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This study aims to understand how pre-service mathematics teachers conduct prospective analyses comprehensively. A qualitative research method with a case study design was used. The participant was Mrs N, a pre-service mathematics teacher who conducted research using DDR methodology in a grade 9 junior high school in Sindang, Majalengka, involving 48 students. Data were collected by analyzing empirical evidence from Mrs. N's prospective analysis process by uncovering the various stages of a prospective analysis. An iterative approach was used to analyze the data by refining the research questions through discussions and regular meetings with Mrs. N. The process ensured adaptability to new insights and understandings from the empirical data. Our findings reveal that the teacher draws upon fundamental philosophical principles from didactical design research, including hermeneutics, phenomenology, and ethnomethodology. By embracing these approaches, the teacher gains valuable insights into conducting research within an interpretive paradigm, allowing for a deeper exploration of the meaning of concepts, the purpose of learning, and the cultural influences that shape the educational process. Additionally, our study sheds light on the emergence of transpositional didactics theory as the prospective teacher delves into understanding the meaning of the geometrics transformation concept.

Purpose. Scientific research in the field of mobile technologies shows that every year there is an increasing need to optimize geometric transformation algorithms to improve the performance of graphic applications. This study is dedicated to the analysis of various image transformation methods, their impact on performance, and the quality of display in mobile applications. Methodology. A comparative analysis of various geometric transformation algorithms was performed to determine the most effective ones for use in mobile graphic applications. Bilinear interpolation and affine transformations are considered as the primary methods, and the use of neural network-based methods is also evaluated. Findings. It was found that the use of optimization algorithms for geometric transformation reduces response time, effectively uses resources, improves display quality, and increases the stability and reliability of applications. Originality. A new approach to the application of neural network-based methods for geometric transformations is proposed, which allows automating the process of determining optimal transformation parameters. Practical value. The use of the proposed methods contributes to the improvement of the performance of mobile graphic applications by optimizing response time and improving image quality. [ABSTRACT FROM AUTHOR]

Achieving unsupported 3D printing still faces challenges in handling large-angle overhangs and improving printing precision. This paper presented a cone slicing algorithm for multi-freedom unsupported 3D printing of NURBS volume parametric models. Though the geometric mapping of the 3D model file of the model, it applied a horizontal slicing algorithm to this mapped model, resulting in a continuous print path G-code of the deformed model. This G-code was then subjected to inverse mapping, generating multi-degree-of-freedom continuous printing paths suitable for six-axis robotic arms. Utilizing the conical slicing algorithm to plan printing paths enabled printing of overhanging structures without the need for support. It validates the accuracy, feasibility, and effectiveness of the conical slicing algorithm through simulation experiments and comparative trials. The introduction of the conical slicing algorithm offers a more efficient, economical, and green solution for unsupported 3D printing of NURBS-based parametric models. [ABSTRACT FROM AUTHOR]

