as a denosing task.To validate our approach, we conducted assessments of SatensoRF using subsets from the spacenet multi-view dataset, which includes both multi-date and single-date multi-view RGB images. Our results clearly demonstrate that SatensoRF surpasses the state-of-the-art Sat-NeRF series in terms of novel view synthesis performance. Significantly, SatensoRF requires fewer parameters for training, resulting in faster training and inference speeds and reduced computational demands.
SparGE: Sparse Coding-based Patient Similarity Learning via Low-rank Constraints and Graph Embedding
Feb 03, 2022
Patient similarity assessment (PSA) is pivotal to evidence-based and personalized medicine, enabled by analyzing the increasingly available electronic health records (EHRs). However, machine learning approaches for PSA has to deal with inherent data deficiencies of EHRs, namely missing values, noise, and small sample sizes. In this work, an end-to-end discriminative learning framework, called SparGE, is proposed to address these data challenges of EHR for PSA. SparGE measures similarity by jointly sparse coding and graph embedding. First, we use low-rank constrained sparse coding to identify and calculate weight for similar patients, while denoising against missing values. Then, graph embedding on sparse representations is adopted to measure the similarity between patient pairs via preserving local relationships defined by distances. Finally, a global cost function is constructed to optimize related parameters. Experimental results on two private and public real-world healthcare datasets, namely SingHEART and MIMIC-III, show that the proposed SparGE significantly outperforms other machine learning patient similarity methods.