Three-Dimensional Summarization of Face Shape

In the weak-field and slow-motion approximation of the General Relativity theory the relativistic theory of construction of nonrotating harmonic coordinate reference systems is developed. The general case of an isolated astronomicalN-body system is considered. The bodies are assumed to consist of a perfect fluid and to possess any number of the internal mass and current multipole moments characterizing the internal structure and own gravitational field of the bodies. The description of the coordinate reference systems and gravitational field is realized by the specific forms of the metric tensor. A metric is determined by the method of the Post-Newtonian Approximations (PNA) from the inhomogeneous Einstein equations under the harmonic coordinate condition. We have obtained two different specific forms of a metric, which are related to the inertial and quasiinertial coordinate reference systems. The metric in inertial coordinates is a near-zone solution of the Einstein equations for anN-body system. The metric in quasi-inertial coordinates is a solution of Einstein equations in the body's neighborhood, which is a world tube surrounding the body under consideration and extending up to another nearest body. The coordinate transformation between the inertial and quasiinertial reference systems is derived by a matching of both solutions in the body's neighborhood. A new method is proposed for construction of the body's proper reference system. This coordinate system has an origin which moves along a nongeodesic (in the general case) worldline of the body's center of inertia. The proper reference system is used for derivation of the Newtonian equations of translational and rotational motion of the body. The equations give us exhaustive information about the nonlinear Newtonian interaction between gravitational fields of the bodies in terms of internal mass multipole moments. Finally, the coordinate transformation between the inertial and proper reference systems is discussed in the first PNA.

Geoscience modellers develop numerical models where constraints are placed on how the model domain and sampling relates to location in the modelled world and the real world. The shape of the model domain is a significant factor for numerical algorithms and computational solvers. This leads to a number of interesting definitions of coordinate reference systems. I will summarise some requirements the modelling community have for specifying and working with coordinate reference systems. Post processing and presentation of analyses are important factors; archiving for future use is a crucial consideration. I will present examples of horizontal and vertical coordinate system definitions in common use in the meteorology and oceanography domains and the challenges they may bring. The conclusion will be a discussion how specifications and tools for defining, interpreting and transforming coordinate reference systems, such as Well Known Text (WKT), European Petroleum Survey Group (EPSG) and PROJ.4 are able or unable to meet the requirements of a geosciences modeller.

The article focuses on the need to evaluate the distribution of coordinates of the object nodes and their filtering (discharge) in order to implement algorithms for calculating the optimal parameters of projection coordinate systems. To solve this task, it is proposed to use the uniform distribution function, the value of which characterizes the concentration degree of the nodes that form the contour of linear objects. At the same time, the Chi-square criterion, as an estimation indicator, allows implementing iterative procedures for combining nodes and generalizing parts of objects to approximate the initial data to the uniform distribution. Studies have shown that it leads to the reduction in the excess concentration of nodes of linear terrain objects, which negatively affects the calculation of optimal parameters for coordinate reference systems. The paper also considers the examples of coordinate systems parameters, which are, moreover, implemented on the basis of oblique map projections, the use of which is possible for solving a wide range of engineering tasks for transport facilities, agriculture and environment studies of the Republic of Chile. The article also provides a graphical comparison of the suggested single 6-degree zone for the specified class of projections with the SIRGAS-Chile coordinate system using the Universal Transverse Mercator coordinate system (UTM Zone 18 and Zone 19). In conclusion the author presents the data that prove the necessity for the mandatory evaluation of the uniformity of initial geodata distribution in order to find the best projection parameters.

With recent progress of mobile devices and indoor positioning technologies, it becomes possible to provide location-based services in indoor space as well as outdoor space. It is in a seamless way between indoor and outdoor spaces or in an independent way only for indoor space. However, we cannot simply apply spatial models developed for outdoor space to indoor space due to their differences. For example, coordinate reference systems are employed to indicate a specific position in outdoor space, while the location in indoor space is rather specified by cell number such as room number. Unlike outdoor space, the distance between two points in indoor space is not determined by the length of the straight line but the constraints given by indoor components such as walls, stairs, and doors. For this reason, we need to establish a new framework for indoor space from fundamental theoretical basis, indoor spatial data models, and information systems to store, manage, and analyse indoor spatial data. In order to provide this framework, an international standard, called IndoorGML has been developed and published by OGC (Open Geospatial Consortium). This standard is based on a cellular notion of space, which considers an indoor space as a set of non-overlapping cells. It consists of two types of modules; core module and extension module. While core module consists of four basic conceptual and implementation modeling components (geometric model for cell, topology between cells, semantic model of cell, and multi-layered space model), extension modules may be defined on the top of the core module to support an application area. As the first version of the standard, we provide an extension for indoor navigation.

