Related papers: Beyond the ABCDs: A better matrix method for geome…
We propose a compact and efficient tetrahedral mesh representation to improve the ray-tracing performance. We reorder tetrahedral mesh data using a space-filling curve to improve cache locality. Most importantly, we propose an efficient ray…
Active stereo vision is important in reconstructing objects without obvious textures. However, it is still very challenging to extract and match the projected patterns from two camera views automatically and robustly. In this paper, we…
Ray-tracing-based 3D Gaussian splatting (3DGS) methods overcome the limitations of rasterization -- rigid pinhole camera assumptions, inaccurate shadows, and lack of native reflection or refraction -- but remain slower due to the cost of…
For paraxial light beams and electromagnetic fields, the Stokes vector and polarization matrix provide equivalent scalar measures of optical chirality, widely used in linear optics. However, growing interest in non-paraxial fields, with…
Using a series of detector measurements taken at different locations to localize a source of radiation is a well-studied problem. The source of radiation is sometimes constrained to a single point-like source, in which case the location of…
In this paper, a method for solving the initial structure of an off-axis multi-mirror system applied to extreme ultraviolet (EUV) lithography using a paraxial ray-tracing algorithm based on Seidel aberration theory is proposed. By tracing…
Until now, despite their high accuracy, the utilization of the conventional image theory method ray tracers was limited to simple simulation environments with small number of field observation points and low maximum ray bouncing order due…
We present here an alternative method for calculating magnifications in gravitational lensing calculations -- the Ray Bundle method. We provide a detailed comparison between the distribution of magnifications obtained compared with analytic…
This paper presents a method to detect reflection of 3D light detection and ranging (Lidar) scans and uses it to classify the points and also map objects outside the line of sight. Our software uses several approaches to analyze the point…
The goal of the proposed method is to directly obtain a pose matrix of a known rectangular target, without estimation, using geometric techniques. This method is specifically tailored for real-time, extreme imaging setups exceeding…
This paper proposes a new extrinsic calibration of kaleidoscopic imaging system by estimating normals and distances of the mirrors. The problem to be solved in this paper is a simultaneous estimation of all mirror parameters consistent…
Eye tracking is an important tool with a wide range of applications in Virtual, Augmented, and Mixed Reality (VR/AR/MR) technologies. State-of-the-art eye tracking methods are either reflection-based and track reflections of sparse point…
We propose a method to efficiently compute tomographic projections of a 3D volume represented by a linear combination of shifted B-splines. To do so, we propose a ray-tracing algorithm that computes 3D line integrals with arbitrary…
Acoustic rays can be described by null geodesics of a pseudo-Riemannian manifold. This allows for the immediate generalization of paraxial ray systems via geodesic deviation. The technique has appeared in the literature for the past decade…
To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the…
Optical coherence tomography (OCT) is a powerful and noninvasive method for retinal imaging. In this paper, we introduce a fast segmentation method based on a new variant of spectral graph theory named diffusion maps. The research is…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
3D Gaussian Splatting has gained widespread adoption across diverse applications due to its exceptional rendering performance and visual quality. While most existing methods rely on rasterization to render Gaussians, recent research has…
We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…
We show how to enhance the redshift accuracy of surveys consisting of tracers with highly uncertain positions along the line of sight. Photometric surveys with redshift uncertainty delta_z ~ 0.03 can yield final redshift uncertainties of…