Related papers: Symmetry in Image Registration and Deformation Mod…

In general, the problem of non-rigid registration is about matching two different scans of a dynamic object taken at two different points in time. These scans can undergo both rigid motions and non-rigid deformations. Since new parts of the…

We study creating and analyzing symmetry and broken symmetry in digital art. Our focus is not so much on computer-generating artistic images, but rather on analyzing concepts and templates for incorporating symmetry and symmetry breaking…

Deep learning has emerged as a strong alternative for classical iterative methods for deformable medical image registration, where the goal is to find a mapping between the coordinate systems of two images. Popular classical image…

Image registration is a classical problem in machine vision which seeks methods to align discrete images of the same scene to subpixel accuracy in general situations. As with all estimation problems, the underlying difficulty is the partial…

Image registration has played an important role in image processing problems, especially in medical imaging applications. It is well known that when the deformation is large, many variational models cannot ensure diffeomorphism. In this…

We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic…

Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…

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…

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…

The task of image restration is to find the spatial correspondence of two or more given images. In this paper we assume that the correspondence is given either by an Euclidean, or by an affine volume-preserving transformation. Since the…

Automated symmetry detection is still a difficult task in 2021. However, it has applications in computer vision, and it also plays an important part in understanding art. This paper focuses on aiding the latter by comparing different…

In this paper, we propose a new approach to deformable image registration that captures sliding motions. The large deformation diffeomorphic metric mapping (LDDMM) registration method faces challenges in representing sliding motion since it…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

The goal of point set registration is to find point-by-point correspondences between point sets, each of which characterizes the shape of an object. Because local preservation of object geometry is assumed, prevalent algorithms in the area…

In current biological and medical research, statistical shape modeling (SSM) provides an essential framework for the characterization of anatomy/morphology. Such analysis is often driven by the identification of a relatively small number of…

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was…

This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to…

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…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

Image registration is fundamental in medical imaging applications, such as disease progression analysis or radiation therapy planning. The primary objective of image registration is to precisely capture the deformation between two or more…