The use of Worksheet teaching materials and textbooks from the government at MTs Darul Ulum Ranupakis and learning methods that are still teacher-centered. The lack of involvement in the context around students has resulted in a lack of student interest in learning mathematics, especially in class IX. One alternative to overcome this is to develop contextually based Students’ Worksheet with the object of the Lumajang Central Park building. This Research aims to develop a teaching material design in the form of a Students’ Worksheet on geometric transformations based on the context of the Lumajang Central Park Building that is valid, practical, and effective. This type of Research is Research and Development by following the ADDIE development model procedure with the stages of Analysis, Design, Development, Implementation, and Evaluation. This Research uses data collection techniques: observation, documentation, interviews, and questionnaires. The subjects in this Research were class IX students at MTs Darul Ulum Ranupakis. The results of the Research show that teaching materials in the form of geometric transformation worksheets based on the context of the Lumajang Regency Square building meet the criteria of valid, practical, and effective with percentages of 94.43% (very valid), 84.3% (very practical ) and 80% respectively (Good). These results show that the geometric transformation of Students’ Worksheet in the context of the Lumajang Central Park building is suitable for learning. This Research can be a reference and open up opportunities for future researchers to integrate contextual approaches to mathematics material and develop local context-based teaching materials or explore more innovative learning methods to attract interest in learning mathematics, especially class IX students. Penggunaan bahan ajar LKS dan buku paket dari pemerintah di MTs Darul Ulum Ranupakis dan metode pembelajaran yang masih berpusat pada guru serta kurangnya melibatkan konteks disekitar siswa membuat kurangnya minat peserta didik dalam belajar matematika, khususnya kelas IX. Salah satu alternatif untuk menanggulangi hal itu ialah mengembangkan LKPD berbasis kontekstual dengan objek bangunan alun-alun Kabupaten Lumajang. Penelitian ini bertujuan untuk mengembangkan desain bahan ajar berupa Lembar Kerja Peserta Didik (LKPD) transformasi geometri berbasis konteks bangunan alun-alun Kabupaten Lumajang yang valid, praktis dan efektif. Jenis penelitian ini yaitu Research and Development dengan mengikuti prosedur model pengembangan ADDIE dengan tahapan Analysis, Design, Development, Implementation, dan Evaluation. Teknik pengumpulan data yang digunakan dalam penelitian ini berupa observasi, dokumentasi, wawancara dan angket. Subjek dalam penelitian ini adalah siswa kelas IX MTs Darul Ulum Ranupakis. Hasil dari penelitian menunjukkan bahwa bahan ajar berupa LKPD transformasi geometri berbasis konteks bangunan alun-alun Kabupaten Lumajang memenuhi kriteria valid, praktis dan efektif dengan persentase masing-masing 94,43% (sangat valid), 84,3% (sangat praktis) dan 80% (baik). Melalui hasil tersebut dapat disimpulkan bahwa LKPD transformasi geometri dengan konteks bangunan alun-alun Kabupaten Lumajang layak untuk digunakan dalam pembelajaran. Penelitian ini dapat menjadi referensi dan membuka peluang untuk peneliti selanjutnya dalam mengintegrasikan pendekatan kontekstual pada materi matematika serta mengembangkan bahan ajar berbasis konteks lokal atau eksplorasi metode pembelajaran yang lebih inovatif untuk menarik minat belajar matematika terutama peserta didik kelas IX.

In this paper we introduce the use of several different Infinite Mapping Layers to model open boundaries in the 2-D Finite Element Method for the computation of transmission line parameters. The transformation maps a semi-infinite interval to a finite interval, thereby providing a simple and accurate description of open boundaries while keeping the size of the computational domain very compact. The method has been evaluated and tested on a variety of common transmission line geometries appearing in the literature and its accuracy is validated by comparing the results with canonical cases having closed expressions and with arbitrary geometries computed with commercial software tools. Various geometrical transformations have been developed and tested, and their performances evaluated in terms of accuracy and efficiency. Finally, the possibility of using a radial Infinite Mapping Layer has also been considered.

Banyumasan batik is one of Indonesia's cultural heritages from Banyumas Regency, which has unique and interesting patterns and motifs. This research paper describes the mathematical modelling of geometric transformations in Banyumasan batik. Geometric transformation is a mathematical technique for changing the shape or position of an object on a plane. This is qualitative research with an ethnographic approach. Data is collected through observation, interviews, and documentations. The data obtained were analysed using content analysis to identify various Banyumasan batik motifs that can be transformed into geometric forms. This study describes the basic geometric transformations, namely translations in Sekar Tirta batik motif, reflections in Bawor Kembar batik motif, dilations in Kawung Jenggot batik motif, and rotations in Manggar Bawor batik motif which applied to Banyumasan batik motifs. The results of this study include geometric transformations of Banyumasan batik motifs which are expected to positively contribute to the development of Indonesian art and culture, especially in the field of batik, enrich insight and knowledge about the application of mathematics in everyday life, and can be used for mathematical modelling and mathematics education based on local culture.

Cancer classification based on microarray data plays a very important role in cancer diagnosis and detection. Indeed, since microarray data contains a huge number of genes and a small number of samples, it is also nonlinear and noisy, which has led to the need to find a way to reduce the data dimensionality. In order to solve this problem, we need to find an effective way to help biologists and medical research scientists. This paper proposes a new bio-inspired algorithm for cancer classification in gene selection called Binary Grey Wolf Optimization Algorithm (BGWOA), which is based on hybridization between Minimum Redundancy-Maximum Relevance (MRMR) and a novel Binary Grey Wolf algorithm. The BGWOA is composed of two stages: The first stage consists of the MRMR pre-filter to obtain the set of relevant genes that reduces the dimensionality of the data sets. The second stage consists of a new Binary Grey Wolf algorithm based on direct similarity and centroid known in the geometric field to update the positions of grey wolves in order to exploit and explore the search spaces. As well, we used a fitness function that depends on the SVM with LOOCV classifier and the rate of unselected genes to evaluate the presented solutions. The primary goal of the last stage is to identify the best relevant subset of genes among those obtained in the first stage. This research used eight microarray datasets to evaluate and compare the proposed method with other existing algorithms. The experimental results produced in this research are able to provide a higher classification accuracy with fewer genes compared to many recently published algorithms. Specifically, the proposed method achieves 100% classification accuracy in five reference datasets with a number of genes ranging from 12 to 25. Therefore, this indicates that our research is promising and significant. [ABSTRACT FROM AUTHOR]

