Showing papers on "Affine transformation published in 2022"

Dimensionality Reduction and Classification of Hyperspectral Image via Multistructure Unified Discriminative Embedding

Abstract: Graph can achieve good performance to extract the low-dimensional features of hyperspectral image (HSI). However, the present graph-based methods just consider the individual information of each sample in a certain characteristic, which is very difficult to represent the intrinsic properties of HSI for the complex imaging condition. To better represent the low-dimensional features of HSI, we propose a multistructure unified discriminative embedding (MUDE) method, which considers the neighborhood, tangential, and statistical properties of each sample in HSI to achieve the complementarity of different characteristics. In MUDE, we design the intraclass and interclass neighborhood structure graphs with the local reconstruction structure of each sample; meanwhile, we also utilize the adaptive tangential affine combination structure to construct the intraclass and interclass tangential structure graphs. To further enhance the discriminating performance between different classes, we consider the influence of the statistical distribution difference for each sample to develop an interclass Gaussian weighted scatter model. Then, an embedding objective function is constructed to enhance the intraclass compactness and the interclass separability and obtain more discriminative features for HSI classification. Experiments on three real HSI datasets show that the proposed method can make full use of the structure information of each sample in different characteristics to achieve the complementarity of different features and improve the classification performance of HSI compared with the state-of-the-art methods.

Stereoscopic Image Description With Trinion Fractional-Order Continuous Orthogonal Moments

Abstract: Some research progress has been made on fractional-order continuous orthogonal moments (FrCOMs) in the past two years. Compared with integer-order continuous orthogonal moments (InCOMs), FrCOMs increase the number of affine invariants and effectively improve numerical stability. However, the existing types of FrCOMs are still very limited, of which all are planar image oriented. No report on stereoscopic images is available yet. To this end, in this paper, FrCOMs corresponding to various types of InCOMs are first deduced, and then, they are combined with trinion theory to construct trinion FrCOMs (TFrCOMs) applicable to stereoscopic images. Furthermore, the reconstruction performance and geometric invariance of TFrCOMs are analyzed theoretically and experimentally. Finally, an application in the stereoscopic image zero-watermarking algorithm is investigated to verify the superior performance of TFrCOMs.

Locally Nonlinear Affine Verification for Multisensor Image Matching

Abstract: Matching local features between two overlapped images is a fundamental task in photogrammetry and remote sensing. However, images acquired by multiple sensors often differ substantially in properties, thus posing a great challenge to the robustness and flexibility of feature matching methods. In this article, we propose a locally non-linear affine verification (LAV) method for robust multisensor image matching. The main idea of the LAV is the development of a nonlinear regression formulation that practically models the nonlinear deviation of a real surface around a point from its tangent plane during affine verification. Specifically, we start by selecting a restricted set of reliable and well-distributed putative matches as the matching seeds and assign them with neighbors to construct search spaces. In each search space, the regression seeks the smoothest affine model consistent with the latent correct matches, thereby deriving a set of affine parameters to verify correspondence hypotheses for true matches. The verification can be extended to all nearest neighbor matches to discover additional inlier matches. Evaluation on multisensor image datasets with different extents of variations in viewpoint, scale, illumination, and appearance shows that the proposed LAV consistently outperforms existing methods. LAV can achieve a considerable number of high-quality matches, in cases where existing methods provide few or no correct matches.

Nonstationary Filtering for Fuzzy Markov Switching Affine Systems With Quantization Effects and Deception Attacks

Abstract: This article focuses on the issue of nonstationary filtering for uncertain fuzzy Markov switching affine systems (FMSASs) with quantization effects and deception attacks (DAs). The resulting FMSASs are comprised of Markov switching piecewise-affine systems over a set of operating regions. To characterize the multinetwork-induced constraints, the measurement output is quantized before being transmitted, and a compensation scheme is applied to tackle the quantized measurement output loss intermittently. Meanwhile, the randomly occurring DAs are involved, in which the attack behaviors are identified by the bounded stochastic signals. Differently, to deal with the multinetwork-induced constraints, a novel nonstationary region-dependent affine filter strategy is developed. By resorting to a mode-dependent and region-dependent Lyapunov functional and S-procedure theory, sufficient conditions are elicited such that the filtering error system is mean-square exponentially stable. Finally, the practicability of the derived results is verified by a practical tunnel diode circuit model.

