Geometric Image Research Articles

Geometric Constraint and Image Inpainting-Based Railway Track Fastener Sample Generation for Improving Defect Inspection

Defective fastener images detection is an essential task in the vision-based railway track safety inspection. Although existing methods have achieved some level of success, the detection accuracy in this field suffers from the defective fasteners being far less common than normal fasteners. One way to tackle this problem is to expand the defect sample. However, current state-of-the-art defective fastener generation methods mainly rely on generative adversarial networks or simply augment the defect data through traditional image processing. These methods may not be ideal as it is difficult to produce images with high quality and rich diversity at the same time. This paper proposes a new method for fastener sample generation that actively divides the sample generation into two independent parts: defective foregrounds generation and complete backgrounds generation. The key to this method is to generate foregrounds and backgrounds based on geometric constraint and image inpainting, respectively. Specifically, we adopt a skeleton mapping algorithm to directionally control the generated types of defective foregrounds. Meanwhile, an image inpainting network is employed to expand the background. The experiments show that this enables us to generate better-quality and richer-diversity images by combining deep learning and image processing advantages. To the best of our knowledge, our method is the first to achieve state-of-the-art performance, i.e., the classification accuracy reaches 97.97%, without using real defective fastener images during the defect classification network training process.

Geometric forms in the art of the ancient population of the Kola Peninsula

Geometric images on rocky surfaces (petroglyphs and paintings), which abound in the sites of Northern Fennoscandia (more than 300 separate locations), as well as similar symbols on ceramics, bone products, horns, stone handicrafts, do not often attract the attention of researchers. Like figurative images, they, undoubtedly, have been included in the arsenal of creative activities of our distant ancestors since ancient times and reflect their worldview, captured by visual means. Pisanitsy (pictograms) of the Rybachy Peninsula is the only site of its kind in the vast territory of the Russian North. The petroglyphs of Kanozera, along with similar objects from Alta, Vingen (Norway), Nämforsen (Sweden), Vyg, Onego (Karelia) are among the largest (each with more than 1000 images) rock art galleries of the hunter-gatherer tradition of Fennoscandia and remains the only site of this kind in the Russian Arctic. Modern studies of petroglyphs by means of night photofixation technique based on special powerful lighting directed at an particular angle to the surface with engravings, as well other non destructive technical methods, including the use of a technique based on the creation of 3D models using photogrammetry and obtaining “pseudo-rubbings” allow reveling new images and refine the outline already known. Sharing similar geometric patterns with petroglyphs, the ground labyrinths of the Kola Peninsula are made in different from petroglyphs techniques and materials. The labyrinths constructed of small boulders in the bays of the Barents Sea they are frequently used by various “pseudo-analysts” to build their esoteric speculations. Working in the direction of scientific study of these phenomena, trying to demonstrate and analyze the objects of historical and cultural heritage themselves, the authors follow the postulate that true human behavior and its conscious activity, in general, begins with the use of symbols, thanks to which the final separation of man from the animal environment took place.

Characterizing Learners’ Construction of Geometry Diagrams in Dynamic Geometry Environments

As a distinct mode of mathematical representation and communication, geometry diagrams are both signs that represent abstract geometric concepts and visual images that offer graphical-spatial properties. Dynamic geometry environment offers a wide range of tools for its users to create and interact with geometry diagrams. In this paper, I propose a framework to characterize geometry diagrams that learners create in DGEs. The framework considers a learner’s approach to creating a geometry diagram (i.e., perceptualbased, measurement-based, construction-based, and transformation-based), the driving force that guides the learner’s specific actions in a DGE (i.e., tool-driven, and property-driven), and the constraints in the resulting diagram (i.e., drawing, underconstrained, overconstrained, and appropriately constrained). Examples of student work on two geometry construction problems are used to illustrate the use of the framework. These examples show that the proposed framework provides a useful tool to characterize geometry diagrams in DGEs.

