Affine Transformation Research Articles

Attentional pixel-wise deformation for pose-based human image generation

Human pose transfer aims to synthesize referred human images with target pose, bringing the substantial economic potential for E-commerce or virtual reality. In this paper, we propose a novel method, the Attentional Pixel-wise Deformation Network (APD-Net), for synthesizing human images with guided pose and referred images. Specifically, we leverage attention-based spatial transformation modules and affine transformation modules to generate accurate appearance and extract pixel-wise details in local regions to generate intermediate results. Additionally, we introduce a confidence map to refine spatial information during the final image synthesis. Domain alignment loss, cycle loss, perceptual and feature matching loss and contextual loss are applied to constrain the synthesized images while attention loss and fusion loss benefit warp images generation. We verify the efficacy of the model on the Market-1501 and DeepFashion datasets, using quantitative and qualitative measures. Our approach surpasses all previously published state-of-the-art results on most evaluation metrics, e.g., achieving 0.780 SSIM score, 9.55 Sliced Wasserstein Distance score, and a 0.963 Semantic Consistency score on DeepFashion and obtaining 0.303 SSIM score, 16.971 Sliced Wasserstein Distance score and 0.729 Semantic Consistency score on Market-1501 Code and pretrained models are available at: https://github.com/LiaoFJ/APD-Net/.

Enhancing fine-detail image synthesis from text descriptions by text aggregation and connection fusion module

Synthesizing images with fine details from text descriptions is a challenge. The existing single-stage generative adversarial networks (GANs) fuse sentence features into the image generation process through affine transformation, which alleviate the problems of missing details and large computation from stacked networks. However, existing single-stage networks ignore the word features in the text description, resulting in a lack of detail in the generated image. To address this issue, we proposed a text aggregation module (TAM) to fuse sentence features and word features in a text by a simple spatial attention mechanism. Then we built a text connection fusion (TCF) block consisting mainly of gated recurrent unit (GRU) and up-sampled block. It can connect text features used in the up-sampled blocks to improve text utilization. Besides, to further improve the semantic consistency between text and the generated images, we introduce the deep attentional multimodal similarity model (DAMSM) loss, which monitors the similarity between text and improves semantic consistency. Experimental results prove that our method is superior to the state-of-the-art models on the CUB and COCO datasets, regarding both image fidelity and semantic consistency with the text.

On the definition of curvature in Regge calculus

Abstract Regge calculus defines a curvature for piecewise constant metrics on simplicial complexes subject to a partial continuity requirement. We prove that if a part of the complex is embedded in a Euclidean space, by a piecewise affine map, and we perform smoothing by convolution there, then the smoothed metrics have a densitized scalar curvature that converges, in the sense of measures, to that defined by Regge, as the smoothing parameter goes to zero.

Finite approximation properties of C*-modules III

Abstract We introduce and study a notion of module nuclear dimension for a C * \mathrm{C}^{*} -algebra A which is a C * \mathrm{C}^{*} -module over another C * \mathrm{C}^{*} -algebra 𝔄 {\mathfrak{A}} with compatible actions. We show that the module nuclear dimension of A is zero if A is 𝔄 {\mathfrak{A}} -NF. The converse is shown to hold when 𝔄 {\mathfrak{A}} is a C ⁢ ( X ) {C(X)} -algebra with simple fibers, with X compact and totally disconnected. We also introduce a notion of module decomposition rank, and show that when 𝔄 {\mathfrak{A}} is unital and simple, if the module decomposition rank of A is finite then A is 𝔄 {\mathfrak{A}} -QD. We study the set 𝒯 𝔄 ⁢ ( A ) {\mathcal{T}_{\mathfrak{A}}(A)} of 𝔄 {\mathfrak{A}} -valued module traces on A and relate the Cuntz semigroup of A with lower semicontinuous affine functions on the set 𝒯 𝔄 ⁢ ( A ) {\mathcal{T}_{\mathfrak{A}}(A)} . Along the way, we also prove a module Choi–Effros lifting theorem. We give estimates of the module nuclear dimension for a class of examples.