Optimal gap-affine alignment in O(s) space

Abstract: Motivation Pairwise sequence alignment remains a fundamental problem in computational biology and bioinformatics. Recent advances in genomics and sequencing technologies demand faster and scalable algorithms that can cope with the ever-increasing sequence lengths. Classical pairwise alignment algorithms based on dynamic programming are strongly limited by quadratic requirements in time and memory. The recently proposed wavefront alignment algorithm (WFA) introduced an efficient algorithm to perform exact gap-affine alignment in O(ns) time, where s is the optimal score and n is the sequence length. Notwithstanding these bounds, WFA’s O(s2) memory requirements become computationally impractical for genome-scale alignments, leading to a need for further improvement. Results In this paper, we present the bidirectional WFA algorithm (BiWFA), the first gap-affine algorithm capable of computing optimal alignments in O(s) memory while retaining WFA’s time complexity of O(ns). As a result, this work improves the lowest known memory bound O(n) to compute gap-affine alignments. In practice, our implementation never requires more than a few hundred MBs aligning noisy Oxford Nanopore Technologies reads up to 1 Mbp long while maintaining competitive execution times. Availability All code is publicly available at https://github.com/smarco/BiWFA-paper Contact santiagomsola@gmail.com

AI-DRIVEN Novel Approach for Liver Cancer Screening and Prediction Using Cascaded Fully Convolutional Neural Network

Abstract: In experimental analysis and computer-aided design sustain scheme, segmentation of cell liver and hepatic lesions by an automated method is a significant step for studying the biomarkers characteristics in experimental analysis and computer-aided design sustain scheme. Patient to patient, the change in lesion type is dependent on the size, imaging equipment (such as the setting dissimilarity approach), and timing of the lesion, all of which are different. With practical approaches, it is difficult to determine the stages of liver cancer based on the segmentation of lesion patterns. Based on the training accuracy rate, the present algorithm confronts a number of obstacles in some domains. The suggested work proposes a system for automatically detecting liver tumours and lesions in magnetic resonance imaging of the abdomen pictures by using 3D affine invariant and shape parameterization approaches, as well as the results of this study. This point-to-point parameterization addresses the frequent issues associated with concave surfaces by establishing a standard model level for the organ's surface throughout the modelling process. Initially, the geodesic active contour analysis approach is used to separate the liver area from the rest of the body. The proposal is as follows: It is possible to minimise the error rate during the training operations, which are carried out using Cascaded Fully Convolutional Neural Networks (CFCNs) using the input of the segmented tumour area. Liver segmentation may help to reduce the error rate during the training procedures. The stage analysis of the data sets, which are comprised of training and testing pictures, is used to get the findings and validate their validity. The accuracy attained by the Cascaded Fully Convolutional Neural Network (CFCN) for the liver tumour analysis is 94.21 percent, with a calculation time of less than 90 seconds per volume for the liver tumour analysis. The results of the trials show that the total accuracy rate of the training and testing procedure is 93.85 percent in the various volumes of 3DIRCAD datasets tested.

Affine Transformation-Enhanced Multifactorial Optimization for Heterogeneous Problems

Abstract: Evolutionary multitasking (EMT) is a newly emerging research topic in the community of evolutionary computation, which aims to improve the convergence characteristic across multiple distinct optimization tasks simultaneously by triggering knowledge transfer among them. Unfortunately, most of the existing EMT algorithms are only capable of boosting the optimization performance for homogeneous problems which explicitly share the same (or similar) fitness landscapes. Seldom efforts have been devoted to generalize the EMT for solving heterogeneous problems. A few preliminary studies employ domain adaptation techniques to enhance the transferability between two distinct tasks. However, almost all of these methods encounter a severe issue which is the so-called degradation of intertask mapping. Keeping this in mind, a novel rank loss function for acquiring a superior intertask mapping is proposed in this article. In particular, with an evolutionary-path-based representation model for optimization instance, an analytical solution of affine transformation for bridging the gap between two distinct problems is mathematically derived from the proposed rank loss function. It is worth mentioning that the proposed mapping-based transferability enhancement technique can be seamlessly embedded into an EMT paradigm. Finally, the efficacy of our proposed method against several state-of-the-art EMTs is verified experimentally on a number of synthetic multitasking and many-tasking benchmark problems, as well as a practical case study.

