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We resolve a longstanding open problem by reformulating the Grassmannian fusion frames to the case of mixed dimensions and show that this satisfies the proper properties for the problem. In order to compare elements of mixed dimension, we…
Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…
3D shape matching is a long-standing problem in computer vision and computer graphics. While deep neural networks were shown to lead to state-of-the-art results in shape matching, existing learning-based approaches are limited in the…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
In this paper, we propose a coarse-to-fine integration solution inspired by the classical ICP algorithm, to pairwise 3D point cloud registration with two improvements of hybrid metric spaces (eg, BSC feature and Euclidean geometry spaces)…
There is increasing demand for automated systems that can fabricate 3D structures. Robotic spatial extrusion has become an attractive alternative to traditional layer-based 3D printing due to a manipulator's flexibility to print large,…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…
We introduce a new approach for estimating the 3D pose and the 3D shape of an object from a single image. Given a training set of view exemplars, we learn and select appearance-based discriminative parts which are mapped onto the 3D model…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
We propose a fully automatic method for fitting a 3D morphable model to single face images in arbitrary pose and lighting. Our approach relies on geometric features (edges and landmarks) and, inspired by the iterated closest point…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
We present a computational methodology for obtaining rotationally symmetric sets of points satisfying discrete geometric constraints, and demonstrate its applicability by discovering new solutions to some well-known problems in…