Related papers: Symmetry Discovery Beyond Affine Transformations
Discovering governing equations, whether manually or by data-driven methods, has been central in physics and related areas. Since governing equations are typically constrained by a set of symmetries, using symmetry constraints to restrict…
To address the problem of 3D point matching where the poses of two point sets are unknown, we adapt a recently proposed path following based method to use similarity transformation instead of the original affine transformation. The reduced…
We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the…
Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration…
Edge detection serves as a critical foundation for numerous computer vision applications, including object detection, semantic segmentation, and image editing, by extracting essential structural cues that define object boundaries and…
Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of…
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
We study a class of nonlinear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of…
Anomaly detection consists in identifying, within a dataset, those samples that significantly differ from the majority of the data, representing the normal class. It has many practical applications, e.g. ranging from defective product…
We introduce a weak form of the realignment separability criterion which is particularly suited to detect continuous-variable entanglement and is physically implementable (it requires linear optics transformations and homodyne detection).…
In this work, we introduce the Equivariance Seeker Model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances…
Many modern applications require detecting change points in complex sequential data. Most existing methods for change point detection are unsupervised and, as a consequence, lack any information regarding what kind of changes we want to…
The generation of high-quality images has become widely accessible and is a rapidly evolving process. As a result, anyone can generate images that are indistinguishable from real ones. This leads to a wide range of applications, including…
Machine learning offers potential solutions to current issues in industrial systems in areas such as quality control and predictive maintenance, but also faces unique barriers in industrial applications. An ongoing challenge is extreme…
We present a method for estimating the maximal symmetry of a continuous regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries.…
Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is…
The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…