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We present an active-set method for minimizing an objective that is the sum of a convex quadratic and $\ell_1$ regularization term. Unlike two-phase methods that combine a first-order active set identification step and a subspace phase…

We introduce an adaptive regularization approach. In contrast to conventional Tikhonov regularization, which specifies a fixed regularization operator, we estimate it simultaneously with parameters. From a Bayesian perspective we estimate…

We introduce neural cortical maps, a continuous and compact neural representation for cortical feature maps, as an alternative to traditional discrete structures such as grids and meshes. It can learn from meshes of arbitrary size and…

Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic…

Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…

Image registration is a classical problem in machine vision which seeks methods to align discrete images of the same scene to subpixel accuracy in general situations. As with all estimation problems, the underlying difficulty is the partial…

Rigid slice-to-volume registration is a challenging task, which finds application in medical imaging problems like image fusion for image guided surgeries and motion correction for volume reconstruction. It is usually formulated as an…

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a…

3D alignment has become a very important part of 3D scanning technology. For instance, we can divide the alignment process into four steps: key point detection, key point description, initial pose estimation, and alignment refinement.…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…

Non-rigid point cloud registration is a crucial task in computer vision. Evaluating a non-rigid point cloud registration method requires a dataset with challenges such as large deformation levels, noise, outliers, and incompleteness.…

Neural implicit functions have recently shown promising results on surface reconstructions from multiple views. However, current methods still suffer from excessive time complexity and poor robustness when reconstructing unbounded or…

Registration of pre-operative 3-D volumes to intra-operative 2-D X-ray images is important in minimally invasive medical procedures. Rigid registration can be performed by estimating a global rigid motion that optimizes the alignment of…

In this work, we conducted a survey on different registration algorithms and investigated their suitability for hyperspectral historical image registration applications. After the evaluation of different algorithms, we choose an intensity…

Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a…

Computing the gradients of a rendering process is paramount for diverse applications in computer vision and graphics. However, accurate computation of these gradients is challenging due to discontinuities and rendering approximations,…

We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…

We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…