This research explores the application of artificial intelligence in generating Karawo motifs, a traditional Indonesian pattern. The research involves collecting a dataset of existing Karawo motifs and utilizing genetic algorithms to evolve and create novel pattern variations. The generated motifs are evaluated based on their adherence to traditional design principles and aesthetic appeal. The formation of Karawo motifs begins with randomly selecting image data from a database. Then, the selection of transformation treatments is performed by optimizing the fitness function within the genetic algorithm. The applied types of transformations include geometric transformations, Boolean transformations, and arithmetic transformations. The outlined genetic algorithm steps include determining the fitness function, performing its evaluation, selecting fitness values, applying crossover, implementing mutation, managing survivor selection, and terminating iterations. The results indicate that the developed system is capable of creating diverse and appealing Karawo motif patterns, showcasing the potential of combining traditional artistry with artificial intelligence. This study has the potential to expand the possibilities of Karawo motif design and contribute to the preservation and promotion of Indonesian cultural heritage. [ABSTRACT FROM AUTHOR]

Hand gesture recognition (HGR) is a challenging and fascinating research topic in computer vision with numerous daily life applications. In HGR, computers aim to identify and classify hand gestures. The limited diversity of the dataset used in HGR is due to the limited number of hand gesture demonstrators, acquisition environments, and hand pose variations despite previous efforts. Geometric image augmentations are commonly used to address these limitations. These augmentations include scaling, translation, rotation, flipping, and image shearing. However, research has yet to focus on identifying the best geometric transformations for augmenting the HGR dataset. This study employed three commonly utilized pre-trained models for image classification tasks, namely ResNet50, MobileNetV2, and InceptionV3. The system's performance was evaluated on five static HGR datasets: DLSI, HG14, ArabicASL, MU HandImages ASL, and Sebastian Marcell. The experimental results demonstrate that many geometric transformations are unnecessary for HGR image augmentation. Image shearing and horizontal flipping are the most influential transformations for augmenting the HGR dataset and achieving better classification performance. Moreover, ResNet50 outperforms MobileNetV2 and InceptionV3 for static HGR. [ABSTRACT FROM AUTHOR]

Three dimensional symmetry plane detection is a hot research topic in the field of computer vision. When detecting the symmetry plane, the integrity of the three-dimensional point cloud is often ignored, and it is often defaulted to be complete and absolutely symmetrical, which makes the mirror key points relatively easy to be found.This proposes a method for 3D symmetry plane detection based on 2D image and transformation. In detail, the proposed method firstly detects the mirror key points in a single 2D image of the target, then selects the corresponding points in the 2D image and the 3D point cloud to construct a transformation matrix, and finally obtains the mirror key points in the 3D point cloud based on the 2D mirror key points and the transformation matrix to detect the symmetry plane. Experimental evaluations are performed on both synthetic and real point cloud datasets. The results show that the proposed approach is effective for the complete point cloud as well as the incomplete point cloud. Compared with the other two methods, it is proved that the symmetry plane detected by the proposed method is more accurate. The experimental results show that the symmetry plane detected by the proposed method is more accurate than the other two comparison methods. Then the experimental results on incomplete point clouds show that the proposed method could detect symmetry plane effective. [ABSTRACT FROM AUTHOR]

