Invariant Transform Research Articles

FaultSeg3D plus: A comprehensive study on evaluating and improving CNN-based seismic fault segmentation

Convolutional neural networks (CNNs) have been widely used for seismic fault segmentation and show more powerful performance than conventional attribute-based methods to obtain a fault map with noise-free and continuously trackable fault features. However, CNN-based methods face the potential problem of poor generalization in field seismic images, and factors affecting fault segmentation remain incompletely studied or unexplored. Moreover, the existing pixel-wise metrics, borrowed from the natural image segmentation tasks, cannot fairly or reasonably evaluate the fault segmentation results. We first develop a distance-based metric to provide a geologically more reasonable evaluation on fault interpretation. We then use the most commonly used U-net architecture as an example to study how the CNN-based fault segmentation is affected by some significant factors such as training data, many kinds of network hyperparameters, and scaling and rotation in the inference step. Experimental results show that a training data set with more realistic reflection features and multiple sampling rates can enrich the data set variations in the structure and waveform signatures, thus significantly enhancing the fault segmentation. Moreover, a novel loss function we developed outperforms others with notable margins. Last, but not least, it is necessary to apply a test-time augmentation strategy by merging predictions with multiple scales and rotations in the reference step because the CNN does not preserve transformation invariance. Based on the studies, we optimally train a properly designed CNN and apply it to multiple field examples, where we obtain accurate, clean, continuous fault detections, and quantitatively evaluate them with manual interpretations.

Flexible Trilinearity Alignment (FTA) and Shift Invariant Transformation (SIT) Constraints in Three‐Way Multivariate Curve Resolution Data Analysis

ABSTRACTIn this work, two alternative ways of analyzing three‐way data with multivariate curve resolution alternating least squares (MCR‐ALS) using the trilinearity constraint are described and compared. Different synthetic datasets and experimental three‐way datasets covering different scenarios are analyzed, and the results obtained are compared. The two new different ways of applying the trilinearity constraint are named flexible trilinearity alignment (FTA) and shift invariant transformation (SIT). The effects of noise in the application of both types of constraints are investigated in detail. Results show that both approaches are particularly adequate for those cases like in gas chromatography and especially in liquid chromatography where the elution profiles of the same chemical component in different chromatographic runs are not totally reproducible because they are time shifted, although they preserve their shape. When strong time shifts and co‐elution occur, then the “standard” trilinear model does not work, and alternative approaches should be used, such as the MCR extended bilinear model to multiset (multirun) data, or the proposed relaxation of the trilinearity constraint in the FTA and SIT methods to capture the time drift changes produced in the elution profiles of the resolved components.

Crack-tip plastic zone and initiation mechanism of rock based on Eshelby stress

The crack initiation and propagation mechanism of rock is significantly related to characteristics of the crack-tip plastic zone due to energy dissipation. In this paper, conservation integral and configurational stress/force is derived by the Noether’s method. The crack-tip configurational stress field is then deduced and analyzed. Additionally, the Drucker–Prager yield criterion of configurational stress is derived and it is used to predict the crack-tip plastic zone of rock. The fracture criteria of rock are also developed based on the critical area and minimum polar radius of the crack-tip plastic zone. Subsequently, the effects of bedding dip angles and porosity on rock mixed mode fracture are investigated, and the fracture resistance of rock is assessed using the resistivity and wave velocity. It is shown that the configurational force as the crack driving force is induced by the invariant transformation of an action integral with respect to translation of a defect. It is also found that the crack-tip plastic zone assessed by Drucker–Prager yield criterion of Cauchy stress is discontinuous at the crack surface while that predicted by yield criterion of configurational stress is continuous. The present fracture criteria take into account the internal friction angle, and the predicted initiation angles and fracture loads are in good agreement with those determined by the maximum tensile stress (MTS) fracture criterion and experiments. The fracture loading envelope decreases with the porosity, bedding dip angles and resistivities of rock, but increases with wave velocity.

Machine Learning Clifford Invariants of ADE Coxeter Elements

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for A8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_8$$\\end{document}, D8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_8$$\\end{document} and E8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_8$$\\end{document} for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results.

Graph-Based Contrastive Learning for Description and Detection of Local Features.