Recurrent Affine Transformation for Text-to-Image Synthesis

Text-to-image synthesis aims to generate realistic images conditioned on text descriptions. To fuse text information into synthesized images, conditional affine transformations (CATs), such as conditional batch normalization (CBN) and conditional instance normalization (CIN), are usually used to predict batch statistics of different layers. However, ordinary CAT blocks control the batch statistics independently disregarding the consistency among neighboring layers. To address the above issue, we propose a new fusion approach names recurrent affine transformation (RAT) for synthesizing images conditioned on text information. RAT connects all the CAT blocks with recurrent connections for explicitly fitting the temporal consistency between CAT blocks. To verify the effectiveness of RAT, we propose a novel visualization method to show how generative adversarial network (GAN) fuses conditional information. Our microscopic and macroscopic visualizations not only demonstrate the effectiveness of RAT but also turn out to be a useful perspective to analyze how GAN fuses conditional information. In addition, we propose a more stable spatial attention mechanism for the discriminator, which helps the text description to supervise the generator to synthesize more relevant image contents. Extensive experiments on the CUB, Oxford-102, and COCO datasets demonstrate the proposed model's superiority in comparison to state-of-the-art models. Our code is available on <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/senmaoy/RAT-GAN</uri> .

Multimedia Interactive Technology for Improving Language Perception in English Teaching and Learning

Abstract Based on Direct Show software, this paper acquires English teaching videos and stores them in the corresponding files. As the position of the teaching projection screen may be different in height, it will lead to the phenomenon that the captured image will be tilted, and it is necessary to use the affine transformation and perspective transformation methods to realize the correction of the teaching projection image. In order to promote the general application of multimedia interactive technology in the teaching process, dynamic gesture tracking with Kalzmann filtering is utilized to construct a non-contact human-computer interaction system, which is applied to the process of English teaching, thus designing an English teaching model incorporating multimedia interactive technology and analyzing the effect of the model. It was found that the mean score of the experimental group’s pre-experimental evaluation was 19.225, and the mean score for the post-experimental assessment was 23.087, t=2.274, P (two-sided)=0.018&lt;0.05 at the 0.05 significance level, which is a significant difference. It shows that compared with traditional English teaching methods, the teaching mode that integrates multimedia interactive technology can effectively improve the English language perception ability of college students in China.

An image quality assessment index based on image features and keypoints for X-ray CT images.

Optimization tasks in diagnostic radiological imaging require objective quantitative metrics that correlate with the subjective perception of observers. However, although one such metric, the structural similarity index (SSIM), is popular, it has limitations across various aspects in its application to medical images. In this study, we introduce a novel image quality evaluation approach based on keypoints and their associated unique image feature values, focusing on developing a framework to address the need for robustness and interpretability that are lacking in conventional methodologies. The proposed index quantifies and visualizes the distance between feature vectors associated with keypoints, which varies depending on changes in the image quality. This metric was validated on images with varying noise levels and resolution characteristics, and its applicability and effectiveness were examined by evaluating images subjected to various affine transformations. In the verification of X-ray computed tomography imaging using a head phantom, the distances between feature descriptors for each keypoint increased as the image quality degraded, exhibiting a strong correlation with the changes in the SSIM. Notably, the proposed index outperformed conventional full-reference metrics in terms of robustness to various transformations which are without changes in the image quality. Overall, the results suggested that image analysis performed using the proposed framework could effectively visualize the corresponding feature points, potentially harnessing lost feature information owing to changes in the image quality. These findings demonstrate the feasibility of applying the novel index to analyze changes in the image quality. This method may overcome limitations inherent in conventional evaluation methodologies and contribute to medical image analysis in the broader domain.

8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign

&lt;abstract&gt; &lt;p&gt;This research paper is supplemented with a unique formation to design state-of-the-art S-boxes. The invented approach is simple but has the capability of creating confusion in our newly proposed algorithm. Our core planned work refined the method of already designed S-boxes to accomplish more compact ones. Various structures were merged here, namely affine transformation, fractional linear transformation, structure of Klein four-group, and the algebraic structures of the Galois fields, $ GF\left({2}^{4}\right) $ and $ GF\left({2}^{8}\right). $ These structures were utilized to synthesize newly $ 1600 $ robust S-boxes. Besides, we discussed encryption steps of AES with these newly generated S-boxes. We highlighted some specific characteristics, performance of parameter's improvement, and their utilization. Nonlinear properties were mainly set to inspect the behavior of I/O bits and could apply image encryption. Then, the performance of proposed S-boxes and newly structured AES was tested in comparison with other prevailing S-boxes.&lt;/p&gt; &lt;/abstract&gt;

Deep learning-based Alzheimer's disease detection: reproducibility and the effect of modeling choices.