Person tracking is considered an important application in the field of video surveillance. A top view camera provides a wide coverage of scene and better handling of occlusion as compared to frontal view. The proposed top view based person tracking method mainly contains four modules, namely BLOB detection, standardisation, size estimation and tracking. In blob detection, foreground is extracted using segmentation, statistical operation, connected component labelling and morphological operations. The top view is radial symmetric thus using this property, the extracted blob is transformed to upright position using geometric transformations. This effectively makes the blob/person rotation invariant in the scene. Basic shape based features including width, height and body ratio are measured for each blob. On the basis of these features, the algorithm effectively distinguishes a person, no person as well as merged person blob. A simple tracker for each blob is formerly created to maintain different parameters for example, blob name, blob width & height, blob x & y coordinates, blob time, blob history, blob size and blob ratio. The proposed algorithm along with the seven attractive/popular tracking methods have been tested on different test sequences. The experimental results show that the proposed algorithm significantly improves results by achieving true detection rate of 95%. [ABSTRACT FROM AUTHOR]

Anomalies (or outliers) indicate a minority of data items that are quite different from the majority (inliers) of a dataset in a certain aspect. Unsupervised anomaly detection (UAD) is an important but not yet extensively studied research topic. Recent deep learning based methods exploit the reconstruction gap between inliers and outliers to discriminate them. However, it is observed that the reconstruction gap often decreases rapidly as the training process goes. And there is no reasonable way to set the training stop point. To support effective UAD, we propose a new UAD framework by introducing a Latent Feature Reconstruction (LFR) layer that can be applied to recent UAD methods. The LFR layer acts as a regularizer to constrain the latent features in a low-rank subspace from which inliers can be reconstructed well while outliers cannot. We develop two new UAD methods by implementing the proposed framework with autoencoder architecture and geometric transformation scheme. Experiments on five benchmarks show that our proposed methods can achieve state-of-the-art performance in most cases. [ABSTRACT FROM AUTHOR]

Using deep learning (DL) technology, neural networks have achieved great success in various fields of computer vision. Among them, anomaly detection is a promising application of image defect analysis. The purpose of the detector is to find the out-of-distribution when predicting the probability of a DL network for abnormal samples, after some normal sample images are given for training. Geometric transformation (GT) based anomaly detection is one of the recent best methods for classifying abnormal samples among many normal ones. However, the GT method training process is unstable and too inaccurate to be used in industrial applications. The goal of this study is to suggest a method to improve the performance of a GT-based anomaly detector (GTnet). Using observations of GTnet behavior and its training properties, we propose the addition of three techniques that can improve anomaly detection performance for defect inspection in a factory production process. Specifically, k-Winners-Take-All (k-WTA) was applied to the GTnet base model to resist data corruption such as dust on the sample, the temperature scaling method was added to consider correlations between GT classes with similar appearance, and loss redefinition was applied to improve the efficiency of optimal training. Accuracy was improved from 98.56% to 99.86% in the inspection of vehicle part assembly defects, which requires extremely high accuracy. Experimental evaluations were conducted to verify the performance improvement of the GT anomaly detector. [ABSTRACT FROM AUTHOR]

Image authentication based on robust image hashing has been paid large attention by researchers. However, most of the existing methods are unable to authenticate, if the image is processed through geometric transformations and tampered. In this paper, we have proposed a blind geometric correction approach, which eliminates the effect of geometric transformation, including rotation-scaling-translation (RST). We have incorporated Lifting Wavelet Transform (LWT) and Discrete Cosine Transform (DCT) to construct a short hash. Furthermore, an algorithm to generate an image map from the hash is proposed to detect the tampered regions. The main objective is to keep the hash length short with better performance, i.e., perceptually robust to content-preserving operations and image tampering detection. Based on the difference of image maps obtained from "source image" and "query images", tampering regions have been localized. The proposed method can detect tampering, even if tampering and composite RST geometric transformations occur simultaneously, due to blind geometric correction. The experimental results show that the proposed image authentication method outperforms the state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

Overhead transmission lines are important lifelines in power systems, and the research and application of their intelligent patrol technology is one of the key technologies for building smart grids. The main reason for the low detection performance of fittings is the wide range of some fittings' scale and large geometric changes. In this paper, we propose a fittings detection method based on multi-scale geometric transformation and attention-masking mechanism. Firstly, we design a multi-view geometric transformation enhancement strategy, which models geometric transformation as a combination of multiple homomorphic images to obtain image features from multiple views. Then, we introduce an efficient multiscale feature fusion method to improve the detection performance of the model for targets with different scales. Finally, we introduce an attention-masking mechanism to reduce the computational burden of model-learning multiscale features, thereby further improving model performance. In this paper, experiments have been conducted on different datasets, and the experimental results show that the proposed method greatly improves the detection accuracy of transmission line fittings. [ABSTRACT FROM AUTHOR]