Confronted with the task environment full of repetitive textures, the state-of-art description and detection methods for local features greatly suffer from the "pseudo-negatives," bringing inconsistent optimization objectives during training. To address this problem, this article develops a self-supervised graph-based contrastive learning framework to train the model for local features, GCLFeat. The proposed approach learns to alleviate the pseudo-negatives specifically from three aspects: 1) designing a graph neural network (GNN), which focuses on mining the local transformational invariance across different views and global textual knowledge within individual images; 2) generating the dense correspondence annotations from a diverse natural dataset with a self-supervised paradigm; and 3) adopting a keypoints-aware sampling strategy to compute the loss across the whole dataset. The experimental results show that the unsupervised framework outperforms the state-of-the-art supervised baselines on diverse downstream benchmarks including image matching, 3-D reconstruction and visual localization. The code will be made public and available at https://github.com/RealZihaoWang/GCLFeat.

Scalar-potential mapping of the steady-state magnetosheath model

Abstract. The steady-state magnetosheath model has various applications for studying the plasma and magnetic field profile around the planetary magnetospheres. In particular, the magnetosheath model is analytically obtained by solving the Laplace equation for parabolic boundaries (bow shock and magnetopause). We address the question, how can we utilize the magnetosheath model by transforming into a more general, empirical, non-parabolic magnetosheath geometry? To achieve the goal, we develop the scalar-potential mapping method which provides a semi-analytic estimate of steady-state flow velocity and magnetic field in the empirical magnetosheath domain. The method makes use of a coordinate transformation from the empirical magnetosheath domain into the parabolic magnetosheath domain and evaluates a set of variables (shell variable and connector variable) to utilize the solutions of the Laplace equation obtained for the parabolic magnetosheath domain. Our model uses two invariants of transformation: the zenith angle within the magnetosheath with respect to the direction to the Sun and the ratio of the distance to the magnetopause and the thickness of magnetosheath along the magnetopause-normal direction. The use of magnetopause-normal direction makes a marked difference from the earlier model construction using the radial direction as reference. The plasma flow and magnetic field can be determined as a function of the upstream condition (flow velocity or magnetic field) in a wide range of zenith angles. The scalar-potential mapping method is computationally inexpensive, using analytic expressions as much as possible, and is applicable to various planetary magnetosheath domains.

Overlap-Aware Hierarchical Decoder for point cloud registration

Extracting high-quality correspondences is a critical challenge in current feature-learning based point cloud registration methods. Recently, coarse-to-fine network structures have shown great potential in addressing this challenge. Inspired by such structures, we investigate the effectiveness of two-stage network optimization in matching and propose a non-keypoint registration model called Overlap-Aware Hierarchical Decoder (OAH-Net). The construction of this model focuses on reducing outliers in the matching results and improving the understanding of geometric transformation invariance. To achieve this goal, we propose a point-to-point perception module for encoding the paired point clouds and perceiving the overlapping regions, as well as a pyramid hierarchical decoder for decoding multi-level features. We design an optimal matching mechanism adapted to the pyramid structure to handle accurate correspondences from multi-level matching, thereby improving the accuracy of the final registration. Experimental evaluations conducted on indoor and outdoor benchmark tests validate the outstanding performance of OAH-Net, which not only ensures low parameter count and computational efficiency but also demonstrates accuracy and stability comparable to state-of-the-art models.

Discrepancy of coordinate system selection in backscattering Mueller matrix polarimetry: exploring photon coordinate system transformation invariants.

In biomedical studies, Mueller matrix polarimetry is gaining increasing attention because it can comprehensively characterize polarization-related vectorial properties of the sample, which are crucial for microstructural identification and evaluation. For backscattering Mueller matrix polarimetry, there are two photon coordinate selection conventions, which can affect the following Mueller matrix parameters calculation and information acquisition quantitatively. In this study, we systematically analyze the influence of photon coordinate system selection on the backscattering Mueller matrix polarimetry. We compare the Mueller matrix elements in the right-handed-nonunitary and non-right-handed-unitary coordinate systems, and specifically deduce the changes of Mueller matrix polar decomposition, Mueller matrix Cloude decomposition and Mueller matrix transformation parameters widely used in backscattering Mueller matrix imaging as the photon coordinate system varied. Based on the theoretical analysis and phantom experiments, we provide a group of photon coordinate system transformation invariants for backscattering Mueller matrix polarimetry. The findings presented in this study give a crucial criterion of parameters selection for backscattering Mueller matrix imaging under different photon coordinate systems.

Mutual Information Driven Equivariant Contrastive Learning for 3D Action Representation Learning.