Machine Learning (ML) has emerged as a promising approach in healthcare, outperforming traditional statistical techniques. However, to establish ML as a reliable tool in clinical practice, adherence to best practices in data handling, and modeling design and assessment is crucial. In this work, we summarize and strictly adhere to such practices to ensure reproducible and reliable ML. Specifically, we focus on Alzheimer's Disease (AD) detection, a challenging problem in healthcare. Additionally, we investigate the impact of modeling choices, including different data augmentation techniques and model complexity, on overall performance. We utilize Magnetic Resonance Imaging (MRI) data from the ADNI corpus to address a binary classification problem using 3D Convolutional Neural Networks (CNNs). Data processing and modeling are specifically tailored to address data scarcity and minimize computational overhead. Within this framework, we train 15 predictive models, considering three different data augmentation strategies and five distinct 3D CNN architectures with varying convolutional layers counts. The augmentation strategies involve affine transformations, such as zoom, shift, and rotation, applied either concurrently or separately. The combined effect of data augmentation and model complexity results in up to 10% variation in prediction accuracy. Notably, when affine transformation are applied separately, the model achieves higher accuracy, regardless the chosen architecture. Across all strategies, the model accuracy exhibits a concave behavior as the number of convolutional layers increases, peaking at an intermediate value. The best model reaches excellent performance both on the internal and additional external testing set. Our work underscores the critical importance of adhering to rigorous experimental practices in the field of ML applied to healthcare. The results clearly demonstrate how data augmentation and model depth-often overlooked factors- can dramatically impact final performance if not thoroughly investigated. This highlights both the necessity of exploring neglected modeling aspects and the need to comprehensively report all modeling choices to ensure reproducibility and facilitate meaningful comparisons across studies.

О размерности алгебр Ли инфинитезимальных аффинных преобразований прямых произведений более двух пространств аффинной связности первого типа

The theory of motions in generalized spaces is one of the directions in modern differential geometry. Such scientists as E. Cartan, P. K. Rashev­sky, P. A. Shirokov, I. P. Egorov, A.Ya. Sultanov and other scientists were engaged in the study of movements in various spaces of affine connec­tions. The question of movements in direct products of two spaces of af­fine connection was considered in M. V. Morgun’s work. In the case of a direct product of more than two spaces of affine con­nection, the question of the dimension of Lie algebras of infinitesimal affine transformations of a given space remained open. In this article, an estimate of the upper bound of the dimension of the Lie algebra of infinitesimal affine transformations of affine connection spaces, representing a direct reproduction of at least three non-projective Euclidean spaces of a certain type, is obtained. To solve this problem, a system of linear homogeneous equations is obtained, which is satisfied by the components of an arbitrary infinitesi­mal affine transformation. This system is found using the properties of the Lie derivative applied to the tensor field of curvature of the spaces under consideration. The evaluation of the rank of this system allows us to ob­tain an estimate from below of the rank of the matrix of the system under consideration.

Hybrid Gromov-Wasserstein Embedding for Capsule Learning.

Capsule networks (CapsNets) aim to parse images into a hierarchy of objects, parts, and their relationships using a two-step process involving part-whole transformation and hierarchical component routing. However, this hierarchical relationship modeling is computationally expensive, which has limited the wider use of CapsNet despite its potential advantages. The current state of CapsNet models primarily focuses on comparing their performance with capsule baselines, falling short of achieving the same level of proficiency as deep convolutional neural network (CNN) variants in intricate tasks. To address this limitation, we present an efficient approach for learning capsules that surpasses canonical baseline models and even demonstrates superior performance compared with high-performing convolution models. Our contribution can be outlined in two aspects: first, we introduce a group of subcapsules onto which an input vector is projected. Subsequently, we present the hybrid Gromov-Wasserstein (HGW) framework, which initially quantifies the dissimilarity between the input and the components modeled by the subcapsules, followed by determining their alignment degree through optimal transport (OT). This innovative mechanism capitalizes on new insights into defining alignment between the input and subcapsules, based on the similarity of their respective component distributions. This approach enhances CapsNets' capacity to learn from intricate, high-dimensional data while retaining their interpretability and hierarchical structure. Our proposed model offers two distinct advantages: 1) its lightweight nature facilitates the application of capsules to more intricate vision tasks, including object detection; and 2) it outperforms baseline approaches in these demanding tasks. Our empirical findings illustrate that HGW capsules (HGWCapsules) exhibit enhanced robustness against affine transformations, scale effectively to larger datasets, and surpass CNN and CapsNet models across various vision tasks.