Ground-based multiple-input multiple-output synthetic aperture radar (MIMO-SAR) is a new type of deformation monitoring sensor that has the advantages of no mechanical motion and fast echo acquisition. Ground-based MIMO-SAR can significantly improve the data rate of deformation monitoring. In this paper, a fast imaging algorithm tailored for ground-based MIMO-SAR data is proposed, which can be applied in both far-field and near-field scenarios. First, the phase center approximation error of the non-collinear array in the near field is analyzed. Then, a fast imaging algorithm based on geometric transformation for the coherent synthesis of subimages is put forward. The algorithm uses the geometric transformation to convert the subaperture imaging results into the full aperture coordinate system, which avoids the point-by-point interpolation calculation and further reduces the computational cost of the subimage coherent synthesis algorithm. Simulations and experiments show that the algorithm can achieve high-precision focusing imaging, and its operation efficiency is significantly improved compared with the algorithm based on interpolation. [ABSTRACT FROM AUTHOR]

Hand gesture recognition (HGR) is a challenging and fascinating research topic in computer vision with numerous daily life applications. In HGR, computers aim to identify and classify hand gestures. The limited diversity of the dataset used in HGR is due to the limited number of hand gesture demonstrators, acquisition environments, and hand pose variations despite previous efforts. Geometric image augmentations are commonly used to address these limitations. These augmentations include scaling, translation, rotation, flipping, and image shearing. However, research has yet to focus on identifying the best geometric transformations for augmenting the HGR dataset. This study employed three commonly utilized pre-trained models for image classification tasks, namely ResNet50, MobileNetV2, and InceptionV3. The system’s performance was evaluated on five static HGR datasets: DLSI, HG14, ArabicASL, MU HandImages ASL, and Sebastian Marcell. The experimental results demonstrate that many geometric transformations are unnecessary for HGR image augmentation. Image shearing and horizontal flipping are the most influential transformations for augmenting the HGR dataset and achieving better classification performance. Moreover, ResNet50 outperforms MobileNetV2 and InceptionV3 for static HGR.

The culture was carefully associated with regular lifestyles, such as inside the discipline of education. However, there needs to be awareness among school members of the absorption of the culture around them through learning, especially mathematics. Therefore, this study aims to explore the geometric contents in the form of geometric transformations and the values of local batik Indonesia. This study was a qualitative study with an ethnographic approach. The techniques used in this study are observation, literature review, and interviews with Lampung cultural and batik craftsmen. Observations were made by observing batik activities and Lampung batik motifs and conducting interviews to find the mathematical and philosophical elements contained in them. The data were then completed and checked for correctness based on the results from the literature review. The outcomes of this observation imply that the human beings of Lampung utilize the idea of geometric transformation in making batik motifs, which include the Siger motif, pohon hayat motif, and kapal motif. The idea of geometric transformation used is reflection, dilation, and translation. Thus, this research can be a reference for learning mathematics and exploring other Lampung batiks motifs.

The repeatability rate is an important measure for evaluating and comparing the performance of keypoint detectors. Several repeatability rate measurementswere used in the literature to assess the effectiveness of keypoint detectors. While these repeatability rates are calculated for pairs of images, the general assumption is that the reference image is often known and unchanging compared to other images in the same dataset. So, these rates are asymmetrical as they require calculations in only one direction. In addition, the image domain in which these computations take place substantially affects their values. The presented scatter diagram plots illustrate how these directional repeatability rates vary in relation to the size of the neighboring region in each pair of images. Therefore, both directional repeatability rates for the same image pair must be included when comparing different keypoint detectors. This paper, firstly, examines several commonly utilized repeatability rate measures for keypoint detector evaluations. The researcher then suggests computing a two-fold repeatability rate to assess keypoint detector performance on similar scene images. Next, the symmetric mean repeatability rate metric is computed using the given two-fold repeatability rates. Finally, these measurements are validated using well-known keypoint detectors on different image groups with various geometric and photometric attributes. [ABSTRACT FROM AUTHOR]

Geometry is a mathematical science that studied points, lines, planes, spaces, and the relationships of them. One of the topic is geometric transformation. The Several research found that students hadn’t understood the concept of transformation, so that it needed a teaching material especially student’s worksheet. The research aimed to develop valid, practical and effective student’s worksheet with GeoGebra on the geometry transformation in junior high school. The research method was used R&D (Research and Development) using a modification of the 4-D model. The development model consists defined, designed and developed. The results of the research indicated that (1) this product was valid according to media experts and material experts, (2) it was practical, (3) effective to be used in mathematics learning, especially geometric transformation.