A new approach for road extraction using data augmentation and semantic segmentation

Accurate road extraction from remote sensing images is a challenging task. Several methods of extraction have been developed but the precision of extraction is still limited for the unpaved and small-width roads. This paper proposes an accurate road extraction approach called DAA-SSEG since it uses data augmentation architecture (DAA) and semantic segmentation model (SSEG). The proposed approach DAA-SSEG is based on a modified full convolutional neural network that overcomes the vanishing gradient and the training saturation issues. It recognizes roads at the pixel level. Furthermore, The DAA-SSEG approach uses a new plan of data augmentation based on geometric transformation and images refinement techniques. It allows getting a richer dataset thus better training and an accurate extraction. The experiment denotes that the proposed approach DAA-SSEG, that combine data augmentation architecture and semantic segmentation method, outperforms some state-of-the-art methods in terms of F-measures. The results demonstrate that it ensures accurate extraction of unpaved and small-width roads, in urban and rural areas. Moreover, the proposed approach distinguishes between roads and trails and can extract some roads not labeled beforehand.

Parallel cryo electron tomography on in situ lamellae.

In situ cryo electron tomography of cryo focused ion beam milled samples has emerged in recent years as a powerful technique for structural studies of macromolecular complexes in their native cellular environment. However, the possibilities for recording tomographic tilt series in a high-throughput manner are limited, in part by the lamella-shaped samples. Here we utilize a geometrical sample model and optical image shift to record tens of tilt series in parallel, thereby saving time and gaining access to sample areas conventionally used for tracking specimen movement. The parallel cryo electron tomography (PACE-tomo) method achieves a throughput faster than 5 min per tilt series and allows for the collection of sample areas that were previously unreachable, thus maximizing the amount of data from each lamella. Performance testing with ribosomes in vitro and in situ on state-of-the-art and general-purpose microscopes demonstrated the high throughput and quality of PACE-tomo.

Efficient Scattering Center Prediction Method for Targets With Coating Defects Through Deep Learning

The dielectric coating defects existing on the surface of low detectable targets have nonnegligible impacts on their electromagnetic (EM) scattering characteristics. Due to the large electrical dimension of the target, traditional EM analysis methods are inefficient and cannot meet the requirement of real-time analysis. To address this issue, this article proposed a U-net-based deep neural network (DNN) to perform efficient scattering center (SC) prediction for targets with coating defects from the input 2-D geometric image of it. Furthermore, facing the difficulty of limited training dataset due to the high cost of full-wave numerical simulations, this article proposed a transfer learning method by pretraining the network on a large dataset obtained by the shooting and bouncing ray (SBR) and then fine-tuning it on the target small dataset obtained by the multilevel fast multipole method (MLFMM), which greatly reduced the training difficulty and improved the accuracy and generalization ability of the model. Numerical results are presented to evaluate the performance of the proposed method. It is proven that the proposed method is promising in providing efficient SC prediction in real-time EM analysis scenarios.

Experimental Evaluation of Display Field Communication Based on Machine Learning and Modem Design

Display field communication (DFC) is a frequency-domain unobtrusive display-to-camera (D2C) communication, in which an electronic display serves as a transmitter and a camera serves as a receiver. In this paper, we propose a machine learning-based DFC scheme and evaluate its performance in a lab test scenario. First of all, we adopt the Discrete Cosine Transform (DCT) to transform a spatial-domain image into its spectral-domain equivalent. To reduce the computational complexity during the data-embedding process, addition allocation and subtraction data retrieval techniques are used. Moreover, channel coding is applied to overcome the data error caused by the optical wireless channel. In particular, robust turbo coding is used for error detection and correction. Afterward, we perform the experiments to validate the performance of the proposed system. After capturing the displayed image with a camera, data restoration is done using a deep learning technique. Extensive real-world experiments were performed considering various geometric distortions, noise, and different standard input images. As a result, we found that by increasing the transmit display image size (upsampling), the overall error rate can be reduced. In addition, real-world noise analysis is performed and it is notified that the actual noise is dominant in the low-frequency region of an image. The experimental results confirm the robust performance of the proposed DFC scheme and show that an error-free performance can be achieved up to a distance of 1m in the given lab test environment setting.