The uniformly continuous theorem of fractal interpolation surface function and its proof

&lt;abstract&gt; &lt;p&gt;In order to research uniform continuity of fractal interpolation surface function on a closed rectangular area, the accumulation principle was applied to prove uniform continuity of fractal interpolation surface function on a closed rectangular area. First, fractal interpolation surface function was constructed by affine mapping. Second, the continuous concept of fractal interpolation surface function at a planar point in a three-dimensional cartesian coordinate space system and uniform continuity of fractal interpolation surface function on a closed rectangular area were defined in the paper. Finally, the uniformly continuous theorem of fractal interpolation surface function was proven through accumulation principle in the paper. The conclusion showed that fractal interpolation surface was uniformly continuous function on a closed rectangular area.&lt;/p&gt; &lt;/abstract&gt;

Notice to Reader: Optimizing Data Reuse for Loop Mapping on CGRAs With Joint Affine and Non-Affine Transformations

Notice to Reader: Optimizing Data Reuse for Loop Mapping on CGRAs With Joint Affine and Non-Affine Transformations

Admissible Control Laws for Constrained Linear Power Flow: The General Case

Linearized power flow with line flow and voltage constraints can be modeled as a system of linear inequalities depending on the power injections. When some injections are controlled by the grid operator while others are determined exogenously, robust control aims at determining grid operator's actions under imperfect system observability such that the grid state is feasible for all possible realizations of the exogenous actions. It was shown how to design and analyze such admissible control policies efficiently for the subclass of affine control laws, but this paper shows that there are important cases that require more general control policies. We show that, for the constrained linear power flow setting, general admissible control policies can always be chosen as piecewise affine (PWA) mappings. The PWA mapping can be explicitly characterized offline or control actions can be computed online by solving an optimization problem given a current observation. For the latter setup, we provide an algorithm that verifies offline that the online control scheme is admissible. This verification step is a crucial precondition to apply the online control scheme in real, safety-critical power grids. The proposed framework is demonstrated with applications to voltage regulation in active distribution grids subject to uncertain prosumers and low observability.

High-Quality Fusion and Visualization for MR-PET Brain Tumor Images via Multi-Dimensional Features.

The fusion of magnetic resonance imaging and positron emission tomography can combine biological anatomical information and physiological metabolic information, which is of great significance for the clinical diagnosis and localization of lesions. In this paper, we propose a novel adaptive linear fusion method for multi-dimensional features of brain magnetic resonance and positron emission tomography images based on a convolutional neural network, termed as MdAFuse. First, in the feature extraction stage, three-dimensional feature extraction modules are constructed to extract coarse, fine, and multi-scale information features from the source image. Second, at the fusion stage, the affine mapping function of multi-dimensional features is established to maintain a constant geometric relationship between the features, which can effectively utilize structural information from a feature map to achieve a better reconstruction effect. Furthermore, our MdAFuse comprises a key feature visualization enhancement algorithm designed to observe the dynamic growth of brain lesions, which can facilitate the early diagnosis and treatment of brain tumors. Extensive experimental results demonstrate that our method is superior to existing fusion methods in terms of visual perception and nine kinds of objective image fusion metrics. Specifically, in the results of MR-PET fusion, the SSIM (Structural Similarity) and VIF (Visual Information Fidelity) metrics show improvements of 5.61% and 13.76%, respectively, compared to the current state-of-the-art algorithm. Our code is publicly available at: https://github.com/22385wjy/MdAFuse.

Effect and mechanism analysis of surface hydrogenation and fluorination on the electronic properties of th-GeC2.

A two-dimensional (2D) tetrahex-GeC2 nanosheet demonstrates excellent electronic properties such as a finite direct band gap and high carrier mobilities, as predicted from theoretical calculations. To further expand its potential applications, various strategies can be employed to tailor its electronic properties. These strategies include alloying, strain application, and edge and surface functionalization. This work specifically focuses on the impact of surface functionalization with hydrogen and fluorine adsorption on the 2D tetrahex-GeC2 nanostructures. It was discovered that the electronic properties of these nanostructures undergo significant alterations through surface functionalization by adjusting the adsorption sites and coverage of H/F species. The underlying mechanisms responsible for these property changes have been thoroughly analyzed and discussed in detail. Our calculations, based on density functional theory, reveal that the band gap of tetrahex-GeC2 widens as the surface coverage of H atoms increases. Conversely, the band gap narrows in the case of F adsorption. Additionally, the indirect-direct band gap transition can be triggered through surface functionalization. Such modifications in the electronic band structure are primarily due to the disappearance of the π bond when the C atom is converted from sp2 to sp3 hybridization through the adsorption of surface functionalized species. Furthermore, the results indicate that surface adsorption can regulate the effective mass of carriers, electron affinity, and work function in the 2D tetrahex-GeC2 nanostructure.