Self-supervised contrastive learning has proven to be successful for skeleton-based action recognition. For contrastive learning, data transformations are found to fundamentally affect the learned representation quality. However, traditional invariant contrastive learning is detrimental to the performance on the downstream task if the transformation carries important information for the task. In this sense, it limits the application of many data transformations in the current contrastive learning pipeline. To address these issues, we propose to utilize equivariant contrastive learning, which extends invariant contrastive learning and preserves important information. By integrating equivariant and invariant contrastive learning into a hybrid approach, the model can better leverage the motion patterns exposed by data transformations and obtain a more discriminative representation space. Specifically, a self-distillation loss is first proposed for transformed data of different intensities to fully utilize invariant transformations, especially strong invariant transformations. For equivariant transformations, we explore the potential of skeleton mixing and temporal shuffling for equivariant contrastive learning. Meanwhile, we analyze the impacts of different data transformations on the feature space in terms of two novel metrics proposed in this paper, namely, consistency and diversity. In particular, we demonstrate that equivariant learning boosts performance by alleviating the dimensional collapse problem. Experimental results on several benchmarks indicate that our method outperforms existing state-of-the-art methods.

Does the Brain Infer Invariance Transformations from Graph Symmetries?

Does the Brain Infer Invariance Transformations from Graph Symmetries?

Unsupervised Part Discovery via Dual Representation Alignment.

Object parts serve as crucial intermediate representations in various downstream tasks, but part-level representation learning still has not received as much attention as other vision tasks. Previous research has established that Vision Transformer can learn instance-level attention without labels, extracting high-quality instance-level representations for boosting downstream tasks. In this paper, we achieve unsupervised part-specific attention learning using a novel paradigm and further employ the part representations to improve part discovery performance. Specifically, paired images are generated from the same image with different geometric transformations, and multiple part representations are extracted from these paired images using a novel module, named PartFormer. These part representations from the paired images are then exchanged to improve geometric transformation invariance. Subsequently, the part representations are aligned with the feature map extracted by a feature map encoder, achieving high similarity with the pixel representations of the corresponding part regions and low similarity in irrelevant regions. Finally, the geometric and semantic constraints are applied to the part representations through the intermediate results in alignment for part-specific attention learning, encouraging the PartFormer to focus locally and the part representations to explicitly include the information of the corresponding parts. Moreover, the aligned part representations can further serve as a series of reliable detectors in the testing phase, predicting pixel masks for part discovery. Extensive experiments are carried out on four widely used datasets, and our results demonstrate that the proposed method achieves competitive performance and robustness due to its part-specific attention. The code will be released upon paper acceptance.

Explicitly learning augmentation invariance for image classification by Consistent Augmentation

Data augmentation is a powerful and widely used technique to improve the generalization of convolutional neural networks. The majority of data augmentation methods emphasize transforming samples to bolster network robustness. However, these methods overlook learning the invariance between the samples augmented by different transformations, impairing the quality of learned representations and generalization of the model. In this paper, we introduce a straightforward yet highly effective method called Consistent Augmentation (CA) to compel networks to learn explicitly the invariance of transformations. Specifically, CA minimizes the bidirectional KL divergence between the predicted distributions of different variants generated from the same samples using different transformations, explicitly enforcing consistency among various semantics-preserving transformations. Implementing CA is intuitive, uncomplicated, and does not introduce additional computational costs during inference. The validation experiments performed on conventional and fine-grained classification tasks demonstrate that CA can be employed across various network architectures and consistently improve their generalization ability. Notably, convolutional neural networks benefit significantly on fine-grained classification tasks, with an improvement of 5.18% and 6.61% compared with other augmentation methods in accuracy observed for the ShuffleNetV2 model on the Stanford Dogs and CUB-200-2011 datasets. Compatibility experiments conducted on the CIFAR-100 dataset reveal that CA improves the accuracy of the Mixup and CutMix methods by 1.25% and 2.11%, respectively. These results underscore the effectiveness of our approach when employed alongside mix-based augmentation methods, further enhancing the capabilities of the model.