Wide field of view chiral imaging with a liquid crystal planar lens enabled by digitalized nanogratings.

To compensate for the inability for polarization imaging by conventional methods, metasurface optics with compactness and multi-function emerge as an approach to provide images with different linear and circular polarizations. Here, we propose a liquid crystal (LC) geometric phase-based chiral imaging lens (CIL) that simultaneously forms images of objects with opposite helicity. The CIL (Diameter 2.3 cm) was optimized by a spatial multiplexing algorithm and realized using the digital holography technique, where the LC domains were regulated by pixelated nanogratings with varied orientation. We investigated the potential of the patterning technique toward high order LC alignment by balancing the periodicity and depth of the nanogratings. The CIL exhibited a wide field of view of ±20°, which is attributed to the self- assembling effects of LC molecules. The compactness, lightness, and ability to produce chiral images of the LC CIL even at large angles have significant potential for practical polarization imaging.

High speed melt flow monitoring and development of an image processing algorithm for laser fusion cutting

This contribution presents high-speed camera monitoring of melt pool dynamics for steel during laser fusion cutting and compares the images with recordings in aluminum. The experiments are performed by a 4 kW multimode fiber laser with an emission wavelength of 1070 nm. To visualize the thermal radiation from the process zone during the cutting process, the kerf is captured at sample rates of up to 170 000 frames per second without external illumination with a spectral response between 400 and 700 nm, allowing measurements of the melt flow dynamics from geometric image features. The dependencies of the melt flow dynamics on laser processing parameters, such as feed rate, gas pressure, and laser power, can be evaluated. The monitoring system is placed both off-axis and mounted to a conventional cutting head, with the monitoring path aligned to the processing laser for a coaxial and lateral view of the cut kerf. The measured signal characteristics of the images captured from the melt pool are examined in the visible spectral range of the emitted thermal radiation from the process zone. Moreover, a specifically developed image processing algorithm is developed that process and analyze the captured images and extract geometric information for a measurement of the melt flow.

The Lobachevsky geometry method in the relativistic kinematics of particle collisions: special frame of reference

The use of the geometry of the Lobachevsky momentum space in the relativistic kinematics of particle collisions is demonstrated by the example of the problem of a special reference system. That system complements the geometric image of the process of elastic scattering of two particles of unequal masses. The speed of a special reference system relative to the center of mass and the angle of scattering of particles in it are determined. The conditions for the existence of such a reference system are analyzed. It is shown that in the case of a process with equal masses, the point corresponding to such a system goes into the ideal region of the extended Lobachevsky space - beyond the cone, and the lines intersecting in it become diverging lines in the sense of Lobachevsky geometry. In this case, the angle between the divergent straight lines (geodesics) of the geometric image is purely imaginary and connected to the minimum length of the segment perpendicular to the diverging straight lines (geodesics).

Hermann Cohen’s logic of the pure knowledge as a philosophy of science

The connection of Hermann Сohen’s “The Logic of Pure Knowledge” with the revolutionary transformations in physics and mathematics at the end of the 19th century is shown. Сohen criticised Kant’s answer to the question “How is mathematics possible”? If Kant refers to a priori forms of pure intuition, Сohen sees in it a restriction of freedom of mathematical thinking by limits of intuition. It has been shown that Cohen's position is in accordance with the main development of mathematics in the last decades of the 19th century, in particular, with K. Weierstrass’ striving to get rid of geometrical or mechanical images and intuitions in the mathematical analysis. Cohen was also well informed about the latest ideas in physics of his time. They are also discussed in “The Logic of Pure Knowledge.” The revolutionary spirit of physics and mathematics was appealing to Cohen, and he felt a corresponding enthusiasm for it. The ongoing scientific revolution is consonant with Cohen’s assertion that the foundations of science are hypotheses. The purity of pure thinking does not guarantee the correctness of any of its constructions. Each step in the development of science requires a critique of existing notions. The development of knowledge from the naive to the critical one shows a movement from a picture of the world as a set of stable things to a picture of continuous movement and change, where change is more important than what changes. Cohen sees such a development in an evolution of the concept of substance in modern physics and he welcomes the replacement of material substance by energy, seeing this movement as a confirmation of critical idealism. Finally, it is discussed whether we can speak of the actuality of Cohen’s logic of pure knowledge.

