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We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e. using a overly complicated model to…
We recently developed a new approach to get a stabilized image from a sequence of frames acquired through atmospheric turbulence. The goal of this algorihtm is to remove the geometric distortions due by the atmosphere movements. This method…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and…
We present a semi-sparsity model for 3D triangular mesh denoising, which is motivated by the success of semi-sparsity regularization in image processing applications. We demonstrate that such a regularization model can be also applied for…
This paper presents an optimised algorithm implementing the method of slices for analysing the stability of slopes. The algorithm adopts an improved physically based parameterisation of slip lines according to their geometrical…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
Diffeomorphic matching (only one of several names for this technique) is a technique for non-rigid registration of curves and surfaces in which the curve or surface is embedded in the flow of a time-series of vector fields. One seeks the…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
This paper introduces a novel partial differential equation (PDE) framework for single-image dehazing. We embed the atmospheric scattering model into a PDE featuring edge-preserving diffusion and a nonlocal operator to maintain both local…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
Atmospheric turbulence in long-range imaging significantly degrades the quality and fidelity of captured scenes due to random variations in both spatial and temporal dimensions. These distortions present a formidable challenge across…
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…
Optical multiplexing is a key technique that enhances the capacity of optical systems by independently modulating various optical parameters to carry distinct information. Among these parameters, wavelength, polarization, and angle are the…