Matrix newton interpolation and progressive 3D imaging: PC-based computation

Progressive image coding by hierarchical linear approximation

Precise real-time GPS orbit at a high rate is required for a number of applications, including real-time Precise Point Positioning (PPP), long range RTK and weather forecasts. To support these applications, the International GNSS Service (IGS) has developed a precise orbital service. At present, users may take advantage of the predicted part of the IGS ultra-rapid orbit for real-time and near real-time applications. Unfortunately, however the data rate of such precise orbits is usually limited to 15 minutes. In addition, the precision of the predicted part of the IGS ultrarapid orbit is limited to about 10 cm. for the 24-hour predicted part, which may not be sufficient for the above applications, This research proposes algorithms for interpolation and prediction methods that are intended to reduce the effect of such limitations. This research examines the performance of four interpolation methods for IGS precise GPS orbits, nameley Lagrange, Newton Divided Difference, Bernese Polynomial, Cubic Spline and Trigonometric Interpolation. In addition, a comparison between this research and earlier studies were conducted. A new approach that utilizes the residuals between the broadcast and precise ephemeris to generate a high-density precise ephemeris is also introduced in this research. A three-step neural network-based model is then developed in this research to generate a 6-hour predicted orbital arc. First, an initial predicted orbit is generated by extrapolating a concentrated group of previous precise ephemeris for 5 days. GPS observations for 35 globally distributed tracking stations, corresponding to the 24-hour period preceding the predicted part, are then utilized within the Bernese software to further enhance the predicted orbit. FInally, the predicted orbit is refined by implementing a modular - three-layer feed-forward back-propagation neural network. A comparison is made between our predicted orbit and the IGS ultra-rapid orbit to verify the efficiency of the newly developed neural network-based model. It is shown that the newly developed neural network-based model improved the orbit prediction by 47%, 22% and 37% for three randomly selected satellites from Blocks IIA, IIR and IIR-M respectively.

The Crout factorization of a Vandermonde matrix is related with the Newton polynomial interpolation formula expressed in terms of divided differences. Another triangular factorization, which can be related with the Newton formula in terms of finite differences, is provided by the Doolittle factorization. The influence of the order of the nodes on the conditioning of the corresponding linear system is analyzed, considering the three cases of increasing order, Leja order and increasing distances to the origin. The lower triangular systems for the computation of divided and finite differences are analyzed and the conditioning of the corresponding lower triangular matrices is studied. Numerical examples are included.

This study aims to simulate the 3 dimensional (3D) model of Keum-man connection canal using geographic information system (GIS) as well as considering design in viewpoint of engineering. The canal connects from Keumkang to Mangyungkang in order to supply fresh water into Saemankeum lake. This study used 3 dimensional spatial planning model (3DSPLAM) process to generate the 3D model, which has not only several planning layers in actual process, but also their corresponding layers in modeling process to simulate 3D space of rural villages. The discharge of the canal is <TEX>$20m^3/s$</TEX> on slope of 1/28,400 in the canal length of 14.2km, which consists of pipe line and open channel. This study surveyed the route of the canal and its surrounding environment for facilities to make images in the 3D graphic model. Besides, the present study developed data set in GIS for geogrphical surface modeling as well as parameters in hydraulic analysis for water surface profile on the canal using HEC-RAS model. From the data set constructed, this study performed analysis of water surface profile with HEC-RAS, generation of digital elevation model (DEM) and 3D objects, design of the canal section and route on DEM in AutoCAD, and 3D canal model and its surrounding 3D space in 3DMAX with virtual reality. The study result showed that the process making 3D canal model tried in this study is very useful to generate computer graphic model with the designed canal on the surface of DEM. The generated 3D canal can be used to assist decision support for the canal policy.

In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.

Augmented Reality (AR) is a technology that can be used to provide personalized and contextualized information regarding physical objects in form of digital overlays. We use this technology in our research project Ambient Learning Spaces (ALS) to provide museum visitors with specific additional digital 3D information regarding the exhibits presented. With this technology, we enable museum curators to use a new form of transporting contextualized information without the need for additional physical space. However, the use of AR brings up new challenges for the creation and placement of digital contents into the museum space. In this context, we ran an anonymous survey on the use of AR in museums throughout Germany and studied responses of (N = 133) museum professionals. The results indicate that, although many museum professionals are interested in using AR technology, currently the integration is very costly and complex. This paper proposes a system we developed in a user-centered design process with a museum. This system provides an interface that helps museum professionals to cope with the complexity when placing and aligning digital 3D objects in their exhibition using mobile devices. Through this solution, visitors have the chance to experience the virtual objects spatially embedded in the exhibition by the curators themselves. In multiple user studies during the development phase we measured the usability of the interface. The findings show that the system provides a high degree of usability and can be applied effectively by museum professionals.

We describe a digital design process that interfaces real-time data with 3D modeling and 3D printing techniques. Digital Impressionism (DI) is a platform that explores new material possibilities, by 3D modeling physical and digital objects, as affected by invisible forces that act upon them in real time. Using a 3D pointcloud as a medium, we describe an experimental project run with students in our programme, incorporating realtime audio data to manipulate 3D physical forms, resulting in new static and dynamic shapes with what we call a hybrid materiality. The modeling platform of DI treats materials as composites, through which substance becomes physical via the digital interference the environment applies to digital forms. We describe dynamic modeling processes through which data enables a new hybrid tectonic made of composite shapes and materials. This abstract introduces the project and describes our methodology and results so far.

