Affine Transformation Research Articles

SPA: Self-Peripheral-Attention for central–peripheral interactions in endoscopic image classification and segmentation

Peripheral vision is a vital component of human visual processing that allows for efficient and accurate recognition of visual features across diverse regions of the visual field. Analogously, endoscopic images often exhibit peripheral regions of blur, due to their inherent imaging properties. Previous strategies employing either coarse-grained global attention or fine-grained local attention to enhance performance have often inadvertently compromised the intrinsic self-attention mechanism of multilayer transformers, leading to less optimal solutions. This research introduces Self-Peripheral-Attention (SPA), an innovative mechanism that incorporates peripheral vision modeling into self-attention, so as to enhance the accuracy and efficiency of classification and segmentation tasks in endoscopic imaging. SPA synthesizes fine-grained central and coarse-grained peripheral interactions and possesses three primary characteristics: (i) peripheral contextualization aggregation; (ii) interaction between coarse-grained peripheral and fine-grained central features facilitated by depthwise dilated convolution; (iii) element-wise affine transformation to integrate attention into the value. The effectiveness and generalizability of the proposed SPA-Net were assessed on XJUEE, XJUEE-SEG, Kvasir and Kvasir-SEG endoscopy datasets. The results underscore the potential of peripheral vision modeling in self-attention for augmenting machine perception models. The associated code can be accessed at https://github.com/huoxiangzuo/SPA.

Mixed Integer Linear Programming Based Speed Profile Optimization for Heavy-Haul Trains

Automatic heavy-haul train (HHT) operation technology has recently received considerable attention in the field of rail transportation. In this paper, a discrete-time-based mathematical formulation is proposed to address the speed profile optimization problem in order to ensure the safe, efficient, and economical operation of heavy-haul trains (HHTs). Due to the presence of long and steep downgrades (LSDs) on some heavy-haul lines, the brake forces of the HHT are typically jointly determined by air braking and electric braking. The time characteristics of the air braking, such as the command delay and the change process caused by the air pressure, are taken into account, and then formulas are presented to calculate the air brake force. In addition, the influence of the neutral section on the control of the electric braking is considered via space-based constraints. The resulting problem is a nonlinear optimal control problem. To achieve linearization, auxiliary 0-1 binary variables and the big-M approach are introduced to transform the nonlinear constraints regarding slope, curve, neutral section, air brake force, and air-filled time into linear constraints. Moreover, piecewise affine (PWA) functions are used to approximate the basic resistance of the HHT. Finally, a mixed integer linear programming (MILP) model is developed, which can be solved by CPLEX. The experiments are carried out using data from a heavy-haul railway line in China, and the results show that the proposed approach is effective and flexible.

Determination of Black Sea Coastline Length with Oblique Stereographic Projection Using Affine Transformation

The Black Sea basin has rich oil and natural gas resources. As a result, determining the continental shelf in international relations and maritime law is a critical issue for countries with a shoreline on the Black Sea, which is a semi-enclosed sea. Global projections are generally used for the projection of satellites used to image the earth. The use of global projections causes increased deformation in applications in local areas. For this reason, the deformation of satellite images used as a base can be reduced by converting them to the appropriate projection. In this study, the coastline lengths of the countries neighboring the Black Sea were calculated by using remote sensing images and selecting the appropriate cartographic projection due to the aim of minimum map deformation. By using different numbers of control points to determine the six parameters of the 2D Affine transformation used for coordinate transformation, the change in the accuracy of the transformation depending on the number of control points was examined. The Black Sea coastline, which was digitized in the local coordinate system via the MODIS satellite image, was transformed into coordinates in the oblique stereographic projection system with 2D affine transformation. 11 test points were used in the affine transformation parameters calculated using different control points, and root mean square error (RMSE) of approximately 6 km on the X axis and approximately 10 km on the Y axis was achieved using 25 control points. As a result of the transformation, the coastline lengths of each country bordering the Black Sea were determined in oblique stereographic projection.

