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Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
Image registration techniques usually assume that the images to be registered are of a certain type (e.g. single- vs. multi-modal, 2D vs. 3D, rigid vs. deformable) and there lacks a general method that can work for data under all…
Dense vertex-to-vertex correspondence between 3D faces is a fundamental and challenging issue for 3D&2D face analysis. While the sparse landmarks have anatomically ground-truth correspondence, the dense vertex correspondences on most facial…
In recent years, implicit functions have drawn attention in the field of 3D reconstruction and have successfully been applied with Deep Learning. However, for incremental reconstruction, implicit function-based registrations have been…
Image registration is the inference of transformations relating noisy and distorted images. It is fundamental in computer vision, experimental physics, and medical imaging. Many algorithms and analyses exist for inferring shift, rotation,…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…
We present two algorithms for large-scale low-rank Euclidean distance matrix completion problems, based on semidefinite optimization. Our first method works by relating cliques in the graph of the known distances to faces of the positive…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Correlative microscopy aims at combining two or more modalities to gain more information than the one provided by one modality on the same biological structure. Registration is needed at different steps of correlative microscopies…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do…
Registration of 3D human body has been a challenging research topic for over decades. Most of the traditional human body registration methods require manual assistance, or other auxiliary information such as texture and markers. The…
This paper presents an approach to fast image registration through probabilistic pixel sampling. We propose a practical scheme to leverage the benefits of two state-of-the-art pixel sampling approaches: gradient magnitude based pixel…
One of the widespread solutions for non-rigid tracking has a nested-loop structure: with Gauss-Newton to minimize a tracking objective in the outer loop, and Preconditioned Conjugate Gradient (PCG) to solve a sparse linear system in the…
Image registration is a fundamental step in medical image analysis. Ideally, the transformation that registers one image to another should be a diffeomorphism that is both invertible and smooth. Traditional methods like geodesic shooting…