Skeletonization is a way to reduce dimensionality of digital objects and is of interest in a number of tasks for image analysis. In this paper, efficient approaches to skeletonization of 2D and 3D digital objects are illustrated.

A novel real-time and progressive secret image sharing with flexible shadows based on compressive sensing

Modern advances in optical metrology and computer vision have provided an unprecedented ability to generate a wide variety of 3D digital content. The mouse, trackpad, and touch screens are typical 2D interactive interfaces of digital content. However, such interfaces are restrictive to manipulate 3D content such as models, object scans, and environments. In this work, a 3D pointer based on stereo vision to interact virtually with digital 3D objects is proposed. The theoretical principles and the experimental calibration procedure are provided. The proposed 3D pointer is evaluated experimentally by simple interaction routines with objects reconstructed by fringe projection profilometry.

The article deals problems with the security of software for Intelligent Transport systems that form the basis of national digital economies and critical information infrastructures. An extended system of software security criteria has been proposed, issues of confidence in its security have been considered. A method of software security is proposed, based on the integration of information security requirements and technological independence of software. An example of the implementation of the proposed methodology for ensuring the security of digital economy objects and critical information infrastructures is presented. An example of the implementation of the proposed methodology for ensuring the security of digital economy objects and critical information infrastructures is presented.

In computerized numerical control (CNC) systems, the communication bus between the controller and axis servo drives must offer high bandwidth, noise immunity, and time determinism. More and more CNC systems use real-time Ethernet protocols such as Ethernet Powerlink (EPL). Many modern controllers are closed costly hardware-based solutions. In this paper, the implementation of EPL communication bus in a PC-based CNC system is presented. The CNC system includes a PC, a software CNC controller running under Linux Real-Time Application Interface real-time operating system and servo drives communicating via EPL. The EPL stack was implemented as a real-time kernel module. Due to software-only implementation, this system is a cost-effective solution for a broad range of applications in machine control. All software systems are based on GNU General Public License or Berkeley Software Distribution licenses. Necessary modifications to the EPL stack, Linux configurations, computer basic input/output system, and motherboard configurations were presented. Experimental results of EPL communication cycle jitter on three different PCs were presented. The results confirm good performance of the presented system.

The work is devoted to the development of a technique for predicting the coefficient passage of metamaterials based on topological structure and chemical composition with the use of machine learning techniques, namely artificial neural networks using convolution. In modern scientific and technical research, the methods of machine learning, namely: convolutional neural networks, occupy the most rapidly researched method in the design tasks of metamaterials and their properties. The advantage of this technique is the ease of implementation, the availability of data for this approach, the speed of calculations compared to the exact methods of predicting properties and topological structure based on physical laws. Of course, artificial neural networks are a rather complex process that has its own drawbacks – the need for a large amount of data, the relative complexity of optimization, and the complexity of problem formulation. With the development of machine learning technologies, these disadvantages are more and more eliminated, and therefore their use becomes more accessible. A large amount of information about metamaterials from relevant sources was used, namely the topology, chemical composition and measurement conditions of metamaterials. Software environments were used for writing digital code and building 3D objects of metamaterials with defined properties. An algorithm for predicting the transmission coefficient based on the structure, chemical composition of metamaterials based on a convolutional neural network using experimental data of laboratory metamaterials has been developed. An algorithm for saving information about the chemical composition of metamaterials has been developed. It is shown that using information about the electromagnetic properties of chemical elements, it is possible to predict the transmission coefficient of metamaterials. The process of presenting the coefficient of passage of metamaterials in a form convenient for training a convolutional neural network is described. Two methods were used to compare the effectiveness of both methods. It is shown that the method of representing experimental characteristics in the form of polynomial coefficients is faster, but not suitable for solving problems of predicting the characteristics of metamaterials. Data augmentation is shown to be the most effective method for improving forecasting results. Nevertheless, performance improvement methods based on architecture changes and hyperparameter changes should be continually evaluated and used whenever possible.

This paper proposes a method that incorporates secret image sharing with progressive transmission based on the integer discrete cosine transform (IntDCT). The idea is to apply IntDCT coefficients after a combination process as input of the (r, n)-threshold model instead of directly sharing the secret pixels. A coarse version of the secret image can be decrypted by Lagrange interpolation with a small quantity of coefficients received. Moreover, the secret image is refined with more shared data received. It can be losslessly reconstructed as long as all coefficients received. Our method can be used for progressive share images transmission. Experimental results demonstrate the effectiveness of the proposed technique.

Autistic children suffer from distraction and difficulty in learning. The research is still ongoing continues to find suitable ways to help autistic children learn and live normally. Recently, the use of digital technologies in supporting children with Autism has increased dramatically. We focus on problems that autistic children face in the learning process. We propose a new learning system based on Augmented Reality overlie digital objects on top of physical cards and rendering them as a 3D object on mobile devices to help in teaching eating food skills using related phrases and sounds. We aim to improve the learning abilities to repeat the correct behavior.