Upgrading Epoxy Supports for Enzyme Immobilization by Affinity Function Doping—A Case Study with Phenylalanine Ammonia-Lyase from Petroselinum crispum

This article provides a method to upgrade epoxy-functionalized carriers for covalent enzyme immobilization to selective carriers suitable for covalent immobilization of metal affinity-tagged enzymes without the need of preliminary enzyme purification. Affinity function doping of the epoxy-functionalized surface introduces an advanced possibility to avoid the costly and time-consuming downstream processes required for efficient immobilization on non-selective epoxy carriers. Our approach is based on the partial functionalization of surface epoxides via a proper diamine-derived linker and an ethylenediaminetetraacetic dianhydride-based chelator charged with cobalt ions. The solid macroporous carriers, doped with metal affinity functions, have both coordinative binding ability (rapid anchoring the metal affinity-tagged enzymes to the surface) and subsequent covalent bond-forming ability (preferred binding of the tagged enzyme to the surface after proper washing by the residual epoxide functions), enabling a single operation for the enrichment and immobilization of a recombinant phenylalanine ammonia-lyase from parsley fused to a polyhistidine affinity tag. The immobilized PcPAL was applied in the ammonia elimination of racemic phenylalanine, 4-chlorophenylalanine, and 4-bromophenylalanine to produce the corresponding d-phenylalanines, in addition to the formation of (E)-cinnamates, as well as in ammonia addition reactions to (E)-cinnamates, yielding the corresponding enantiopure l-phenylalanines.

The β-Blocker Carvedilol and Related Aryloxypropanolamines Promote ERK1/2 Phosphorylation in HEK293 Cells with K A Values Distinct From Their Equilibrium Dissociation Constants as β 2-Adrenoceptor Antagonists: Evidence for Functional Affinity.

The determination of affinity by using functional assays is important in drug discovery because it provides a more relevant estimate of the strength of interaction of a ligand to its cognate receptor than radioligand binding. However, empirical evidence for so-called, "functional affinity" is limited. Herein, we determined whether the affinity of carvedilol, a β-adrenoceptor antagonist used to treat heart failure that also promotes extracellular signal-regulated kinases 1 and 2 (ERK1/2) phosphorylation, differed between these two pharmacological activities. Four structurally related β-adrenoceptor antagonists (alprenolol, carazolol, pindolol, propranolol) that also activated ERK1/2 were included as comparators to enhance our understanding of how these drugs work in the clinical setting. In HEK293 cells stably expressing the human β 2-adrenoceptor carvedilol and related aryloxypropanolamines were partial agonists of ERK1/2 phosphorylation with potencies ([A]50s) that were lower than their equilibrium dissociation constants (K Bs) as β 2-adrenoceptor antagonists. As the [A]50 of a partial agonist is a good approximation of its K B, then these data indicated that the affinities of carvedilol and related ligands for these two activities were distinct. Moreover, there was a significant negative rank order correlation between the [A]50 of each ligand to activate ERK1/2 and their intrinsic activities (i.e., as intrinsic activity for ERK1/2 phosphorylation increased, so did affinity). Genome editing revealed that the transducer that coupled the β 2-adrenoceptor to ERK1/2 phosphorylation in response to carvedilol and other β 2-adrenoceptor antagonists was Gαs. Collectively, these data support the concept of "functional affinity" and indicate that the ability of the β 2-adrenoceptor to recruit Gαs may influence the affinity of the activating ligand. SIGNIFICANCE STATEMENT: In HEK293 cells overexpressing the human β2-adrenoceptor carvedilol and four related aryloxypropanolamines behaved as β2-adrenoceptor antagonists and partial agonists of ERK1/2 phosphorylation with rank orders of affinity that were distinct. These data imply that carvedilol and other β-blockers can stabilize the β2-adrenoceptor in different affinity conformations that are revealed when functionally distinct responses are measured. This is the basis for the pharmacological concept of "functional affinity."

On concave functions over lotteries

This note discusses functions over lotteries that are concave and continuous, but are not necessarily superdifferentiable. Earlier work claims that concave continuous utility for lotteries that satisfy best-outcome independence can be written as the minimum of affine functions. We give a counter-example that cannot be written as the minimum of affine functions, because there is no tangent hyperplane that dominates the functions at the boundary. We then review the fact that concavity and upper semi-continuity are equivalent to a representation as the infimum of affine functions, and show that these assumptions imply continuity for functions on finite-dimensional lotteries. Therefore, in finite-dimensional simplices, concavity and continuity are equivalent to the “infimum” representation. The “minimum” representation is equivalent to the existence of local utilities (supporting affine functions) at every lottery, a property that is equivalent to superdifferentiability.

