相关论文: Sparse Representation of Gaussian Molecular Surfac…
Deblurring is a fundamental inverse problem in bioimaging. It requires modelling the point spread function (PSF), which captures the optical distortions entailed by the image formation process. The PSF limits the spatial resolution…
Inspired by the robustness and efficiency of sparse representation in sparse coding based image restoration models, we investigate the sparsity of neurons in deep networks. Our method structurally enforces sparsity constraints upon hidden…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…
Detailed analysis of scanning probe microscopy (SPM) data acquired for faceted and non-flat surfaces is usually complicated due to the presence of a large number of surface areas tilted by large/variable angles relative to the scanning…
Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
Accurate and compact representation of signed distance functions (SDFs) of implicit surfaces is crucial for efficient storage, computation, and downstream processing of 3D geometry. In this work, we propose a general learning method for…
3D Gaussian splatting has experienced explosive popularity in the past few years in the field of novel view synthesis. The lightweight and differentiable representation of the radiance field using the Gaussian enables rapid and high-quality…
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon…
Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
In recent years, Neural Radiance Fields (NeRF) has revolutionized three-dimensional (3D) reconstruction with its implicit representation. Building upon NeRF, 3D Gaussian Splatting (3D-GS) has departed from the implicit representation of…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
The quantum simulation of real molecules and materials is one of the most highly anticipated applications of quantum computing. Algorithms for simulating electronic structure using a first-quantized plane wave representation are especially…
Fast scanning probe microscopy enabled via machine learning allows for a broad range of nanoscale, temporally resolved physics to be uncovered. However, such examples for functional imaging are few in number. Here, using piezoresponse force…
3D Gaussian splatting (3DGS) has shown its detailed expressive ability and highly efficient rendering speed in the novel view synthesis (NVS) task. The application to inverse rendering still faces several challenges, as the discrete nature…
The reconstruction of 3D objects from calibrated photographs represents a fundamental yet intricate challenge in the domains of computer graphics and vision. Although neural reconstruction approaches based on Neural Radiance Fields (NeRF)…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
Human face recognition has been a long standing problem in computer vision and pattern recognition. Facial analysis can be viewed as a two-fold problem, namely (i) facial representation, and (ii) classification. So far, many face…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…