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In this work, we propose a disentangled latent optimization-based method for parameterizing grouped deforming 3D objects into shape and deformation factors in an unsupervised manner. Our approach involves the joint optimization of a…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
Data-driven approaches have become a dominant paradigm for robotic grasp planning. However, the performance of these approaches is enormously influenced by the quality of the available training data. In this paper, we propose a framework to…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization…
We introduce a novel sketch-to-image tool that aligns with the iterative refinement process of artists. Our tool lets users sketch blocking strokes to coarsely represent the placement and form of objects and detail strokes to refine their…
This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…
Accurate measurement of gravitational shear from images of distant galaxies is one of the most direct ways of studying the distribution of mass in the universe. We describe an implementation of a technique that is based on the shapelets…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
Group zero-attracting LMS and its reweighted form have been proposed for addressing system identification problems with structural group sparsity in the parameters to estimate. Both algorithms however suffer from a trade-off between…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…