A Multistage Rigid-Affine-Deformable Network for Three-Dimensional Multimodal Medical Image Registration

Multimodal image registration is an important component of medical image processing, allowing the integration of complementary information from various imaging modalities to improve clinical applications like diagnosis and treatment planning. We proposed a novel multistage neural network for three-dimensional multimodal medical image registration, which addresses the challenge of larger rigid deformations commonly present in medical images due to variations in patient positioning in different scanners and rigid anatomical structures. This multistage network combines rigid, affine and deformable transformations in three stages. The network was trained unsupervised with Mutual Information and Gradient L2 loss. We compared the results of our proposed multistage network with a rigid-affine-deformable registration with the classical registration method NiftyReg as a baseline and a multistage network, which combines affine and deformable transformation, as a benchmark. To evaluate the performance of the proposed multistage network, we used four three-dimensional multimodal in vivo datasets: three renal MR datasets consisting of T1-weighted and T2-weighted MR scans and one liver dataset containing CT and T1-weighted MR scans. Experimental results showed that combining rigid, affine and deformable transformations in a multistage network leads to registration results with a high structural similarity, overlap of the corresponding structures (Dice: 76.7 ± 12.5, 61.1 ± 14.0, 64.8 ± 16.2, 68.1 ± 24.6 for the four datasets) and a low level of image folding (|J| ≤ 0: less than or equal to 1.1%), resulting in a medical plausible registration result.

Fixed cost allocation using asymmetrical core-Nash bargaining DEA game

This paper introduces cooperative game theory into the data envelopment analysis (DEA) method for building a novel fixed cost allocation (FCA) approach from group and individual consciousness. We start by acknowledging the divergences of decision-making units (DMUs) and propose an asymmetrical Nash bargaining DEA game, where DMUs’ bargaining powers are defined through the functions of cross-efficiency and operation scale. However, the asymmetrical Nash bargaining solution is proposed from an individual perspective, without providing the theoretical support of full cooperation. To narrow this gap, we further introduce the core concept of a coalitional cooperative game into the built asymmetrical Nash bargaining DEA game, resulting in the asymmetrical core-Nash bargaining DEA game. The asymmetrical core-Nash bargaining solution is based on the common weights, with the properties of stability, fairness, Pareto-efficiency, and invariance to affine transformation. Furthermore, our proposed approach inherently ensures the uniqueness of the fixed cost scheme. Finally, numerical analysis and case study are provided to show the concrete application of the new method.

Unitary groups, $\boldsymbol{K}$ -theory, and traces

AbstractWe show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplices. Under certain $K$ -theoretic regularity conditions, these maps can be seen to commute with the pairing between $K_0$ and traces. If the homomorphism is contractive and sends the unit circle to the unit circle, the map between spaces of continuous real-valued affine functions can further be shown to be unital and positive (up to a minus sign).

Research of immune clone algorithm applying in the LED lamp automatic lock screw workstation

A new automatic lock screw machine for LED lamp has been researched in the paper, which is based on the immune clone algorithm. Firstly, the robot automatic lock screw system has been setup. Vision sensor captured LED lampshade images in real-time. Median filtering operation has been performed to the captured images. On this basis, a new image segmentation method based on the immune clone algorithm has been researched. The antibody and antigen of LED lampshade image have been defined. The immune affinity function has been setup at the same time. Several artificial immune operators have been designed, which can be used to obtain the optimum image segmentation threshold value in real time. The final results showed that the optimum image threshold value can been obtained after less than ten times iterative computation. Compared with the traditional Ostu method, the new method can reduce the disturbance information around the threaded hole, which made basis for threaded hole recognition and location.

