Related papers: The Block-wise Circumcentered-Reflection Method
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
Unidirectional optical systems enable selective control of light through asymmetric processing of radiation, effectively transmitting light in one direction while blocking unwanted propagation in the opposite direction. Here, we introduce a…
In this paper, we present a variant of the circumcenter method for the Convex Feasibility Problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto…
The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections…
Neural 3D scene representations have shown great potential for 3D reconstruction from 2D images. However, reconstructing real-world captures of complex scenes still remains a challenge. Existing generic 3D reconstruction methods often…
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…
Recovering the shape and appearance of real-world objects from natural 2D images is a long-standing and challenging inverse rendering problem. In this paper, we introduce a novel hybrid differentiable rendering method to efficiently…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
In this article, we study two methods for solving monotone inclusions in real Hilbert spaces involving the sum of a maximally monotone operator, a monotone-Lipschitzian operator, a cocoercive operator, and a normal cone to a vector…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
Our interest lies in developing some efficient methods for minimizing the sum of two geodesically convex functions on Hadamard manifolds, with the aim to enhance the convergence of the Douglas-Rachford algorithm in Hadamard manifolds.…
Video frame interpolation aims to synthesize realistic intermediate frames between given endpoints while adhering to specific motion semantics. While recent generative models have improved visual fidelity, they predominantly operate in a…
The Douglas-Rachford algorithm is widely used in sparse signal processing for minimizing a sum of two convex functions. In this paper, we consider the case where one of the functions is weakly convex but the other is strongly convex so that…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
Accurately rendering scenes with reflective surfaces remains a significant challenge in novel view synthesis, as existing methods like Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) often misinterpret reflections as physical…
We develop the ultraspherical rectangular collocation (URC) method, a collocation implementation of the sparse ultraspherical method of Olver \& Townsend for two-point boundary-value problems. The URC method is provably convergent, the…
Recently, significant progress has been made in the study of methods for 3D reconstruction from multiple images using implicit neural representations, exemplified by the neural radiance field (NeRF) method. Such methods, which are based on…
Traditional and deep learning-based fusion methods generated the intermediate decision map to obtain the fusion image through a series of post-processing procedures. However, the fusion results generated by these methods are easy to lose…
Image recognition is a classic and common task in the computer vision field, which has been widely applied in the past decade. Most existing methods in literature aim to learn discriminative features from labeled images for classification,…
In computational optics, numerical modeling of diffraction between arbitrary planes offers unparalleled flexibility. However, existing methods suffer from the trade-off between computational accuracy and efficiency. To resolve this dilemma,…