Quantifying the direct and indirect interactions for EEG signals by using detrended permutation mutual information

In this paper, we extend detrended cross-correlations analysis (DCCA) and introduce a novel method called detrended permutation mutual information (DPMI) by utilizing information-theoretic tools. The main mechanism of this paper is to use the invariance of the nonlinear monotonic transformation and robustness in permutation mutual information (PMI), which solves the limitations of DCCA only applicable to linear measurements and enhances the robustness of DPMI to noise. We compare the performance of DPMI with DCCA on multifractal binomial measures and Hénon maps for testing the effectiveness of the new method. By analyzing EEG signals obtained from children with attention deficit hyperactivity disorder (ADHD) as well as healthy children, we demonstrate that DPMI surpasses DCCA in processing physiological signals. Furthermore, we conclude that DPMI is more effective in distinguishing between different states within distinct groups. Given that EEG signals in physiological systems are associated with other channel signals, we propose a method called partial DPMI (PDPMI) that combines partial-correlation technique with DPMI. PDPMI can further reveal the direct interactions between two considered signals by eliminating potential influences from other unconsidered signals. In summary, PDPMI serves as a complementary perspective to DPMI, enhancing our understanding in the interactive structure of physiological network.

EVALUATION OF LATTICE BASED XAI

With multiple methods to extract explanations from a black box model, it becomes significant to evaluate the correctness of these Explainable AI (XAI) techniques themselves. While there are many XAI evaluation methods that need manual intervention, in order to be objective, we use computable XAI evaluation methods to test the basic nature and sanity of an XAI technique. We pick four basic axioms and three sanity tests from existing literature that the XAI techniques are expected to satisfy. Axioms like Feature Sensitivity, Implementation Invariance, Symmetry preservation and sanity tests like Model parameter randomization, Model-Outcome relationship, Input transformation invariance are used. After reviewing the axioms and sanity tests, we apply it on existing XAI techniques to check if they satisfy them or not. Thereafter, we evaluate our lattice based XAI technique with these axioms and sanity tests using a mathematical approach. This work proves these axioms and sanity tests to establish the correctness of explanations extracted from our Lattice based XAI technique.

Partial discharge based recognition of water droplets location in high voltage insulator using convolutional neural network – Bacterial foraging algorithm based optimized machine learning classifier

Measurement and analysis of Partial Discharge (PD) patterns have appeared as an emerging field in assessing insulation failure in High Voltage apparatus. This paper uses a PD signal combined with the deep convolution-optimized learning machine classifier (DC-OLMC) to predict the location of water droplets in 11 kV polymer insulators subjected to alternating currents. There are two major confront when applying the proposed algorithm: i) Contamination is a significant issue in PD signal measurement, which causes a reduction in recognition rate (RR), and ii) with minimal computing time, high-level feature extraction and recognition. Traditional condition monitoring methods of insulators concentrated on extracting fewer priority features from the input patterns. In the current work, to address this problem, an Alexnet with Bacterial Foraging Algorithm (BFO) based optimized kernel parameter classifier and Translation Invariant Wavelet Transform (TIWT) is employed to remove interference from PD signals. The analysis demonstrates that the suggested technique, with an identification rate of 99.17%, is considered a valuable tool for locating water droplets in high-voltage insulators.

Towards a classification of holographic multi-partite entanglement measures

In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in [1]. We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in 2d CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.

Implication of electromagnetohydrodynamic and heat transfer analysis in nanomaterial flow over a stretched surface: Applications in solar energy

The limited availability of non-renewable energy resources, the need to protect ecosystems, and financial considerations create a powerful driving force for studying renewable energy and improving thermal energy systems. The utilization of solar radiation and nanofluids containing polyvinyl alcohol–water-based fluids with copper nanoparticles offers an opportunity to improve the efficiency of sustainable solar heating systems. Owing to its usage, this research examines the electromagnetohydrodynamic and thermal transfer of Jeffrey nanofluid flow over a stretchable surface by employing the influence of gyrotactic microorganisms on this flow. Additionally, the current research focused on creating an advanced numerical model that accurately exemplifies the flow and thermal properties of a parabolic trough solar collector (PTSC) installed on a solar plate to generate a continuous energy source. The unique aspect of our research lies in the integrated approach, combining EMHD, nanofluid flow, and stretchable surface technology to investigate the thermal performance of the coating. This innovative combination opens up new possibilities for efficient thermal management in solar energy applications. The effectiveness of thermal transport in PTSC is evaluated by investigating several factors such as the electric field parameter, solar radiation, exponential heat source, bioconvection Rayleigh, and diffusion parameter. This research utilizes invariant transformations to simplify partial differential equations into ordinary differential equations. These equations are then solved using the wavelets and the Chebyshev wavelets scheme (CWS) with the help of MATHEMATICA 11.3 software. The research outcomes revealed that an increase in the solar thermal radiation, and electric field parameters leads to a higher temperature distribution in concentrated solar power. Therefore, this research aims to improve industrial performance by increasing the efficiency of thermal power generation systems.

