Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a point-wise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multi-scale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to 4th order. These scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.
Different tasks in the computational pipeline of single-particle cryo-electron microscopy (cryo-EM) require enhancing the quality of the highly noisy raw images. To this end, we develop an efficient algorithm for signal enhancement of cryo-EM images. The enhanced images can be used for a variety of downstream tasks, such as 2-D classification, removing uninformative images, constructing {ab initio} models, generating templates for particle picking, providing a quick assessment of the data set, dimensionality reduction, and symmetry detection. The algorithm includes built-in quality measures to assess its performance and alleviate the risk of model bias. We demonstrate the effectiveness of the proposed algorithm on several experimental data sets. In particular, we show that the quality of the resulting images is high enough to produce ab initio models of $\sim 10$ \AA resolution. The algorithm is accompanied by a publicly available, documented and easy-to-use code.
Offline estimation of the dynamical model of a Markov Decision Process (MDP) is a non-trivial task that greatly depends on the data available in the learning phase. Sometimes the dynamics of the model is invariant with respect to some transformations of the current state and action. Recent works showed that an expert-guided pipeline relying on Density Estimation methods as Deep Neural Network based Normalizing Flows effectively detects this structure in deterministic environments, both categorical and continuous-valued. The acquired knowledge can be exploited to augment the original data set, leading eventually to a reduction in the distributional shift between the true and the learned model. Such data augmentation technique can be exploited as a preliminary process to be executed before adopting an Offline Reinforcement Learning architecture, increasing its performance. In this work we extend the paradigm to also tackle non-deterministic MDPs, in particular, 1) we propose a detection threshold in categorical environments based on statistical distances, and 2) we show that the former results lead to a performance improvement when solving the learned MDP and then applying the optimized policy in the real environment.
The inherent challenge of detecting symmetries stems from arbitrary orientations of symmetry patterns; a reflection symmetry mirrors itself against an axis with a specific orientation while a rotation symmetry matches its rotated copy with a specific orientation. Discovering such symmetry patterns from an image thus benefits from an equivariant feature representation, which varies consistently with reflection and rotation of the image. In this work, we introduce a group-equivariant convolutional network for symmetry detection, dubbed EquiSym, which leverages equivariant feature maps with respect to a dihedral group of reflection and rotation. The proposed network is built end-to-end with dihedrally-equivariant layers and trained to output a spatial map for reflection axes or rotation centers. We also present a new dataset, DENse and DIverse symmetry (DENDI), which mitigates limitations of existing benchmarks for reflection and rotation symmetry detection. Experiments show that our method achieves the state of the arts in symmetry detection on LDRS and DENDI datasets.
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 state-of-the-art automated symmetry detection algorithms. For one of such algorithms aimed at reflectional symmetries, we propose post-processing improvements to find localised symmetries in images, improve the selection of detected symmetries and identify another symmetry type (rotational). In order to detect rotational symmetries, we contribute a machine learning model which detects rotational symmetries based on provided reflection symmetry axis pairs. We demonstrate and analyze the performance of the extended algorithm to detect localised symmetries and the machine learning model to classify rotational symmetries.
Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and especially reflectional symmetries, are also important in drawings of graphs. Detecting and classifying symmetries can be very useful in algorithms that aim to create symmetric graph drawings and in this paper we present a machine learning approach for these tasks. Specifically, we show that deep neural networks can be used to detect reflectional symmetries with 92% accuracy. We also build a multi-class classifier to distinguish between reflectional horizontal, reflectional vertical, rotational, and translational symmetries. Finally, we make available a collection of images of graph drawings with specific symmetric features that can be used in machine learning systems for training, testing and validation purposes. Our datasets, best trained ML models, source code are available online.
In this paper, we establish a baseline for object reflection symmetry detection in complex backgrounds by presenting a new benchmark and an end-to-end deep learning approach, opening up a promising direction for symmetry detection in the wild. The new benchmark, Sym-PASCAL, spans challenges including object diversity, multi-objects, part-invisibility, and various complex backgrounds that are far beyond those in existing datasets. The end-to-end deep learning approach, referred to as a side-output residual network (SRN), leverages the output residual units (RUs) to fit the errors between the object ground-truth symmetry and the side-outputs of multiple stages. By cascading RUs in a deep-to-shallow manner, SRN exploits the 'flow' of errors among multiple stages to address the challenges of fitting complex output with limited convolutional layers, suppressing the complex backgrounds, and effectively matching object symmetry at different scales. SRN is further upgraded to a multi-task side-output residual network (MT-SRN) for joint symmetry and edge detection, demonstrating its generality to image-to-mask learning tasks. Experimental results validate both the challenging aspects of Sym-PASCAL benchmark related to real-world images and the state-of-the-art performance of the proposed SRN approach.
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 feature-centered, it has certain computational advantages when the object sizes are known a priori, as demonstrated in an ellipse detection application. The method outperforms the best-performing algorithm on the CVPR 2013 Symmetry Detection Competition Database in the single-symmetry case. Code and a new database for 2D symmetry detection is available.
In this paper, we establish a baseline for object symmetry detection in complex backgrounds by presenting a new benchmark and an end-to-end deep learning approach, opening up a promising direction for symmetry detection in the wild. The new benchmark, named Sym-PASCAL, spans challenges including object diversity, multi-objects, part-invisibility, and various complex backgrounds that are far beyond those in existing datasets. The proposed symmetry detection approach, named Side-output Residual Network (SRN), leverages output Residual Units (RUs) to fit the errors between the object symmetry groundtruth and the outputs of RUs. By stacking RUs in a deep-to-shallow manner, SRN exploits the 'flow' of errors among multiple scales to ease the problems of fitting complex outputs with limited layers, suppressing the complex backgrounds, and effectively matching object symmetry of different scales. Experimental results validate both the benchmark and its challenging aspects related to realworld images, and the state-of-the-art performance of our symmetry detection approach. The benchmark and the code for SRN are publicly available at https://github.com/KevinKecc/SRN.
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 and their neighborhood behavior, resulting incomplete symmetrical axis candidates to discover the mirror similarities on a global scale. In this paper, we propose a new reflection symmetry detection scheme, based on a reliable edge-based feature extraction using Log-Gabor filters, plus an efficient voting scheme parameterized by their corresponding textural and color neighborhood information. Experimental evaluation on four single-case and three multiple-case symmetry detection datasets validates the superior achievement of the proposed work to find global symmetries inside an image.