Adaptive Control Barrier Functions

Abstract: It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of quadratic programs (QPs) by using control barrier functions (CBFs) and control Lyapunov functions (CLFs). In this article, we introduce adaptive CBFs (aCBFs) that can accommodate time-varying control bounds and noise in the system dynamics while also guaranteeing the feasibility of the QPs if the original quadratic cost optimization problem itself is feasible, which is a challenging problem in current approaches. We propose two different types of aCBFs: parameter-adaptive CBF (PACBF) and relaxation-adaptive CBF (RACBF). Central to aCBFs is the introduction of appropriate time-varying functions to modify the definition of a common CBF. These time-varying functions are treated as high-order CBFs with their own auxiliary dynamics, which are stabilized by CLFs. We demonstrate the advantages of using aCBFs over the existing CBF techniques by applying both the PACBF-based method and the RACBF-based method to a cruise control problem with time-varying road conditions and noise in the system dynamics, and compare their relative performance.

Adaptive Interleaved Reinforcement Learning: Robust Stability of Affine Nonlinear Systems With Unknown Uncertainty

Abstract: This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matched or unmatched uncertainties. To this end, the robust control problem is converted into the optimal control problem for nominal systems by selecting an appropriate utility function. The performance evaluation and control policy update combined with neural networks approximation are alternately implemented at each time step for solving a simplified Hamilton-Jacobi-Bellman (HJB) equation such that the uniformly ultimately bounded (UUB) stability of DT affine nonlinear systems can be guaranteed, allowing for all realization of unknown bounded uncertainties. The rigorously theoretical proofs of convergence of the proposed interleaved RL algorithm and UUB stability of uncertain systems are provided. Simulation results are given to verify the effectiveness of the proposed method.

Distributed observer based event‐triggered affine formation maneuver control for underactuated surface vessels with positive minimum inter‐event times

Abstract: This article investigates the distributed event‐triggered affine formation maneuver control problem for multiple underactuated surface vessel (USV) systems with positive minimum inter‐event times (MIET). Unlike common formation control methods that only ensure the formation system to keep a fixed geometric shape, the proposed scheme enables multiple USVs maneuver as a group in translation, shearing, rotation, or combinations of them. The proposed control strategy is composed of two parts. First, a distributed event‐triggered observer (DETO) is proposed to observe the time‐varying target formation under the lack of global leaders' information and govern the inter‐vessel communications among the formation group. Besides, the MIET of the designed communication strategy is proved to be strictly positive and computable from formation configurations and control parameters. With these guarantees, the maximum communication frequency can be known in advance. Then, upon the DETO signals, the adaptive local tracking controller is subsequently synthesized for each vessel to realize the target formation track. Rigorous theoretical analysis and simulation results are finally conducted to verify the validness and effectiveness of the proposed algorithm.

Control Barrier Functions in Sampled-Data Systems

Abstract: This letter presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the conservativeness of sufficient conditions on forward invariance under piecewise-constant controllers. Then, we propose three approaches for guaranteeing forward invariance, two motivated by continuous-time barrier functions, and one motivated by discrete-time barrier functions. All proposed conditions are control affine, and thus can be incorporated into quadratic programs for control synthesis. We show that the proposed conditions are less conservative than those in earlier studies, and show via simulation how this enables the use of barrier functions that are impossible to implement with the desired time-step using existing methods.

