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The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
We present a novel 3D shape completion method that operates directly on unstructured point clouds, thus avoiding resource-intensive data structures like voxel grids. To this end, we introduce KAPLAN, a 3D point descriptor that aggregates…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet construction makes use of integration rules that are exact for…
We present a technique for rendering highly complex 3D scenes in real-time by generating uniformly distributed points on the scene's visible surfaces. The technique is applicable to a wide range of scene types, like scenes directly based on…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect),…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
The orthonormal basis generated by a wavelet of $L^2(\mathbb R)$ has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions…
This paper propose a interactive 3D modeling method and corresponding system based on single or multiple uncalibrated images. The main feature of this method is that, according to the modeling habits of ordinary people, the 3D model of the…
The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper…
In this paper, we report on a parallel freeviewpoint video synthesis algorithm that can efficiently reconstruct a high-quality 3D scene representation of sports scenes. The proposed method focuses on a scene that is captured by multiple…
3D image processing is an important problem in computer vision and pattern recognition fields. Compared with 2D image processing, its computation difficulty and cost are much higher due to the extra dimension. To fundamentally address this…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
We introduce a general approach for generation of sets of three-dimensional quasi-non-spreading wavepackets propagating in linear media, also referred to as linear light bullets. The spectrum of rigorously non-spreading wavepackets in media…
We propose a method for constructing high-quality, closed-surface meshes from confined 3D point clouds via a physically-based simulation of flexible foils under spatial constraints. The approach integrates dynamic elasticity,…
Contemporary registration devices for 3D visual information, such as LIDARs and various depth cameras, capture data as 3D point clouds. In turn, such clouds are challenging to be processed due to their size and complexity. Existing methods…
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…
In this paper, we propose a novel object detection algorithm named "Deep Regionlets" by integrating deep neural networks and a conventional detection schema for accurate generic object detection. Motivated by the effectiveness of regionlets…