Overhead transmission lines are important lifelines in power systems, and the research and application of their intelligent patrol technology is one of the key technologies for building smart grids. The main reason for the low detection performance of fittings is the wide range of some fittings’ scale and large geometric changes. In this paper, we propose a fittings detection method based on multi-scale geometric transformation and attention-masking mechanism. Firstly, we design a multi-view geometric transformation enhancement strategy, which models geometric transformation as a combination of multiple homomorphic images to obtain image features from multiple views. Then, we introduce an efficient multiscale feature fusion method to improve the detection performance of the model for targets with different scales. Finally, we introduce an attention-masking mechanism to reduce the computational burden of model-learning multiscale features, thereby further improving model performance. In this paper, experiments have been conducted on different datasets, and the experimental results show that the proposed method greatly improves the detection accuracy of transmission line fittings.

The study aimed to investigate the mathematics achievement of eighth grade students on geometric transformation and geometric thinking levels. This research was carried out in the fall semester of 2018-2019. The sample was 88 students from two different middle schools in an urban area of Erzincan, Turkey. The survey model was used. The geometric transformation achievement test with 20 questions and the first 15 questions of the van Hiele geometric thinking test, which are suitable for the middle school student level, were administered to students at different times. SPSS was used to conduct analysis for descriptive statistics, standard deviation, percentage, mean and frequency, independent samples t test, and Pearson correlation. Pearson correlation was conducted to determine the relationship between the total scores that the students got from the van Hiele geometric thinking test and geometric transformation achievement test. While there was a significant relationship between the van Hiele geometry test and transformation geometry test, the geometric thinking levels of the students were below the expected level. There was no statistically significant mean difference between the boy and girl students across the schools. [ABSTRACT FROM AUTHOR]

Conventionally, geometric computing problems are treated as algebraic computing problems by representing a geometric object in a global reference coordinate system. This approach has two problems. The first problem is that the intuitive view of the interaction of objects is lost, and the second problem is that algebraic computing is prone to errors for degenerated cases related to the interaction of (e.g., notable case of “divided by zero”). In this paper, we propose a new approach to geometric computing especially to analyze the interaction of two objects (e.g., two triangles). The main idea behind this new approach is a specially-tailored local coordinate system for two interacting objects is defined, which makes the projection of the objects on this local coordinate system represent the true geometry of the objects. This idea significantly departs from the conventional approach which is primarily based on the concept of the global coordinate system. Three examples are provided to illustrate the effectiveness of the proposed approach. Among them, one example is related to the robustness of methods for analyzing the relations of two interacting objects, which is still an open issue in the field of geometric computing and suggests that the proposed approach could have some benefit to robustness in analysis.

Compressed sensing (CS) represents an efficient framework to simultaneously acquire and compress images/signals while reducing acquisition time and memory requirements to process or transmit them. Specifically, CS is able to recover an image from a random measurements. Recently, deep neural networks (DNNs) are exploited not only to acquire and compress but also for recovering signals/images from a highly incomplete set of measurements. Super-resolution (SR) algorithms attempt to generate a single high resolution (HR) image from one or more low resolution (LR) images of the same scene. Despite the success of the existing SR networks to recover HR images with better visual quality, there are still some challenges that need to be addressed. Specifically, for many practical applications, the original images may be affected by various transformation effects including rotation, scaling, and translation. Moreover, in real-time transmissions, image compression is carried out first, followed by acquisition time reduction. To address this problem, we propose a novel robust deep CS framework that is able to mitigate the geometric transformation and recover HR images. Specifically, the proposed framework is able to perform two tasks. First, it is able to compress the transformed image with the help of an optimized generated measurement matrix. Second, the proposed framework is able not only to recover the original image from the compressed version but also to mitigate the transformation effects. The simulation results reported in this article show that the proposed framework is able to achieve high level of robustness against different geometric transformations in terms of peak signal-to-noise-ratio (PSNR) and similar structure index measurements (SSIM). For the convenience of dissemination, we make our source codes available at GitHuba.