Принципы построения геометрических моделей нанокластеров по тетраэдрической линии

In connection with the development of new methods of nanotechnology, the article discusses the features of the morphology of nanoobjects that determine the relevance of the modernization of the training of undergraduates in the study of the disciplines «Nanomaterial Science», «Nanotechnology», «Descriptive geometry, engineering and computer graphics» and «Computer modeling».
 Recently, the concept of «cluster» has become relevant due to the trend in the development of nanomaterials. Such nanomaterials obtained using unconventional growth mechanisms (including oriented attachment) are extremely interesting in the field of electronics, photonics and are of great interest for catalysis.
 The article considers homoatomic clusters constructed from identical structural units. The desire to minimize energy is expressed in the tendency to the densest arrangement of structural units in the cluster. This allows us to assert that cluster structures with the maximum number of connections per structural unit will be the most stable; that clusters tend to a quasi-spherical shape (i.e., cluster sizes along three Cartesian axes should be close if possible, while dense structures are formed, the surface of which is minimal, and the number of connections is maximum); that clusters with higher symmetry are preferable (identical structural units composing the cluster framework should strive to stay in an indistinguishable state and position from each other).
 The work applies the knowledge and skills laid down by students in the course of engineering and computer graphics to the study of the patterns of processes in the nanowire on the example of the principles of building nanoclusters along a tetrahedral line using three-dimensional modeling in the Autodesk 3ds Max environment. Visualization and visual representation of geometric images of nanoclusters will allow students to avoid a primitive geometric representation of nanoobjects and will serve as motivation to study other natural science subjects.
 The content of the article is intended for specialists working in the fields of nanotechnology, solid-state electronics, micro- and nanoelectronics, micro- and nanosystem technology, thin-film sensors.

Построение сферы по мнимым точкам

Euclidean spaces of various dimensions do not contain imaginary images and objects by definition, but are inextricably linked with them through special cases, and this leads to the need to expand the field in geometry into the region of imaginary values [1, 19, 26]. Such an extension, i.e. adding to the field of real coordinates spaces of different dimensions, the field of imaginary coordinates leads to different variants of spaces of different dimensions, depending on the chosen axiomatics. Earlier in a number of articles, examples of solving some actual problems of geometry using imaginary geometric images and objects were shown [4, 5, 6, 13, 21, 22, 29]. 
 The article provides constructions for constructing a sphere from four predetermined points, of which one pair or both pairs of points can be imaginary complex conjugate. The construction is carried out on combined diagrams by the methods of descriptive geometry by analogy with the well-known problem of constructing a sphere from four real points. The construction of a sphere is based on seven auxiliary constructions for constructing a circle from points that can be imaginary conjugates. Both 3D problems of constructing spheres for given points and methods of 2D construction problems for determining the required imaginary points are considered. A method for calculating the parameters of the obtained sphere is described. The application of the method to other problems of descriptive geometry, for example, to the problems of finding geometric places of points, is considered. equidistant from two given surfaces. Recently, this issue has been intensively studied, for example, in the works [5, 6].

Bathymetry from satellite images: a proposal for adapting the band ratio approach to IKONOS data

