Related papers: Ray-marching Thurston geometries
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…
Implicit neural representation (INR) has proven to be accurate and efficient in various domains. In this work, we explore how different neural networks can be designed as a new texture INR, which operates in a continuous manner rather than…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
This paper presents a new Bayesian spectral unmixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak,…
Being able to see beyond the direct line of sight is an intriguing prospective and could benefit a wide variety of important applications. Recent work has demonstrated that time-resolved measurements of indirect diffuse light contain…
Augmented reality (AR) has gained increasingly attention from both research and industry communities. By overlaying digital information and content onto the physical world, AR enables users to experience the world in a more informative and…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
We present an efficient algorithm designed for and capable of detecting elongated, thin features such as lines and curves in astronomical images, and its application to the automatic detection of gravitational arcs. The algorithm is…
We propose a novel Neural Radiance Field (NeRF) representation for non-opaque scenes that enables fast inference by utilizing textured polygons. Despite the high-quality novel view rendering that NeRF provides, a critical limitation is that…
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
Designing freeform surfaces to control light based on real-world illumination patterns is challenging, as existing caustic lens designs often assume oversimplified point or parallel light sources. We propose representing surface light…
Of the Thurston geometries, those with constant curvature geometries (Euclidean $\EUC$, hyperbolic $\HYP$, spherical $\SPH$) have been extensively studied, but the other five geometries, $\HXR$, $\SXR$, $\NIL$, $\SLR$, $\SOL$ have been…
We consider Milnor's "tower algorithm" in the space of piecewise monotone maps, an iterative algorithm on the space of metrics which unifies, on the one hand, Thurston's iterative scheme which converges to holomorphic models, and, on the…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
Ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane and simulating the effects of high-quality global illumination at a heavy computational cost. Because of the high computation…
Image segmentation algorithms often depend on appearance models that characterize the distribution of pixel values in different image regions. We describe a new approach for estimating appearance models directly from an image, without…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions…
Object detection and recognition are important problems in computer vision. Since these problems are meta-heuristic, despite a lot of research, practically usable, intelligent, real-time, and dynamic object detection/recognition methods are…