Optical sorting, as one kind of optical tweezers, is used to separate mixed particles in a background environment. This unusual tool has a wide application prospect because the non-contact and non-destructive advantages ideally suit the pressing need of bio-technology. However, most sorting methods and devices have been accomplished based on real-time one-by-one sorting, which ignored the sorting efficiency and is not applicable to high-capacity particles. Although more and more structured light beams are proposed to enhance the sorting efficiency, it is still not enough for desired applications. Here, we propose a method for the massive parallel sorting of particles: polygonal optical vortex (OV) beams are unwound by a geometric transformation to produce linear OV beams with kinked distributions. This structured light is used to greatly enhance the sorting efficiency. We adopt the fractal theory to illustrate the increase of the region over which the beam can interact with particles. We demonstrate that the gradient force of this beam is large enough to manipulate spherical particles in the Rayleigh regime of scattering. These results introduce new possibilities for high-capacity particle sorting.

Robotic Template Library (RTL) is a set of tools for dealing with geometry and point cloud processing, especially in robotic applications. The software package covers basic objects such as vectors, line segments, quaternions, rigid transformations, etc., however, its main contribution lies in the more advanced modules: The segmentation module for batch or stream clustering of point clouds, the fast vectorization module for approximation of continuous point clouds by geometric objects of higher grade and the LaTeX export module enabling automated generation of high-quality visual outputs. It is a header-only library written in C++17, uses the Eigen library as a linear algebra back-end, and is designed with high computational performance in mind. RTL can be used in all robotic tasks such as motion planning, map building, object recognition and many others, but the point cloud processing utilities are general enough to be employed in any field touching object reconstruction and computer vision applications as well.

Deformable Convolutional Networks (DCNs) are proposed to solve the inherent limited geometric transformation in CNNs, showing outstanding performance on sophisticated computer vision tasks. Though they can rule out irrelevant image content and focus on region of interest to some degree, the adaptive learning of the deformation is still limited. In this paper, we delve it from the aspects of deformable modules and deformable organizations to extend the scope of deformation ability. Concretely, on the one hand, we reformulate the deformable convolution and RoIpooling by reconsidering spatial-wise attention, channel-wise attention and spatial-channel interdependency, to improve the single convolution's ability to focus on pertinent image contents. On the other hand, an empirical study is conducted on various and general arrangements of deformable convolutions (e.g., connection type) in DCNs. Especially on semantic segmentation, the study yields significant findings for a proper combination of deformable convolutions. To verify the effectiveness and superiority of our proposed deformable modules, we also provide extensive ablation study for them and compare them with other previous versions. With the proposed contribution, our refined Deformable ConvNets achieve state-of-the-art performance on two semantic segmentation benchmarks (PASCAL VOC 2012 and Cityscapes) and an object detection benchmark (MS COCO). [ABSTRACT FROM AUTHOR]

Purpose: In radiotherapy, geometric indices are often used to evaluate the accuracy of contouring. However, the ability of geometric indices to identify the error of contouring results is limited primarily because they do not consider the clinical background. The purpose of this study is to investigate the relationship between geometric and clinical dosimetric indices. Methods: Four different types of targets were selected (C-shaped target, oropharyngeal cancer, metastatic spine cancer, and prostate cancer), and the translation, scaling, rotation, and sine function transformation were performed with the software Python to introduce systematic and random errors. The transformed contours were regarded as reference contours. Dosimetric indices were obtained from the original dose distribution of the radiotherapy plan. The correlations between geometric and dosimetric indices were quantified by linear regression. Results: The correlations between the geometric and dosimetric indices were inconsistent. For systematic errors, and with the exception of the sine function transformation (R2: 0.023-0.04, P > 0.05), the geometric transformations of the C-shaped target were correlated with the D98% and Dmean (R2: 0.689-0.988), 80% of which were P < 0.001. For the random errors, the correlations obtained by the all targets were R2 > 0.384, P < 0.05. The Wilcoxon signed-rank test was used to compare the spatial direction resolution capability of geometric indices in different directions of the C-shaped target (with systematic errors), and the results showed only the volumetric geometric indices with P < 0.05. Conclusions: Clinically, an assessment of the contour accuracy of the region-of-interest is not feasible based on geometric indices alone. Dosimetric indices should be added to the evaluations of the accuracy of the delineation results, which can be helpful for explaining the clinical dose response relationship of delineation more comprehensively and accurately. [ABSTRACT FROM AUTHOR]