수로정보의 다양한 사용으로 해양지리정보의 상호운용성에 대한 필요성이 증가됨에 따라 개방형지리정보위원회(OGC)는 지리정보의 상호운용을 위한 표준인 GML을 수립하였다. GML은 지리정보의 모델링, 전송, 저장을 위해 XML 스키마 문법에 따라 작성된 XML 언어로서 피쳐, 참조체계, 지오메트리, 토폴로지, 시간, 측도 등의 지리체계를 설명하기 위한 객체를 포함하고 있다. 한편, S-57은 수로정보 전송을 위한 국제수로기구(IHO)의 표준으로 다양한 수로정보를 위한 표준임에도 불구하고 표준에서 채택하고 있는 구조의 한계로 인해 전자해도(ENC) 제작 목적으로 한정되어 사용되었다. 이를 개선하기 위해 IHO는 신규 표준을 준비하고 있으며 특히, GML은 모델링 및 엔코딩 도구로 사용될 것으로 전망되고 있다. 전자해도는 해상교통에 사용될 수 있는 가장 신뢰성 있는 정보로서 그 가치가 인정되나 전자해도 활용을 위한 GML 개발연구는 진행된 바 없다. 이에 본 연구에서는 전자해도 GML 변환을 위한 기초 연구로서 GML 작성을 위한 응용 스키마 개발기법 및 방안에 대해 연구하였다. Recently, bemuse of extensive use of hydrographic information, interoperability of Marine Geographic products is very important for efficient use of geographic information systems. Open GIS Consortium(OGC) developed the Open Geodata Interoperability Specification(OpenGIS) to support the interoperability in the distributed environment, especially Geography Markup Language(GML) Implementation Specification. Geography Markup Language is an XML grammar written in XML Schema for the modelling, transporting, and storing of geographic information GML provides a variety of objects for describing geography including features, coordinate reference systems, geometry, topology, time, units of measure and generalized values. S-57 is currently the IHO standard for the exchange of digital hydrographic data. To date, it ms been used almost exclusively for encoding Electronic Navigational Charts(ENCs). Even though, S-57 is intended to support all types of hydrographic data. In order to meet this requirement, a new standard is being developed. GML will be the core encoding rule of IHO's new standard. But there has been no study that tried to develop the GML for ENC that are recognized as base mop in the Marine GIS. This paper presents the process and results on development of application schema for converting ENC into GML.

This assessment has been informed by a proportionate level of information sufficient to enable a good understanding of the site. The research undertaken to inform the project cannot be considered exhaustive insofar as other information or sources may come to light in the future that contribute further understanding or dispute the established narrative. At the time of issue, the research and previous site assessment (Parfitt 2025) that has informed the research project is considered a robust and comprehensive account of the Elmbridge Decoy Site. The data has been collected from a wide variety of sources, summarised in Table 2.1. Source Data National Heritage List for England (NHLE) Current information relating to designated heritage assets, and heritage assets considered to be 'at risk'. The National Archives No documents are identified that refer specifically to the site or works undertaken to establish the decoy. There is a large collection of documents mostly deposited by the Ministry of Works that discuss the development of the decoy concept and span the evolution of tactics and methods used to create particular types of bomb Decoy Site. Worcestershire Historic Environment Record (HER) Heritage sites and events records, Historic Landscape Characterisation (HLC) data, and other spatial data supplied in digital format (shapefiles) and hardcopy. Historic England Archive (HEA) Additional sites and events records, supplied in digital and hardcopy formats. Worcestershire Archives Historic mapping, historic documentation, and relevant published and grey literature. Historic England's Aerial Photograph Research Unit Vertical and oblique aerial photography ranging in date from the 1940s to present. RAF Museum Collections Additional publications, grey literature and other materials specific to the RAF. Imperial War Museum Collections Additional publications, grey literature and other materials specific to the history of British conflict. Defra Data Services Platform (environment.data.gov.uk) LiDAR imagery and point cloud data, available from the Defra Data Services Platform 8 Fibden Farm Decoy Site, Worcestershire, Research Project � Cotswold Archaeology Source Data Genealogist, Envirocheck, National Library of Scotland & other cartographic websites Historic (Ordnance Survey and Tithe) mapping in digital format. British Geological Survey (BGS) website UK geological mapping (bedrock & superficial deposits) & borehole data. Table 2.1 Key data sources Aerial photographs held at Historic England Archive Aerial photographs held at Historic England were examined as part of this assessment, ranging in date from 1946 to 2014. The aerial photographs show that the site has been utilised as arable and pastoral farmland and that no large developments have occurred on the site since 1946. No direct evidence of the Decoy Site was present in the photographs. LiDAR imagery Existing DEFRA data was analysed with the specific aim of clarifying the extent any potential archaeological remains. Lidar DTM (Digital Terrain Model) and DSM (Digital Surface Model) ASCII files were downloaded from the DEFRA portal (environment.data.gov.uk), under the Open Government Licence v3.0. The lidar data was surveyed in 2019 and available at 1m for DTM and DSM resolution for the extent of the site boundary and buffer. The lidar files contain British National Grid as the "native" coordinate reference system. Where necessary, individual lidar datasets were combined into a mosaic raster dataset using Esri ArcGIS Pro 3.4.2 and exported as a single raster (.tif). The lidar file was then processed using Relief Visualisation Toolbox (RVT) (Kokalj et al 2019 and Zakaek et al 2011) to create several single and blended visualisations. Visualisations were created following Historic England guidelines (HE 2018) and guidance in Airbourne Laser Scanning Raster Visualisation: A guide to good practice (Kokalj & Hesse 2017).

