Related papers: Symmetry Discovery Beyond Affine Transformations

Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so…

We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on the products of complex-valued wavelet convolutions, simplifies previous edge-based pairwise methods. Being parameter-centered, as opposed to…

We explore whether Neural Networks (NNs) can {\it discover} the presence of symmetries as they learn to perform a task. For this, we train hundreds of NNs on a {\it decoy task} based on well-controlled Physics templates, where no…

Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…

Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…

We propose a data-driven Machine-Learning Symmetry Discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates.…

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…

With the widespread application of Light Detection and Ranging (LiDAR) technology in fields such as autonomous driving, robot navigation, and terrain mapping, the importance of edge detection in LiDAR images has become increasingly…

Mirror detection aims to identify the mirror regions in the given input image. Existing works mainly focus on integrating the semantic features and structural features to mine specific relations between mirror and non-mirror regions, or…

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…

Given a multivariate big time series, can we detect anomalies as soon as they occur? Many existing works detect anomalies by learning how much a time series deviates away from what it should be in the reconstruction framework. However, most…

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…

We study the problem of symmetry detection of 3D shapes from single-view RGB-D images, where severely missing data renders geometric detection approach infeasible. We propose an end-to-end deep neural network which is able to predict both…

Image feature matching is to seek, localize and identify the similarities across the images. The matched local features between different images can indicate the similarities of their content. Resilience of image feature matching to large…

Exploitation of symmetries is an indispensable approach to solve certain classes of difficult SAT instances. Numerous techniques for the use of symmetry in SAT have evolved over the past few decades. But no matter how symmetries are used…

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…

Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…

We present a novel unsupervised deep learning framework for anomalous event detection in complex video scenes. While most existing works merely use hand-crafted appearance and motion features, we propose Appearance and Motion DeepNet (AMDN)…

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study…

Object detection is a fundamental task in computer vision and has many applications in image processing. This paper proposes a new approach for object detection by applying scale invariant feature transform (SIFT) in an automatic…