arXiv subjects

Alexander Mai

Publications and source records attributed to Alexander Mai.

9 recordsLinked to original sources

arXiv2025

Radiance Meshes for Volumetric Reconstruction

We introduce radiance meshes, a technique for representing radiance fields with constant density tetrahedral cells produced with a Delaunay tetrahedralization. Unlike a Voronoi diagram, a Delaunay tetrahedralization yields simple triangles that are natively supported by existing hardware. As such, our model is able to perform exact and fast volume rendering using both rasterization and ray-tracing. We introduce a new rasterization method that achieves faster rendering speeds than all prior radiance field representations (assuming an equivalent number of primitives and resolution) across a variety of platforms. Optimizing the positions of Delaunay vertices introduces topological discontinuities (edge flips). To solve this, we use a Zip-NeRF-style backbone which allows us to express a smoothly varying field even when the topology changes. Our rendering method exactly evaluates the volume rendering equation and enables high quality, real-time view synthesis on standard consumer hardware. Our tetrahedral meshes also lend themselves to a variety of exciting applications including fisheye lens distortion, physics-based simulation, editing, and mesh extraction.

cs.GR↗

arXiv2024

EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis

We present Exact Volumetric Ellipsoid Rendering (EVER), a method for real-time differentiable emission-only volume rendering. Unlike recent rasterization based approach by 3D Gaussian Splatting (3DGS), our primitive based representation allows for exact volume rendering, rather than alpha compositing 3D Gaussian billboards. As such, unlike 3DGS our formulation does not suffer from popping artifacts and view dependent density, but still achieves frame rates of $\sim\!30$ FPS at 720p on an NVIDIA RTX4090. Since our approach is built upon ray tracing it enables effects such as defocus blur and camera distortion (e.g. such as from fisheye cameras), which are difficult to achieve by rasterization. We show that our method is more accurate with fewer blending issues than 3DGS and follow-up work on view-consistent rendering, especially on the challenging large-scale scenes from the Zip-NeRF dataset where it achieves sharpest results among real-time techniques.

cs.CV↗

arXiv2023

Neural Microfacet Fields for Inverse Rendering

We present Neural Microfacet Fields, a method for recovering materials, geometry, and environment illumination from images of a scene. Our method uses a microfacet reflectance model within a volumetric setting by treating each sample along the ray as a (potentially non-opaque) surface. Using surface-based Monte Carlo rendering in a volumetric setting enables our method to perform inverse rendering efficiently by combining decades of research in surface-based light transport with recent advances in volume rendering for view synthesis. Our approach outperforms prior work in inverse rendering, capturing high fidelity geometry and high frequency illumination details; its novel view synthesis results are on par with state-of-the-art methods that do not recover illumination or materials.

cs.CV↗

arXiv2022

$J^+$-like Invariants under Bifurcations

We explore how the invariants $J^+$, $J^-$, $\mathcal{J}_1$ and $\mathcal{J}_2$ of immersions -- generic (at most double points and only transverse intersections) planar smooth closed curves with non-vanishing derivative -- change under $k$-bifurcations ($k \ge 2 \in \mathbb{N}$), which are constructed by running $k$ times through an immersion and then perturbing it to be generic.

math.SG↗

arXiv2022

Introduction to Arnold's $J^+$-Invariant

We explore Arnold's $J^+$-invariant of immersions -- planar smooth closed curves with non-vanishing derivative, at most double points and only transverse intersections -- and computation methods like Viro's sum, among others. Only basic undergraduate mathematics is needed to understand the contents of this introductory paper and everything we need that is above that is recalled or introduced. Examples, exercises and solutions are included for practice.

math.DG↗

arXiv2021

Soft Expectation and Deep Maximization for Image Feature Detection

Central to the application of many multi-view geometry algorithms is the extraction of matching points between multiple viewpoints, enabling classical tasks such as camera pose estimation and 3D reconstruction. Many approaches that characterize these points have been proposed based on hand-tuned appearance models or data-driven learning methods. We propose Soft Expectation and Deep Maximization (SEDM), an iterative unsupervised learning process that directly optimizes the repeatability of the features by posing the problem in a similar way to expectation maximization (EM). We found convergence to be reliable and the new model to be more lighting invariant and better at localize the underlying 3D points in a scene, improving SfM quality when compared to other state of the art deep learning detectors.

cs.CV↗

arXiv2019

Training Deep Neural Networks to Detect Repeatable 2D Features Using Large Amounts of 3D World Capture Data

Image space feature detection is the act of selecting points or parts of an image that are easy to distinguish from the surrounding image region. By combining a repeatable point detection with a descriptor, parts of an image can be matched with one another, which is useful in applications like estimating pose from camera input or rectifying images. Recently, precise indoor tracking has started to become important for Augmented and Virtual reality as it is necessary to allow positioning of a headset in 3D space without the need for external tracking devices. Several modern feature detectors use homographies to simulate different viewpoints, not only to train feature detection and description, but test them as well. The problem is that, often, views of indoor spaces contain high depth disparity. This makes the approximation that a homography applied to an image represents a viewpoint change inaccurate. We claim that in order to train detectors to work well in indoor environments, they must be robust to this type of geometry, and repeatable under true viewpoint change instead of homographies. Here we focus on the problem of detecting repeatable feature locations under true viewpoint change. To this end, we generate labeled 2D images from a photo-realistic 3D dataset. These images are used for training a neural network based feature detector. We further present an algorithm for automatically generating labels of repeatable 2D features, and present a fast, easy to use test algorithm for evaluating a detector in an 3D environment.

cs.CV↗

arXiv2018

Loop Closure Detection with RGB-D Feature Pyramid Siamese Networks

In visual Simultaneous Localization And Mapping (SLAM), detecting loop closures has been an important but difficult task. Currently, most solutions are based on the bag-of-words approach. Yet the possibility of deep neural network application to this task has not been fully explored due to the lack of appropriate architecture design and of sufficient training data. In this paper we demonstrate the applicability of deep neural networks by addressing both issues. Specifically we show that a feature pyramid Siamese neural network can achieve state-of-the-art performance on pairwise loop closure detection. The network is trained and tested on large-scale RGB-D datasets with a novel automatic loop closure labeling algorithm. Each image pair is labelled by how much the images overlap, allowing loop closure to be computed directly rather than by labor intensive manual labeling. We present an algorithm to adopt any large-scale generic RGB-D dataset for use in training deep loop-closure networks. We show for the first time that deep neural networks are capable of detecting loop closures, and we provide a method for generating large-scale datasets for use in evaluating and training loop closure detectors.

cs.CV↗

arXiv2011

Quantum criticality of dipolar spin chains

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.

cond-mat.str-el↗