High-energy collisions, scatterings and most decays are, for the most part, relativistic quantum processes. It is therefore imperative to recall relativistic kinematics and the basic rules of tensor calculus; see Appendix B.2 for a more complete introduction. However, this chapter neither replaces nor competes with complete treatments of the special theory of relativity such as the illustrative but perfectly detailed text [512] or the first and original text [566]. Instead, the purpose of this chapter is to provide an introduction and the results that will be useful in following the subsequent material. 3.1 The Lorentz transformations and tensors When describing physical processes, one necessarily uses a mathematical apparatus such as a (reference) coordinate system – equipped with a specific and appropriate collection of coordinates. The choice of any one such coordinate system is arbitrary and should not affect the characteristics of the natural laws. The basic idea (oft cited as one of the two postulates) of Einstein's theory of relativity is that the change in the choice of the coordinate system and corresponding coordinates used to describe spacetime must not change the meaning of natural laws – and so must not have any measurable, i.e., observable consequences. Digression 3.1 Chapter 5 will show that the so-called gauge principle is simply the generalization of this relativity to the spaces of so-called internal degrees of freedom (also a type of coordinates), such as the phase of the complex wave-function of any charged particle. In the special theory of relativity , this idea of relativity is limited to so-called inertial (coordinate) systems, which are usually defined as coordinate systems that differ from each other only in moving one with respect to the other with a constant relative velocity. However, against all intentions, this “definition” does not exclude, for example, a pair of coordinate systems that co-rotate about the same axis with the same angular velocity, but move with a constant relative velocity along the co-rotating axis.

The current need for more precisely defined reference coordinate systems arises for geodynamics because the Earth can certainly not be treated as a rigid body when measurement uncertainties reach the few centimeter scale or its angular equivalent. At least two coordinate systems seem to be required. The first is a system defined in space relative to appropriate astronomical objects. This system should approximate an inertial reference frame, or be accurately related to such a reference, because only such a coordinate system is suitable for ultimately expressing the dynamical equations of motion for the Earth. The second required coordinate system must be associated with the nonrigid Earth in some well defined way so that the rotational motions of the whole Earth are meaningfully represented by the transformation parameters relating the Earth system to the space-inertial system. The Earth system should be defined so that the dynamical equations for relative motions of the various internal mechanical components of the Earth and accurate measurements of these motions are conveniently expressed in this system.

The concepts of coordinate systems required to identify points in space and represent them on maps uses mathematical methods of assigning numbers, called coordinates to each point in space. There are different coordinate systems the commonest being the system of latitudes, longitudes and ellipsoidal heights. The situation is complicated because the latitudes and longitudes of the same point differ slightly depending on the geodetic coordinate system of a country, the result being that different systems of latitude and longitude in use for the same point can disagree in coordinates by more than 200 metres. The GPS for instance uses a WGS84 system and gives latitude and longitude values which can not be integrated directly into the mapping system of a country without suitable mathematical conversions. Similarly, it is not possible to just measure distances from a graticule map without appropriate projection conversions. In order to use data obtained from GPS measurements correctly and effectively in Ghana, we need to use appropriate transformation parameters that relate our Ghana National Survey Mapping coordinate system to that used for the Global Positioning System (GPS). Datum transformation parameters define functional relationship between two reference frames. This paper looked at geodetic coordinate systems and transformations between the WGS84 and the coordinate systems used in Ghana (the Ghana war office system and also the Clarke1880 system) using the Bursa-Wolf model. Particular attention was given to the derivation of ellipsoidal heights through the use of the Abridged Molodensky formulas. Keywords: Coordinate Systems, ellipsoidal heights, Global positioning System, WGS84, Transformation parameters Journal of Science and Technology Vol. 28 (1) 2008 pp. 116-127

The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.