УМОВИ ВИКОРИСТАННЯ КОНФОРМНИХ ВІДОБРАЖЕНЬ ДЛЯ ВИВЧЕННЯ ФРАКТАЛЬНОГО СТИСНЕННЯ ІНФОРМАЦІЇ

To describe the properties of self-similarity and invariance observed in various physical situations, the theory of fractals and multifractals is actively used in modern science. We consider a conformal mapping of the first kind, which is given by the entire linear function w = az + b, where w, z are complex variables, a, b are complex constants, a ≠ 0 . With its help, affine transformations are performed to construct the Sierpinski triangle and the Koch curve by specifying the functions w3(z) and finding the coefficients Re аі, Im аі, Re bi, Im bi, і = 1,2,3 or і = 1,2,3,4. These coefficients encode the image of the object and it can be unambiguously reconstructed by them. It is determined that the method in which self-similar regions in an object are detected and conformal mapping coefficients are found for them works under the condition that each such mapping is compressive. Only then will Banach’s fixed point theorem ensure image collection during decompression. This method of compressing graphic information is called fractal.

The price-elastic knapsack problem

This paper introduces the price-elastic knapsack problem (PEKP), an extension of the classic knapsack problem where instead of fixed item characteristics, the weight of each item and the profit from including an item in the knapsack are a function of a parameter, namely the price. PEKP is first formulated as a generic nonlinear optimization problem and three special cases are investigated. First, we show a polynomial-time solvable case. Next, we formulate the case where the item weights are affine-linear functions as a quadratic program. The computational results show that solving the quadratic program to optimality is computationally challenging, and thus, an approach that decomposes the problem into three mixed integer programs is proposed. Similarly, the case where the weights of the items are piecewise-linear functions is investigated and a quadratic formulation is proposed. A solution approach based on decomposing the problem into three mixed integer programs that are solved independently is also proposed. Using randomly generated instances of varying sizes, the computational results show that the proposed decomposition leads to significant computational advantages compared to solving the quadratic program in the cases of affine-linear and piecewise-linear functions.

Prior knowledge guided text to image generation

Generating a realistic and semantically consistent image from a given text is a challenging task. Due to the limited information of natural language, it is difficult to generate vivid images with fine details. To address this problem, we propose a Prior Knowledge Guided GAN for text to image generation. Specifically, the proposed method consists of several Knowledge Guided Up-Blocks. We decompose the image into a superposition of several visual regions, each of which requires corresponding prior knowledge to enrich its visual details. Correspondingly, we construct each Up-Block by incorporating relevant prior knowledge as input, aiming to enhance the quality of each visual region. Prior knowledge progressively provides more visual detail through affine transformations. Finally, high-quality images are synthesized by fusing all image regions. Experimental results on the CUB and COCO datasets demonstrate the superior performance of the proposed method.

Average consensus time-varying formation control of underactuated autonomous underwater vehicles based on event triggering decoupling mechanism

This paper focuses on the challenge of time-varying formation control for underactuated autonomous underwater vehicles (AUVs). To tackle this challenge, an average consensus time-varying formation control based on event triggering decoupling mechanism (ETDM-ACTVF) is proposed. Firstly, the average consensus time-varying formation (ACTVF) based on the affine transformation are introduced, and the control objective considering the dynamic characteristics of underactuated AUVs is proposed. The trajectory tracking controller is designed by the back stepping method. Secondly, an event triggering decoupling mechanism (ETDM) achieves the state decoupling to constrain the uncontrollable state. Moreover, a dynamic event triggering mechanism is employed to reduce the execution frequency of actuators. Finally, the excellent performance of the proposed algorithm in addressing both the underactuated AUV time-varying formation control and decoupling control problems is demonstrated through simulation results.

Optimization method of 3D reconstruction of metal cultural relics based on 3D laser scanning data reduction