Multi-fidelity data are common in various scientific and engineering fields. High-fidelity data, often more accurate, come with greater expense, such as precision experimental testing or high-resolution simulation. Conversely, low-fidelity data are less accurate but more cost-effective. Multi-fidelity surrogate modeling, which integrates multi-fidelity data to build a model, is widely used for its ability to reduce costs while improving modeling accuracy. In this work, we introduce an innovative method named active learning-assisted multi-fidelity surrogate modeling based on geometric transformation (AL-MFSGT). The AL-MFSGT method comprises three essential components: the two-fidelity surrogate based on geometric transformation (TFSGT), an active learning (AL) strategy, and a multi-fidelity modeling framework. TFSGT utilizes geometric transformations to adjust the low-fidelity surrogate to align it more closely with the high-fidelity data. Then, the transformed low-fidelity surrogate and the high-fidelity surrogate are coupled using correlation functions. The AL strategy combines accelerating error convergence and enhancing sample set diversity to judiciously select high-fidelity incremental samples. Subsequently, the two-fidelity surrogate modeling is extended to a comprehensive multi-fidelity framework. To validate the efficacy of AL-MFSGT, we conduct extensive comparative experiments using ten numerical examples. The results demonstrate the superiority of AL-MFSGT over several compared multi-fidelity surrogate modeling methods. Furthermore, we apply AL-MFSGT to two practical engineering cases, demonstrating its effectiveness in real-world modeling scenarios. • A two-fidelity surrogate model based on geometric transformation is introduced. • A hybrid active learning strategy is proposed for increment sampling. • A multi-fidelity surrogate modeling framework is given. • Three types of engineering errors are considered in the numerical experiments. [ABSTRACT FROM AUTHOR]

The state-of-the-art trackers using deep learning technology have no special strategy to capture the geometric deformation of the target. Based on that the affine manifold can better capture the target shape change and that the higher level of Convolutional Neural Network (CNN) can better describe semantic information of objects, we propose a new tracking algorithm combining affine transformation with convolutional features to track targets with dramatic deformation. First, the affine transformation is applied to predict possible locations of a target, then a correlative filter is designed to compute the appearance confidence score for determining the final target location. Furthermore, a standard discriminative correlation filter is used to develop the effect of convolutional features, which is more efficient than other methods used for CNN Networks. Comprehensive experiments demonstrate the outstanding performance of our tracking algorithm compared to the state-of-the-art techniques in the public benchmarks.

Geometric transformations of images are the predominant factor, which influences the effectiveness of visual tracking and detection tasks in computer vision. Naturally, although it makes significant sense to grasp the process of image geometric transformations, the numerical relationship of geometric transformations cannot be revealed directly from images themselves. Even if the geometric transformation matrices form the three-dimensional special linear group, Sl(3, ℝ) group, it is difficult to comprehend the manifold of this invisible visual motion, which resides in the high-dimensional space. Furthermore, the main challenge is the deficiency of analytic expressions of the Riemannian logarithmic map to compute the geodesic distance on the Sl(3, ℝ) manifold. Facing these issues, this paper comes up with a novel approach to visualize the geometric transformation in images by presenting a new metric, and then, computes a set of coordinate-vectors in the three-dimensional state transition space for visualization using the Riemannian stress majorization. The superiority of the presented framework for visualization, in terms of accuracy and efficiency, is demonstrated through abundant experiments on aerial images and moving objects.

For many practical applications, it is essential to address both geometric corrections and missing information reconstruction of face images and natural images. However, it is unfavorable to separate the problem into two sub-tasks due to error accumulations of sequential tasks. In this paper, we propose a novel robust missing information reconstruction framework via deep feature transformations to simultaneously address both geometric corrections and image completion. Specifically, our proposed framework realizes multiple channel spatial transformations to tackle geometric corrections, and address image completion through non-linear features projections. The flow of our framework includes deep feature extraction, feature enhancement, feature projection, and feature refinement, where deep features are extracted and learnt to achieve robust image completion. Experimental results show the superior performance of our framework for both face images and natural images in various databases. Compared with the conventional approaches approach to split the problem into two sub-tasks, including image inpainting and spatial transformation, our proposed framework achieves a number of advantages, including i) an unified framework to automatically correct the geometric distortions and to reconstruct the missing information simultaneously and ii) achieving much better visual quality for those recovered images.