Related papers: A Deep Learning Framework for Diffeomorphic Mappin…

Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel…

Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular…

Free-boundary diffeomorphism optimization, an important and widely occurring task in geometric modeling, computer graphics, and biological imaging, requires simultaneously determining a planar target domain and a locally bijective map with…

3D face registration is an important process in which a 3D face model is aligned and mapped to a template face. However, the task of 3D face registration becomes particularly challenging when dealing with partial face data, where only…

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…

In shape analysis, finding an optimal 1-1 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surface registration. The difficulty lies in the fact that the…

Three-dimensional (3D) mappings are fundamental in various scientific and engineering applications, including computer-aided engineering (CAE), computer graphics, and medical imaging. They are typically represented and stored as…

Over the past several decades, geometric mapping methods have been extensively developed and utilized for many practical problems in science and engineering. To assess the quality of geometric mappings, one common consideration is their…

This paper presents a novel approach that combines the Deep Ritz Method (DRM) with Fourier feature mapping to solve minimization problems comprised of multi-well, non-convex energy potentials. These problems present computational challenges…

This paper presents a method to compute the {\it quasi-conformal parameterization} (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain $S$ onto a punctured disk $D_S$…

We propose the Topology-Preserving Segmentation Network, a deformation-based model that can extract objects in an image while maintaining their topological properties. This network generates segmentation masks that have the same topology as…

Conventional deformable registration methods aim at solving an optimization model carefully designed on image pairs and their computational costs are exceptionally high. In contrast, recent deep learning based approaches can provide fast…

This paper proposes a deep learning-based beamforming design framework that directly maps a target beam pattern to optimal beamforming vectors across multiple antenna array architectures, including digital, analog, and hybrid beamforming.…

One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…

In medical imaging, surface registration is extensively used for performing systematic comparisons between anatomical structures, with a prime example being the highly convoluted brain cortical surfaces. To obtain a meaningful registration,…

Images degraded by geometric distortions pose a significant challenge to imaging and computer vision tasks such as object recognition. Deep learning-based imaging models usually fail to give accurate performance for geometrically distorted…

A DeepCAPA (Deep Learning for Continuous Aperture Array (CAPA)) framework is proposed to learn beamforming in CAPA systems. The beamforming optimization problem is firstly formulated, and it is mathematically proved that the optimal…

Deep learning-based methods have recently demonstrated promising results in deformable image registration for a wide range of medical image analysis tasks. However, existing deep learning-based methods are usually limited to small…

This paper proposes a novel method for computing bijective density-equalizing quasiconformal (DEQ) flattening maps for multiply-connected open surfaces. In conventional density-equalizing maps, shape deformations are solely driven by…

The spectrum of the Laplace-Beltrami (LB) operator is central in geometric deep learning tasks, capturing intrinsic properties of the shape of the object under consideration. The best established method for its estimation, from a…