Three Serious Mistakes in Einstein’s Original Paper of Special Relativity in 1905

It is revealed in this paper that there were three serious mistakes in the Einstein’s original paper in 1905. Einstein did not prove that the motion equation of classical electromagnetic field could satisfy the invariance of the Lorentz coordinate transformation. The Einstein’s derivations on the formulas of transverse and longitudinal masses, as well as the calculation on the mass-energy relation are wrong. 1. In order to prove that the classical Maxwell electromagnetic field equation satisfied the invariance of Lorentz transformation in free space without charged and current, Einstein introduced the transformations of electromagnetic fields themselves, called the Einstein’s transformations of electromagnetic fields. However, these transformations are completely different from the Lorentz transformations of electromagnetic fields themself, which leads to contradiction and does not hold. 2. For the electromagnetic field equations in non-free space with charge and current, the Einstein’s transformations can not make the electromagnetic fields unchanged under the Lorentz transformation. 3. The constitutive equations of electromagnetic theory in the medium do not satisfy the invariance of the Lorentz transformation too. Therefore, the classical electromagnetic field equations have no the invariance of the Lorentz transformation actually, and the most important theoretical and experimental basis of special relativity do not exist. 4. The Einstein's derivations on the formulas of transverse and longitudinal masses have a series of elementary mistakes in mathematics and physics. Einstein took the relative speed between two reference frames as the arbitrary moving velocity of a particle, and the obtained formulas were completely different from the existing mass-velocity of special relativity. 3. When Einstein derived the mass-energy relationship, he only calculated the work done by the force in the x-axis direction of particle’s motion, ignoring the work done by the force at the y- and z-axes directions. Meanwhile, the constant relative motion velocity between two reference frames was misused as the variable arbitrary velocity of a particle. Therefore, Einstein had not derived the mass-velocity formula and mass-energy relationship used in the present special relativity.

Non-redundant shift-invariant complex wavelet transform and fractional gorilla troops optimization-based deep convolutional neural network for video watermarking

With the development of multimedia processing approaches along with the Internet leads to various issues, like data tampering, data piracy, and illicit dissemination. The quick progression of fast communication networks for digital video transmission has formulated the prerequisite copyright protection for these media. On the other hand, the development of Internet technologies has directed the accessibility of images, audio, and videos in different structures. Moreover, unlicensed users manipulate the utilization of multimedia by broadcasting them on numerous internet sites to get money fraudulently without the involvement of the original copyright holder. Besides, watermarking is a process utilized to hide the watermark sign present in the multimedia statistics that are not perceptible to an intruder for manipulating any information. This paper devised a novel video watermarking technique which uses an optimized deep learning technique. Here, the binary pixel map generation is performed using DCNN for self-embedding in input video. In addition, weights as well as bias of DCNN are trained by designed Fractional Gorilla Troops Optimization-Deep Convolutional Neural Network algorithm, thus FGTO_DCNN algorithm is developed. Accordingly, the FGTO technique is newly introduced by integrating FC along with GTO algorithm. Moreover, non-redundant Shift Invariant Complex Wavelet Transform (SICWT) is employed for extracted key frame and thus watermark image is fed into embedding process. After that, inverse non-redundant SICWT is applied for embedding video, which is further passed to key frame extraction in extraction stage. Finally, non-redundant SICWT is utilized for obtaining extracted watermark image. The developed FGTO-driven DCNN model attained improved performance than other existing video watermarking techniques with Mean Square Error (MSE) of 0.0437, Normalized Correlation Coefficient (NCC) of 0.9998, high Peak Signal-to-Noise Ratio (PSNR) value of 51.93 dB, and high Weighted Signal-to-Noise Ratio (WSNR) of 49.86 dB.

Group properties and similarity transformations for generalized peakon equation with cubic nonlinearities

We perform a detailed analysis of the point transformations which leave invariant the Geng-Xue equation. We find that the Geng-Xue equation admits six Lie point symmetries which possess two three-dimensional subalgebras, the A 2,1 ⊗s A 1 and A 3,8 Lie algebras. For the Lie point symmetries we derive the one-dimensional optimal system and we perform a classification of the corresponding invariant transformations. We demonstrate the application of the Lie symmetries by deriving similarity solutions expressed by closed-form functions.