Related papers: Interactive Design and Optics-Based Visualization …
In this paper we have developed general algorithm for finding all orbifolds of Berglund-Hubsch-type Calabi-Yau manifolds and their mirrors. An explicit construction is formulated for finding all admissible deformations and groups defining…
Let M be a closed hyperbolic three manifold. We construct closed surfaces which map by immersions into M so that for each one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding…
We present a method for improving the efficiency and user experience of freeform illumination design with machine learning. By utilizing orthogonal polynomials to interface with artificial neural networks, we are able to generalize…
Arbitrary manipulation of light across multiple physical dimensions is essential for harnessing its parallelism in fundamental research and advanced applications, such as optical interconnects, computing, imaging, sensing, and quantum…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its…
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…
One major goal of vision is to infer physical models of objects, surfaces, and their layout from sensors. In this paper, we aim to interpret indoor scenes from one RGBD image. Our representation encodes the layout of orthogonal walls and…
We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a…
Holographic display can show pictures in the way that looks like the same with the real world, and is thought as the ultimate display technology. But due to the complexity of the traditional holographic technique, it can hardly be applied…
Large offline learning-based models have enabled robots to successfully interact with objects for a wide variety of tasks. However, these models rely on fairly consistent structured environments. For more unstructured environments, an…
We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…
Research ideation requires navigating trade-offs across multiple evaluative dimensions, yet most AI-assisted ideation tools leave this multi-dimensional reasoning unsupported, or reducing evaluation to unipolar scales where "more is…
We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are…
We present an assistive system for clipart design by providing visual scaffolds from the unseen viewpoints. Inspired by the artists' creation process, our system constructs the visual scaffold by first synthesizing the reference 3D shape of…
We show that a compact, complex analytic space $X$ has a bimeromorphic orbifold modification that is an isomorphism over the locally trivial orbifold locus of $X$.
We present an optical mapping near-eye (OMNI) three-dimensional display method for wearable devices. By dividing a display screen into different sub-panels and optically mapping them to various depths, we create a multiplane volumetric…
3D-aware visual pretraining has proven effective in improving the performance of downstream robotic manipulation tasks. However, existing methods are constrained to Euclidean embedding spaces, whose flat geometry limits their ability to…