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Existing light field representations, such as epipolar plane image (EPI) and sub-aperture images, do not consider the structural characteristics across the views, so they usually require additional disparity and spatial structure cues for…

We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have…

In this chapter, we give an overview of part of our previous work based on the minimal path framework and the Eikonal partial differential equation (PDE). We show that by designing adequate Riemannian and Randers geodesic metrics the…

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…

Dense Passage Retrieval (DPR) typically relies on Euclidean or cosine distance to measure query-passage relevance in embedding space, which is effective when embeddings lie on a linear manifold. However, our experiments across DPR…

Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to…

Neural implicit surface reconstruction with signed distance function has made significant progress, but recovering fine details such as thin structures and complex geometries remains challenging due to unreliable or noisy geometric priors.…

We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization…

Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…

Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis…

Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most…

In this work we study the numerical approximation of a class of ergodic Backward Stochastic Differential Equations. These equations are formulated in an infinite horizon framework and provide a probabilistic representation for elliptic…

Neural signed distance functions (SDFs) have shown powerful ability in fitting the shape geometry. However, inferring continuous signed distance fields from discrete unoriented point clouds still remains a challenge. The neural network…

We present GI-GS, a novel inverse rendering framework that leverages 3D Gaussian Splatting (3DGS) and deferred shading to achieve photo-realistic novel view synthesis and relighting. In inverse rendering, accurately modeling the shading…

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…

We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. To this end, we replace the commonly used eikonal equation with the heat method, carrying over to the neural domain what…

This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface…

We propose a dense indirect visual odometry method taking as input externally estimated optical flow fields instead of hand-crafted feature correspondences. We define our problem as a probabilistic model and develop a generalized-EM…

NeRF-based techniques fit wide and deep multi-layer perceptrons (MLPs) to a continuous radiance field that can be rendered from any unseen viewpoint. However, the lack of surface and normals definition and high rendering times limit their…

We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…