Related papers: Analysis of Amoeba Active Contours
In tomographic imaging, anatomical structures are reconstructed by applying a pseudo-inverse forward model to acquired signals. Geometric information within this process is usually depending on the system setting only, i. e., the scanner…
In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs…
As another critical implementation of moving frames for partial differential equations, this paper proposes a novel numerical scheme by aligning one of three orthogonal unit vectors at each grid point along the direction of a wave…
The "interpretation through synthesis" approach to analyze face images, particularly Active Appearance Models (AAMs) method, has become one of the most successful face modeling approaches over the last two decades. AAM models have ability…
Recent years have witnessed the great success of deep learning on various point cloud analysis tasks, e.g., classification and semantic segmentation. Since point cloud data is sparse and irregularly distributed, one key issue for point…
Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature kernels were recently shown to solve a Goursat PDE. However,…
This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…
We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently…
Active Surface Models have a long history of being useful to model complex 3D surfaces but only Active Contours have been used in conjunction with deep networks, and then only to produce the data term as well as meta-parameter maps…
The visual cortex is a vital part of the brain, responsible for hierarchically identifying objects. Understanding the role of the lateral geniculate nucleus (LGN) as a prior region of the visual cortex is crucial when processing visual…
In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of a bladder during a forced…
The locomotion of flexible membrane-like organisms on top of curved surfaces appears in different contexts and scales. Still, such dynamics have not yet been quantitatively modeled and no realization of such motion in manmade systems has…
A large number of powerful, high-quality, and open-source simulation packages exist to efficiently perform molecular dynamics simulations, and their prevalence has greatly accelerated discoveries across a wide range of scientific domains.…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…
We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…
Image segmentation is the initial step for every image analysis task. A large variety of segmentation algorithm has been proposed in the literature during several decades with some mixed success. Among them, the fuzzy energy based active…
Recently, deep learning becomes the main focus of machine learning research and has greatly impacted many important fields. However, deep learning is criticized for lack of interpretability. As a successful unsupervised model in deep…
An active-sensing-based learning algorithm is proposed to solve the near-field beam alignment problem with the aid of wavenumber-domain transform matrices (WTMs). Specifically, WTMs can transform the antenna-domain channel into a sparse…