Related papers: Ray-marching Thurston geometries
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
This paper uses mathematics to analyze the challenges of geometrically noisy environments on triangulation. Given widely accepted algorithmic triangulation methods, such as O (n ln n) or a simpler O (n^3) method, we can mathematically prove…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
In this paper, we propose a scene-level inverse rendering framework that uses multi-view images to decompose the scene into geometry, SVBRDF, and 3D spatially-varying lighting. While multi-view images have been widely used for object-level…
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform…
A Scene, represented visually using different formats such as RGB-D, LiDAR scan, keypoints, rectangular, spherical, multi-views, etc., contains information implicitly embedded relevant to applications such as scene indexing, vision-based…
This paper is the first of a 3-part series that classifies the 5-dimensional Thurston geometries. The present paper (part 1 of 3) summarizes the general classification, giving the full list, an outline of the method, and some illustrative…
We propose a novel explicit dense 3D reconstruction approach that processes a set of images of a scene with sensor poses and calibrations and estimates a photo-real digital model. One of the key innovations is that the underlying volumetric…
Geometry reconstruction of textureless, non-Lambertian objects under unknown natural illumination (i.e., in the wild) remains challenging as correspondences cannot be established and the reflectance cannot be expressed in simple analytical…
We introduce the first end-to-end learning-based solution to near-field Photometric Stereo (PS), where the light sources are close to the object of interest. This setup is especially useful for reconstructing large immobile objects. Our…
Recent approaches on visual scene understanding attempt to build a scene graph -- a computational representation of objects and their pairwise relationships. Such rich semantic representation is very appealing, yet difficult to obtain from…
We describe a hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes (for example, in illustration). The method makes use of a…
We present a differentiable rendering framework for material and lighting estimation from multi-view images and a reconstructed geometry. In the framework, we represent scene lightings as the Neural Incident Light Field (NeILF) and material…
Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding visual contents. Moment-based image representation has been reported to be…
Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…
Image-based lighting is a widely used technique to reproduce shading under real-world lighting conditions, especially in real-time rendering applications. A particularly challenging scenario involves materials exhibiting a sparkling or…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…