A two-point heuristic to calculate the stepsize in subgradient method with application to a network design problem

We introduce a heuristic rule for calculating the stepsize in the subgradient method for unconstrained convex nonsmooth optimization which, unlike the classic approach, is based on retaining some information from previous iteration. The rule is inspired by the well known two-point stepsize by Barzilai and Borwein (BB) [6] for smooth optimization and it coincides with (BB) in case the function to be minimised is convex quadratic.Under the use of appropriate safeguards we demonstrate that the method terminates at a point that satisfies an approximate optimality condition.The proposed approach is tested in the framework of Lagrangian relaxation for integer linear programming where the Lagrangian dual requires maximization of a concave and nonsmooth (piecewise affine) function. In particular we focus on the relaxation of the Minimum Spanning Tree problem with Conflicting Edge Pairs (MSTC). Comparison with classic subgradient method is presented. The results on some widely used academic test problems are provided too.

Classification of MRI brain tumors based on registration preprocessing and deep belief networks

&lt;abstract&gt;&lt;p&gt;In recent years, augmented reality has emerged as an emerging technology with huge potential in image-guided surgery, and in particular, its application in brain tumor surgery seems promising. Augmented reality can be divided into two parts: hardware and software. Further, artificial intelligence, and deep learning in particular, have attracted great interest from researchers in the medical field, especially for the diagnosis of brain tumors. In this paper, we focus on the software part of an augmented reality scenario. The main objective of this study was to develop a classification technique based on a deep belief network (DBN) and a softmax classifier to (1) distinguish a benign brain tumor from a malignant one by exploiting the spatial heterogeneity of cancer tumors and homologous anatomical structures, and (2) extract the brain tumor features. In this work, we developed three steps to explain our classification method. In the first step, a global affine transformation is preprocessed for registration to obtain the same or similar results for different locations (voxels, ROI). In the next step, an unsupervised DBN with unlabeled features is used for the learning process. The discriminative subsets of features obtained in the first two steps serve as input to the classifier and are used in the third step for evaluation by a hybrid system combining the DBN and a softmax classifier. For the evaluation, we used data from Harvard Medical School to train the DBN with softmax regression. The model performed well in the classification phase, achieving an improved accuracy of 97.2%.&lt;/p&gt;&lt;/abstract&gt;

Transformation of initial cartographic materials for the “Main State Topographic Map” to coordinate system UCS-2000

Abstract Initial cartographic materials were determined to create the topographic database of the “Main State Topographic Map”. They require preparation for creating (updating) digital topographic maps at the scale of 1:50,000. One of the stages of preparation of input cartographic materials is their transformation to the coordinate reference system UCS-2000. The goal of the article is to research the problem of transformation of points coordinates by the rigorous mathematical method for referencing cartographic materials from the coordinate systems CS-42/CS-63 to the State Geodetic Coordinate Reference System UCS-2000 (after this – UCS-2000) by geographic information systems (GIS) for creation (updating) digital topographic maps at the scale of 1:50,000 to create the seamless topographic database of the “Main State Topographic Map” on the territory of Ukraine. Authors propose a method of transformation orthophoto at the scale of 1:10,000 to UCS-2000 in Cartesian coordinates of Gauss-Krüger projection in the corresponding 6-degree zone in the adopted state interchart of topographic maps at the scale of 1:50,000. This method consists of cartographic materials transformation using a transformation field in the form of a GRID model based on the triangulation TIN model using the finite element method. The choice of the finite element method and the peculiarities of affine transformation are mathematically substantiated. Also, the authors determined the requirements for the method of coordinates transformation.

Self-Supervised Random Forest on Transformed Distribution for Anomaly Detection.

Anomaly detection, the task of differentiating abnormal data points from normal ones, presents a significant challenge in the realm of machine learning. Numerous strategies have been proposed to tackle this task, with classification-based methods, specifically those utilizing a self-supervised approach via random affine transformations (RATs), demonstrating remarkable performance on both image and non-image data. However, these methods encounter a notable bottleneck, the overlap of constructed labeled datasets across categories, which hampers the subsequent classifiers' ability to detect anomalies. Consequently, the creation of an effective data distribution becomes the pivotal factor for success. In this article, we introduce a model called "self-supervised forest (sForest)", which leverages the random Fourier transform (RFT) and random orthogonal rotations to craft a controlled data distribution. Our model utilizes the RFT to map input data into a new feature space. With this transformed data, we create a self-labeled training dataset using random orthogonal rotations. We theoretically prove that the data distribution formulated by our methodology is more stable compared to one derived from RATs. We then use the self-labeled dataset in a random forest (RF) classifier to distinguish between normal and anomalous data points. Comprehensive experiments conducted on both real and artificial datasets illustrate that sForest outperforms other anomaly detection methods, including distance-based, kernel-based, forest-based, and network-based benchmarks.