Distortion Robust Relative Radiometric Normalization of Multitemporal and Multisensor Remote Sensing Images Using Image Features

Abstract: In this article, we propose a novel framework to radiometrically correct unregistered multisensor image pairs based on the extracted feature points with the KAZE detector and the conditional probability (CP) process in the linear model fitting. In this method, the scale, rotation, and illumination invariant radiometric control set samples (SRII-RCSS) are first extracted by the blockwise KAZE strategy. They are then distributed uniformly over both textured and texture-less land use/land cover (LULC) using grid interpolation and a set of nearest-neighbors. Subsequently, SRII-RCSS are scored by a similarity measure, and the histogram of the scores is then used to refine SRII-RCSS. The normalized subject image is produced by adjusting the subject image to the reference image using the CP-based linear regression (CPLR) based on the optimal SRII-RCSS. The registered normalized image is finally generated by registration of the normalized subject image to the reference image through a two-pass registration method, namely affine-B-spline and, then, it is enhanced by updating the normalization coefficient of CPLR based on the SRII-RCSS. In this study, eight multitemporal data sets acquired by inter/intra satellite sensors were used in tests to comprehensively assess the efficiency of the proposed method. Experimental results show that the proposed method outperforms the existing state-of-the-art relative radiometric normalization (RRN) methods both qualitatively and quantitatively, indicating its capability for RRN of unregistered multisensor image pairs.

An Open-Source Whole Slide Image Registration Workflow at Cellular Precision Using Fiji, QuPath and Elastix

Abstract: Image analysis workflows for Histology increasingly require the correlation and combination of measurements across several whole slide images. Indeed, for multiplexing, as well as multimodal imaging, it is indispensable that the same sample is imaged multiple times, either through various systems for multimodal imaging, or using the same system but throughout rounds of sample manipulation (e.g. multiple staining sessions). In both cases slight deformations from one image to another are unavoidable, leading to an imperfect superimposition Redundant and thus a loss of accuracy making it difficult to link measurements, in particular at the cellular level. Using pre-existing software components and developing missing ones, we propose a user-friendly workflow which facilitates the nonlinear registration of whole slide images in order to reach sub-cellular resolution level. The set of whole slide images to register and analyze is at first defined as a QuPath project. Fiji is then used to open the QuPath project and perform the registrations. Each registration is automated by using an elastix backend, or semi-automated by using BigWarp in order to interactively correct the results of the automated registration. These transformations can then be retrieved in QuPath to transfer any regions of interest from an image to the corresponding registered images. In addition, the transformations can be applied in QuPath to produce on-the-fly transformed images that can be displayed on top of the reference image. Thus, relevant data can be combined and analyzed throughout all registered slides, facilitating the analysis of correlative results for multiplexed and multimodal imaging.

Data-Driven Optimal Control of Nonlinear Dynamics Under Safety Constraints

Abstract: This letter considers the optimal control problem of nonlinear systems under safety constraints with unknown dynamics. Departing from the standard optimal control framework based on dynamic programming, we study its dual formulation over the space of occupancy measures. For control-affine dynamics, with proper reparametrization, the problem can be formulated as an infinite-dimensional convex optimization over occupancy measures. Moreover, the safety constraints can be naturally captured by linear constraints in this formulation. Furthermore, this dual formulation can still be approximately obtained by utilizing the Koopman theory when the underlying dynamics are unknown. Finally, to develop a practical method to solve the resulting convex optimization, we choose a polynomial basis and then relax the problem into a semi-definite program (SDP) using sum-of-square (SOS) techniques. Simulation results are presented to demonstrate the efficacy of the developed framework.

Asymptotic Tracking Control for Nonaffine Systems With Disturbances

Abstract: This brief intends to address an adaptive asymptotic tracking control with prescribed performance function for a class of nonaffine systems with unknown disturbances. First, the nonaffine system is transformed into an affine system by using a set of alternative state variables. Subsequently, a prescribed performance function with predefined convergence rate, maximum overshoot and steady-state error is introduced. To achieve the asymptotic tracking control performance, the robust integral of the sign of the error (RISE) feedback term is utilized in the control design to reject the unknown external disturbances and NN approximation errors. Finally, an adaptive controller is presented so that the asymptotic tracking performance with guaranteed prescribed performance is achieved. Comparative experiments are provided to show the effectiveness of the proposed control scheme.