The acquisition of bathymetric data in shallower waters is difficult to attain using traditional survey methods because the areas to investigate may not be accessible to hydrographic vessels, due to the risk of grounding. For this reason, the use of satellite detection of depth data (satellite-derived bathymetry, SDB) constitutes a particularly useful and also economically advantageous alternative. In fact, this approach based on analytical modelling of light penetration through the water column in different multispectral bands allows to cover a big area against relatively low investment in time and resources. Particularly, the empirical method named band ratio method (BRM) is based on the degrees of absorption at different bands. The accuracy of the SDB is not comparable with that of traditional surveys, but we can certainly improve it by choosing satellite images with high geometric resolution. This article aims to investigate BRM applied to high geometric resolution images, IKONOS-2, concerning the Bay of Pozzuoli (Italy), and improve the accuracy of results performing the determination of the relation between band ratio and depth. Two non-linear functions such as the exponential function and the 3rd degree polynomial (3DP) are proposed, instead of regression line, to approximate the relationship between the values of the reflectance ratios and the true depth values collected in measured points. Those are derived from an Electronic Navigational Chart produced by the Italian Hydrographic Office. The results demonstrate that the adopted approach allows to enhance the accuracy of the SDB, specifically, 3DP supplies the most performing bathymetric model derived by multispectral IKONOS-2 images.

Multimodality system of x-ray and fluorescence based on Fourier single-pixel imaging for small animals.

.Significance: The multimodality imaging system has become a powerful tool for in-vivo biomedical research. However, a conventional multimodality system generally employs two independent detectors, which is costly and bulky. Meanwhile, the geometric cocalibration and image registration between the imaging modalities are also complicated.Aim: To acquire the multimodality images for small animals with only one visible light sensed single-pixel detector.Approach: The system is built based on a structured detection Fourier single-pixel imaging architecture. A cesium iodide doped with thallium [CsI(Tl)] scintillator plate is placed behind the sample in x-ray imaging, so the x-ray images can be converted to be visible and sensed with the same single-pixel detector as applied in fluorescence imaging.Results: The spatial resolution of x-ray imaging was measured to be 1.81 mm, the sensitivity and the imaging depth of fluorescence imaging was evaluated to be and 4 mm, respectively. In vivo multimodality imaging of a C57BL/6 female mouse bearing tumor targeted with mCherry was carried out.Conclusions: We proposed an x-ray and fluorescence multimodality imaging system for small animals via the structured detection FSI architecture. The system is low cost, with a more compact structure, and free of image registration from different modalities. In vivo multimodality imaging results of a mouse bearing tumor demonstrate its capability for small animal research.

Unstable Depth Perception of Aerial Images in Crossed Mirror Array Can Be Controlled by Changing Fixation Distance

The unstable depth perception of aerial images in a crossed-mirror array (CMA) can be improved by changing the distance of fixation points. The perceived depths of aerial images in CMA suffer from large instability even when an aerial image is a geometrical optical real image. The perceived depth instability of aerial images is mainly influenced by their geometrical position from CMA. The perceived depths of aerial images shift toward the fixation points, and the stable depth perception of aerial images can be obtained if the fixation points are located near the aerial image distance. To stabilize the depth perception of aerial images, it is sufficient to appropriately control the observer's vergence even if the fixation point is not a real object. In addition, the luminance of aerial images affects the stability of their depth perception.

Plane-based self-calibration and improvement of three-dimensional multi-beam laser scanning with two-axis-mirror

The geometry and calibration of three-dimensional multi-beam laser scanning (MBLS) is more difficult than single-beam laser scanning, especially for a one laser emitter and multiple laser-echo detection within the same optical path and scanning with a two-axis-mirror. This paper focuses on the influence of the main systematic errors upon the geometric imagery of the MBLS, and presents a plane-based self-calibration method to improve the geometric positioning. First, the model for geometric imaging and systematic errors for the MBLS is presented, and the adjustment of the plane-based self-calibration is developed. Second, the influence of systematic errors upon geometric imagery of the MBLS is simulated and conducted to find the main errors. Third, a strong network configuration based on planar calibration is addressed and implemented, and the improvement of accuracy is examined via qualitative and quantitative analysis. The results show that the rangefinder offset, horizontal direction circle index and vertical circle index are the main systematic errors. The accuracy of distance is corrected from 29.94 cm to 2.86 cm with an improvement of 86.89% for the plane-based calibration, and validation indicates that this is corrected from 25.47 cm to 5.60 cm with an improvement of 88.25%.

