Related papers: Deep neural networks on diffeomorphism groups for …

We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…

Image segmentation is a fundamental task in computer vision aimed at delineating object boundaries within images. Traditional approaches, such as edge detection and variational methods, have been widely explored, while recent advances in…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

In an earlier article, we have "derived" space, as a part of the Random Dynamics project. In order to get locality we need to obtain reparametrization symmetry, or equivalently, diffeomorphism symmetry. There we sketched a procedure for how…

In this work, the problem of shape optimization, subject to PDE constraints, is reformulated as an $L^p$ best approximation problem under divergence constraints to the shape tensor introduced in Laurain and Sturm: ESAIM Math. Model. Numer.…

We consider the problem of finding the set of architectural parameters for a chosen deep neural network which is optimal under three metrics: parameter size, inference speed, and error rate. In this paper we state the problem formally, and…

Liquify is a common technique for image editing, which can be used for image distortion. Due to the uncertainty in the distortion variation, restoring distorted images caused by liquify filter is a challenging task. To edit images in an…

Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric…

Pan-sharpening is an important technique for remote sensing imaging systems to obtain high resolution multispectral images. Recently, deep learning has become the most popular tool for pan-sharpening. This paper develops a model-based deep…

Accurate geometric modeling of the aortic valve from 3D CT images is essential for biomechanical analysis and patient-specific simulations to assess valve health or make a preoperative plan. However, it remains challenging to generate…

Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage. When the source data is noisy or…

We propose a deep reparametrization of the maximum a posteriori formulation commonly employed in multi-frame image restoration tasks. Our approach is derived by introducing a learned error metric and a latent representation of the target…

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…

A common approach to solve inverse imaging problems relies on finding a maximum a posteriori (MAP) estimate of the original unknown image, by solving a minimization problem. In thiscontext, iterative proximal algorithms are widely used,…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…

We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…

It is challenging to directly estimate the human geometry from a single image due to the high diversity and complexity of body shapes with the various clothing styles. Most of model-based approaches are limited to predict the shape and pose…

This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…