Numerical Evidence for a Haagerup Conformal Field Theory

Abstract: We numerically study an anyon chain based on the Haagerup fusion category and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is ∼2. Fusion categories generalize the concept of finite group symmetries to noninvertible symmetry operations, and the Haagerup fusion category is the simplest one which comes from neither finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries. Basically the same result was independently obtained in the preceding Letter [Phys. Rev. Lett. 128, 231602 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.231602].

A New Approach to Finite-Horizon Optimal Control for Discrete-Time Affine Nonlinear Systems via a Pseudolinear Method

Abstract: In this article, a new time-varying adaptivedynamic programming (ADP) algorithm is developed to solve finite-horizon optimal control problems for a class of discrete-time affine nonlinear systems. Inspired by the pseudolinear method, the nonlinear system can be approximated by a series of time-varying linear systems. In each iteration of the time-varying ADP algorithm, the optimal control law for the time-varying linear system is obtained. For an arbitrary initial state, it is proven that states of the time-varying linear systems converge to the states of discrete-time affine nonlinear systems. It is also shown that the iterative value functions and the iterative control laws converge to the optimal value function and the optimal control law, respectively. Finally, numerical results are presented to verify the effectiveness of the present method.

Virtual Normal: Enforcing Geometric Constraints for Accurate and Robust Depth Prediction

Abstract: Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in the evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric constraints in the 3D space. In this work, we show the importance of the high-order 3D geometric constraints for depth prediction. By designing a loss term that enforces a simple geometric constraint, namely, virtual normal directions determined by randomly sampled three points in the reconstructed 3D space, we significantly improve the accuracy and robustness of monocular depth estimation. Importantly, the virtual normal loss can not only improve the performance of learning metric depth, but also disentangle the scale information and enrich the model with better shape information. Therefore, when not having access to absolute metric depth training data, we can use virtual normal to learn a robust affine-invariant depth generated on diverse scenes. Our experiments demonstrate state-of-the-art results of learning metric depth on NYU Depth-V2 and KITTI. From the high-quality predicted depth, we are now able to recover good 3D structures of the scene such as the point cloud and surface normal directly, eliminating the necessity of relying on additional models as was previously done. To demonstrate the excellent generalization capability of learning affine-invariant depth on diverse data with the virtual normal loss, we construct a large-scale and diverse dataset for training affine-invariant depth, termed Diverse Scene Depth dataset (DiverseDepth), and test on five datasets with the zero-shot test setting. Code is available at: https://git.io/Depth.

Improved Optimal Testing Results from Global Hypercontractivity

Abstract: The problem of testing low-degree polynomials has received significant attention over the years due to its importance in theoretical computer science, and in particular in complexity theory. The problem is specified by three parameters: field size $q$, degree $d$ and proximity parameter $\delta$, and the goal is to design a tester making as few as possible queries to a given function, which is able to distinguish between the case the given function has degree at most $d$, and the case the given function is $\delta$-far from any degree $d$ function. A tester is called optimal if it makes $O(q^d+1/\delta)$ queries (which are known to be necessary). For the field of size $q$, the natural $t$-flat tester was shown to be optimal first by Bhattacharyya et al. for $q=2$, and later by Haramaty et al. for all prime powers $q$. The dependency on the field size, however, is a tower-type function. We improve the results above, showing that the dependency on the field size is polynomial. Our approach also applies in the more general setting of lifted affine invariant codes, and is based on studying the structure of the collection of erroneous subspaces. i.e. subspaces $A$ such that $f|_{A}$ has degree greater than $d$. Towards this end, we observe that these sets are poorly expanding in the affine version of the Grassmann graph and use that to establish structural results on them via global hypercontractivity. We then use this structure to perform local correction on $f$.

Vector stability in quadratic metric-affine theories

Abstract: In this work we study the stability of the four vector irreducible pieces of the torsion and the nonmetricity tensors in the general quadratic metric-affine Lagrangian in 4 dimensions. The goal will be to elucidate under which conditions the spin-1 modes associated to such vectors can propagate in a safe way, together with the graviton. This highly constrains the theory reducing the parameter space of the quadratic curvature part from 16 to 5 parameters. We also study the sub-case of Weyl-Cartan gravity, proving that the stability of the vector sector is only compatible with an Einstein-Proca theory for the Weyl vector.