Related papers: Multidimensional TV-Stokes for image processing
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
Three-dimensional (3D) object reconstruction based on differentiable rendering (DR) is an active research topic in computer vision. DR-based methods minimize the difference between the rendered and target images by optimizing both the shape…
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
In this work, we propose a novel procedure for video super-resolution, that is the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a "sequential" model (i.e., each…
Mathematical methods of image inpainting involve the discretization of given continuous models. We present a method that avoids the standard pointwise discretization by modeling known variational approaches, in particular total variation…
In this paper, we devise a $\operatorname{prox}$-based semi-smooth Newton method for the non-differentiable TV-minimization problem. To this end, the primal-dual optimality conditions are reformulated as a nonlinear operator equation with…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…
Signal models based on sparsity, low-rank and other properties have been exploited for image reconstruction from limited and corrupted data in medical imaging and other computational imaging applications. In particular, sparsifying…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…
We present an algorithm for multi-scale tumor (chimeric cell) detection in high resolution slide scans. The broad range of tumor sizes in our dataset pose a challenge for current Convolutional Neural Networks (CNN) which often fail when…
A detailed analysis of ptychography for 3D phase reconstructions of thick specimens is performed. We introduce multi-focus ptychography, which incorporates a 4D-STEM defocus series to enhance the quality of 3D reconstructions along the beam…
Recent advances in differentiable rendering have enabled high-quality reconstruction of 3D scenes from multi-view images. Most methods rely on simple rendering algorithms: pre-filtered direct lighting or learned representations of…
Existing approaches for Structure from Motion (SfM) produce impressive 3-D reconstruction results especially when using imagery captured with large parallax. However, to create engaging video-content in movies and TV shows, the amount by…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
In this paper, we propose a novel method for joint recovery of camera pose, object geometry and spatially-varying Bidirectional Reflectance Distribution Function (svBRDF) of 3D scenes that exceed object-scale and hence cannot be captured…
Unsupervised object discovery aims to localize objects in images, while removing the dependence on annotations required by most deep learning-based methods. To address this problem, we propose a fully unsupervised, bottom-up approach, for…
Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model…