AbstractThe extraction effect and feature matching are poor in the three‐dimensional reconstruction of metal cultural relics, which leads to a poor reconstruction effect. Therefore, an optimization method of three‐dimensional reconstruction of metal cultural relics based on 3D laser scanning data reduction is proposed. The overall technical design route of the method is shown as follows. Based on this model, the 3D laser scanning method is used to collect 3D images of metal artefacts, combined with colour space and 2D entropy detection methods to pre‐process 3D images, and feature matching of point clouds is carried out to extract and optimize the significant value of superpixels, and a 3D reconstructed visual model is constructed. Affine transformation is used to obtain the affine invariant moment of the structural light parameters of the visual feature lines of metal cultural relics. The light stability adjustment of the three‐dimensional reconstruction of metal cultural relics is realized by using the linear structural light adjustment method in the HSV colour space. The rigid and non‐rigid registration methods are introduced to match the point cloud. The product quantization algorithm is used to linearize the error function, and the block feature detection and matching model of spatial image is obtained. The noise number is judged by the threshold value, and the three‐dimensional reconstruction technology is combined to realize the three‐dimensional reconstruction of metal relics. The simulation results show that this method has good visual expression ability, high feature recognition rate, and improves the three‐dimensional reconstruction ability of metal relics.

Quartic differential systems with a non-degenerate monodromic critical point and multiple line at infinity

The quartic differential systems with a non-degenerate monodromic critical point and non-degenerate infinity are considerated. We show that in this family the maximal multiplicity of the line at infinity is seven. Modulo the affine transformation and time rescaling the classes of systems with the line of infinity of multiplicity two, three, ..., seven are determinated. In the cases when the quartic systems have the line at infinity of maximal multiplicity the problem of the center is solved.

Quartic differential systems with a non-degenerate monodromic critical point and multiple line at infinity

The quartic differential systems with a non-degenerate monodromic critical point and non-degenerate infinity are considerated. We show that in this family the maximal multiplicity of the line at infinity is seven. Modulo the affine transformation and time rescaling the classes of systems with the line of infinity of multiplicity two, three, ..., seven are determinated. In the cases when the quartic systems have the line at infinity of maximal multiplicity the problem of the center is solved.

Fractional calculus applied to the Cournot-type adjustment model

In this contribution, we propose the incorporation of memory in a Cournot-type model for the process of adjusting the production of firms in a duopoly market, through the calculation of fractional order. Under the simplifying assumption that the inverse demand and costs of firms are affine functions of the quantities produced, we show numerically some conditions on memory (fractional derivative order) and on the speed of the adjustment process, so that the model proposed converges to Cournot's generalized stationary points. Under these assumptions, we show that the firm that has more memory obtains greater profit.

Robust anti-perturbation safety control of multi-heterogeneous unmanned vessels

The identical nature of unmanned vessels in a homogeneous formation imposes limitations on their adaptability to diverse task demands in complex environmental conditions or constantly evolving task requirements, hindering their ability to achieve optimal performance. This paper presents the heterogeneous formation comprising fully actuated and underactuated vessels to overcome these limitations. Firstly, an affine transformation is employed to implement arbitrary configuration transformations within the formation system. Secondly, a composite learning formation controller is proposed for the underactuated vessels acting as the leaders to track the arbitrary formation transformation. Thirdly, considering that certain followers have access to the state information of the leaders, a new virtual leader–follower structure is constructed to achieve formation maneuver control by designing distributed estimators to estimate the state information of the virtual leader. Finally, simulation results validate the proposed control law’s effectiveness.

Two‐layer leader‐follower optimal affine formation maneuver control for networked unmanned surface vessels with input saturations

AbstractThis article studies the two‐layer leader‐follower optimal affine formation maneuver (AFM) control problem for multiple unmanned surface vessels (USV). The basic idea of the developed two‐layer control framework is to realize the time‐varying formation for the leader group in advance, and then let the follower USVs agilely respond to the target formation affinely localized by leaders. To realize this goal, a time‐varying formation reference system is first synthesized to describe leaders' target formation in the affine map of the nominal configuration. The reference system is set up by virtual vessel velocity command and unrotated geometric command, which make it possesses an intuitive application structure for operators to plan AFM commands in real‐time sensed surrounding environments. Then, by means of optimized backstepping design and the adaptive dynamic programming technique, actor‐only reinforcement learning controllers are established for USVs in both two layers to realize the optimal target formation tracking objective. For the proposed optimal controllers, the persistent excitation condition that is required by common optimal control schemes is also removed, which endows the presented scheme with lower computational complexity. Finally, theoretical analysis and simulation results illustrate the closed‐loop stability and the effectiveness of the presented scheme.