A coordinate system was previously developed to identify landmarks on the skull surface to help locate the transverse-sigmoid sinus junction in order to reduce surgical morbidity in retrosigmoid craniotomy; however, in practice we found that this system has important flaws. To develop and evaluate a novel reference coordinate system to precisely locate the inferomedial point of the transverse-sigmoid sinus junction (IMTS) and evaluate the effect of gender and skull side (left or right). Forty-two adult skulls (84 sides) were obtained for analyses. The X-axis was defined by point A (where the upper edge of the zygomatic arch joins with the frontal process of the zygomatic bone) and point B (where the upper edge of the zygomatic arch blends posterosuperiorly into the supramastoid crest). The Y-axis was defined by the line perpendicular to the X-axis and extending across the tip of the mastoid. The x and y coordinates of IMTS (IMTS-x and IMTS-y) were measured in this coordinate system. There were 20 male skulls and 22 female skulls. The mean IMTS-x measurements were significantly higher on the right side compared with the left side in both males and females. For the left skull side, the mean IMTS-y measurements were significantly lower in females compared with males. This novel reference coordinate system may be a reliable and practical method for identifying the IMTS during retrosigmoid craniotomy. There are significant differences in location of the axes with regard to gender and skull side.

ABSTRACTThe spatial analysis functionalities of geographic information systems (GIS) are increasingly used across the web. Interface specifications of geoprocessing web services define the syntactic properties of the services (number and type of parameters) and provide textual descriptions of the operations. The discovery and reuse of web services based on these syntactic properties is restricted and has led to the quest for extended operation descriptions. A number of extended operation descriptions have been proposed and are reviewed in this article. The reviewed descriptions focus on particular steps of the workflow development process. In this article we analyse all phases of the development process of a spatial analysis workflow regarding the requirements of operation descriptions. These requirements are translated into a knowledge base that contains information about spatial analysis operations for the operations’ discovery, selection and composition. The knowledge base also foresees the automated discovery of operations in well-defined application contexts such as the transformation of data types or coordinate reference systems. The knowledge base combines the geooperator approach with elements of ontology-based approaches. The geooperator browser is the implementation of the discovery and selection of geoprocessing operations based on the knowledge base. A draft formalization of the knowledge base demonstrates its use and the support it provides during the composition of operations.

Abstract. In surveying projects, a site calibration is the solution to the problem of finding a transformation between the coordinate space of a site local coordinate reference system and a well known coordinate reference system given a set of pairs of corresponding coordinates. A site calibration enables the localization of new positions with cm accuracy using a RTK/PPK GNSS receiver and a transformation, which is a much more cost-effective than using a total station and much faster than other more traditional surveying methods. While site calibration is featured by almost every modern professional-grade GNSS receiver, the implementation is closed source and the output stored in proprietary file formats, tying the user to the vendor’s ecosystem. In this paper we propose a complete solution to the site calibration problem that can be fully implemented with open source software (in particular PROJ for coordinate transformations) and whose output can be represented in terms of an open standard (WKT version 2). Two methods and representations of a site calibration are described, a fully 3D one and a split horizontal and vertical one. Our main contribution is the openness and interoperability of the solution. Another important contribution is the analysis of the sensitivity of these solutions to measurement errors.

The Canadian Spatial Reference System (CSRS) defines latitude, longitude, and heights in Canada, providing the foundation for all types of geospatial data.On a dynamic earth, these standards require constant monitoring and updating to keep pace with evolving technologies and geospatial data accuracy requirements.Currently, the federally adopted coordinate reference system is the North American Datum of 1983 of the CSRS (NAD83(CSRS)).

This paper presents a camera calibration method that could be used in humanoid robot vision system. Extended Kalman Filter is used to estimate camera parameters. This method can take planer board feature points of the image or the object's 3D axis as inputs when doing known motion, test results show this algorithm can get good results. If the camera parameters are known, the relationship between a reference coordinate system and camera coordinate system can not get in high precision, in this paper, a method based on the arm motion is discussed.