An Efficient Ensemble Deep Learning Approach for Semantic Point Cloud Segmentation Based on 3D Geometric Features and Range Images.

Mobile light detection and ranging (LiDAR) sensor point clouds are used in many fields such as road network management, architecture and urban planning, and 3D High Definition (HD) city maps for autonomous vehicles. Semantic segmentation of mobile point clouds is critical for these tasks. In this study, we present a robust and effective deep learning-based point cloud semantic segmentation method. Semantic segmentation is applied to range images produced from point cloud with spherical projection. Irregular 3D mobile point clouds are transformed into regular form by projecting the clouds onto the plane to generate 2D representation of the point cloud. This representation is fed to the proposed network that produces semantic segmentation. The local geometric feature vector is calculated for each point. Optimum parameter experiments were also performed to obtain the best results for semantic segmentation. The proposed technique, called SegUNet3D, is an ensemble approach based on the combination of U-Net and SegNet algorithms. SegUNet3D algorithm has been compared with five different segmentation algorithms on two challenging datasets. SemanticPOSS dataset includes the urban area, whereas RELLIS-3D includes the off-road environment. As a result of the study, it was demonstrated that the proposed approach is superior to other methods in terms of mean Intersection over Union (mIoU) in both datasets. The proposed method was able to improve the mIoU metric by up to 15.9% in the SemanticPOSS dataset and up to 5.4% in the RELLIS-3D dataset.

Detection of loosening angle for mark bolted joints with computer vision and geometric imaging

Mark bars drawn on the surfaces of bolted joints are widely used to indicate the severity of loosening. The automatic and accurate determination of the loosening angle of mark bolted joints is a challenging issue that has not been investigated previously. This determination will release workers from heavy workloads. This study proposes an automated method for detecting the loosening angle of mark bolted joints by integrating computer vision and geometric imaging theory. This novel method contained three integrated modules. The first module used a Keypoint Regional Convolutional Neural Network (Keypoint-RCNN)-based deep learning algorithm to detect five keypoints and locate the region of interest (RoI). The second module recognised the mark ellipse and mark points using the transformation of the five detected keypoints and several image processing technologies such as dilation and expansion algorithms, a skeleton algorithm, and the least square method. In the last module, according to the geometric imaging theory, we derived a precise expression to calculate the loosening angle using the information for the mark points and mark ellipse. In lab-scale and real-scale environments, the average relative detection error was only 3.5%. This indicated that our method could accurately calculate the loosening angles of marked bolted joints even when the images were captured from an arbitrary view. In the future, some segmentation algorithms based on deep learning, distortion correction, accurate angle and length measuring instruments, and advanced transformation methods can be applied to further improve detection accuracy.

Multi-Tone Piano Transcription Based on Visualization and Knowledge Recognition Algorithm

Scientific computing visualization is also known as visualization. In an academic sense, visualization is a way of computing. It can convert data into intuitive geometric images, making it easier to understand. Visualization is the use of computer graphics and image processing techniques. It is a technical means to convert piles of seemingly disorganized data into graphics or images through special computer methods. Recording is the process of recording sound signals on a medium. Specifically, it is the process of converting sound into electrical signals through microphones and amplifiers and recording them with different materials and techniques. Piano tuning is the adjustment of the strings so that they reach a certain high pitch. This paper aims to study the analysis and evaluation of multi-tone piano transcriptions based on scientific computing visualization and knowledge recognition algorithms. It expects to improve the quality of piano recording with the support of scientific visualization technology and knowledge recognition algorithm. This paper briefly explains the big data, and on this basis, the visual data mining technology is mentioned, and the current situation in the visual data mining is explained. A matrix calculation of the characteristic matrix of piano timbres was carried out to achieve the resynthesis of the 25th harmony in piano timbres electronically. The results of the trials in this article demonstrate that when the Gaussian number changes to 5 during the recording process, the difference that exists of the acoustic voltage intensity and the noise level phase is clearly diminished. When the Gauss figure is 10, there is an inversion of the value of the sound pressure phase.