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Deformable surface tracking from monocular images is well-known to be under-constrained. Occlusions often make the task even more challenging, and can result in failure if the surface is not sufficiently textured. In this work, we…
A novel domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations…
During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal…
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…
We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around…
We present a new technique that achieves a significant reduction in the quantity of measurements required for a fusion based dense 3D mapping system to converge to an accurate, de-noised surface reconstruction. This is achieved through the…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation…
Existing depth completion methods are often targeted at a specific sparse depth type and generalize poorly across task domains. We present a method to complete sparse/semi-dense, noisy, and potentially low-resolution depth maps obtained by…
We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary…
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
We present an improved model for MRF-based depth upsampling, guided by image- as well as 3D surface normal features. By exploiting the underlying camera model we define a novel regularization term that implicitly evaluates the planarity of…
Photometric variation of a directly imaged planet contains information on both the geography and spectra of the planetary surface. We propose a novel technique that disentangles the spatial and spectral information from the multi-band…
How might one "reduce" a graph? That is, generate a smaller graph that preserves the global structure at the expense of discarding local details? There has been extensive work on both graph sparsification (removing edges) and graph…
Algorithms based on gradient descent for computing the elastic shape registration of two simple surfaces in 3-dimensional space and therefore the elastic shape distance between them have been proposed by Kurtek, Jermyn, et al., and more…
We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
Nowadays dense stereo matching has become one of the dominant tools in 3D reconstruction of urban regions for its low cost and high flexibility in generating dense 3D points. However, state-of-the-art stereo matching algorithms usually…
In the present work, we introduce a Self-Consistent Density-Functional Embedding technique, which leaves the realm of standard energy-functional approaches in Density Functional Theory and targets directly the density-to-potential mapping…