Re: A universal model for spatial data

From: George Percivall <gpercivall@opengeospatial.org>
Date: Fri, 26 Oct 2018 10:24:32 -0400
Message-Id: <498702C1-5165-49F5-9465-CD25CBBAB9D4@opengeospatial.org>

To: "Knibbe, Frans" <Frans.Knibbe@kadaster.nl>, Chris Little <chris.little@metoffice.gov.uk>
```Some comments trigger by earlier comments from Chris and Frans.

From Chris:
> I guess the fundamental accuracy limit for space would be the smallest ‘ruler’ or thing, such as an atom or sub atomic particle.

from Frans:
> domain-independent model for space should rely heavily on pure mathematics.

A domain independent model of space is be provided by Calculus and mathematical analysis based on infinitesimal limits.  That approach is very powerful but too abstract on its own for our geospatial applications that include the physical world.  This is similar to CRS:  CRS include a Coordinate Systems and Datum.  CS are mathematical constructions that become useful for geospatial when a datum is defined that ties the abstract CS to the physical world.

What smallest "rulers" limits - similar to clocks for time - are relevant to physical space?   It maybe that a relevant physical space ruler is application dependent.
1. For imagery a relevant physical lower limit is Ground Sample Distance for spatial resolution of the image (see notes below)
2. For surveying and other positioning technologies, it might be the something on the order of the wavelength of the signals used to determine distance.
3. At the limit of spatial resolution in physical processes is the photon and its relation to the Planck constant.

On a related note, an ontology for geospatial space should clarify the difference distance and coordinates.  Distance can be measured, e.g. based on the time for a round trip signal to be received.  Coordinates are assigned based on a distance measurement and a CRS.  Clarifying the distinction between distance and coordinates would help correct the misnaming of a GPS calculator as a "GPS Sensor.”  The territory is not the map.

Regards,
George

++++++++++++++++++++++++++++++++++++

Excerpt from ISO 19101-2:2017 Geographic Information - Reference Model - Part 2: Imagery

From section 8.1.4.1 Resolution

The spatial resolution of an image is the minimum separation between two objects that can be distinguished as separate objects in the image. Pixel ground resolution defines the area on the ground represented by each pixel. This is often expressed as the distance between the centers of the areas represented by two adjacent pixels, called Ground Sample Distance (GSD) or Ground Sample Interval (GSI).

Related to the spatial resolution is the Instantaneous Geometric Field of View (IGFOV). IGFOV is the geometric size of the image projected by the detector on the ground through the optical system. IGFOV is also called pixel footprint. ISO 19123 defines the related concept of CV_Footprint. A CV_Footprint is the sample space of a grid in an external coordinate reference system,  e.g. a geographic CRS or a map projection CRS.

> On Oct 26, 2018, at 6:35 AM, Knibbe, Frans <Frans.Knibbe@kadaster.nl> wrote:
>
> Hello Chris,
>
> Thank you for your response. Perhaps it would be good to separate subjects in my original post. One is that there is a need for a fundamental ontology for space, the other is what that ontology should look like. I (shamefully) have to admit that I had not read the QB4ST documentation in that light, but it is interesting to note that Rob has made accommodations for a future space ontology (see https://w3c.github.io/sdw/qb4st/#Spatial <https://w3c.github.io/sdw/qb4st/#Spatial> and https://w3c.github.io/sdw/qb4st/#SpatialConcepts <https://w3c.github.io/sdw/qb4st/#SpatialConcepts>).
>
> As for the mathematical part: I am not a mathematician myself, but I wanted to propose the idea that a truly domain-independent model for space should rely heavily on pure mathematics. Perhaps I should have left it at that J. Exactly how a space ontology should take shape is then best left up to the specialists (geometers).
>
> Regards,
> Frans
>
>
> Van: Little, Chris [mailto:chris.little@metoffice.gov.uk]
> Verzonden: vrijdag 26 oktober 2018 12:09
> Aan: Knibbe, Frans <Frans.Knibbe@kadaster.nl>; public-sdwig@w3.org
> Onderwerp: RE: A universal model for spatial data
>
> Hi Frans,
>
> I am supportive of your idea, though not sure whether it is feasible.
>
> One or two assumptions that are made in maths are:
> 1.      Space dimensions do have a metric
> 2.      Euclidean space is assumed to have a locality property (every point can have a small area/volume drawn around it and ‘shrunk’ to the point.
> 3.      Space in each and all dimensions is assumed to be continuous, and between any two points there is an infinite number of other points
>
> The underlying idea of the OWL-Time ontology is the ‘clock’ which ticks (any physically repeating event that can be counted). There is no accuracy finer than that clock, unless one can find another. E.g. replace the Caesium atomic clocks of BIPM TAI with an ytterbium clock.
>
> I guess the fundamental accuracy limit for space would be the smallest ‘ruler’ or thing, such as an atom or sub atomic particle.
>
> I suggest that the starting point is not the above but Rob Atkinson’s QB4ST ontology.
>
> HTH, Chris
>
> Sent: 24 October 2018 09:11
> To: public-sdwig@w3.org <mailto:public-sdwig@w3.org>
> Subject: A universal model for spatial data
>
> Hello all,
>
> Warning: long text ahead. In short, I try to argue that it would be a good idea to have a domain-independent web ontology for spatial data.
>
> Introduction
> After having to cut back my participation in the Spatial Data on the Web Working Group (SDWWG) I have been (partially) working for the Dutch Cadastre, who are doing a great job at publishing geographic data on the web as Linked Data. Examples of such datasets are buildings, addresses, cadastral parcels, governmental spatial plans and large scale (i.e. detailed) topography, all with national coverage. In working on these efforts, and trying to make those data work for society, a familiar and very basic problem keeps turning up: the various domain models for geometry have poor interoperability. Consequently, the same can be said for data formats. I believe this is very harmful for getting spatial data on the web to really work. And by extension, it is harmful for the web of data itself.
>
> It was not possible to address this issue fully in the SDWWG, but I am glad to see the charter of the Spatial Data on the Web Interest Group fully supportive of what I would like to suggest in this message: That a universal basic web ontology for spatial data should be developed.
>
> The current problem
> We live in an age where data from many different sources can live together in one information system: the world wide web. Data are interlinked and self-describing, making it possible to decouple publication of data from fixed ways of putting data to use. People as well as machines are free to mix and process data as they please. Many types of usage will involve space, in one way or another, because  space is a fundamental aspect of our reality. Consequently, many data have spatial aspects. But spatial data are modelled in many different ways, and can appear in many different formats. This diversity is a result of historical developments. Before the foundations for a global web of data were in place, there was a need to digitize spatial data in many information domains, which led to development of different ways of digitizing what is essentially the same thing, but looked at from different perspectives. For example, there is the domain of geography, from which the current set of standards of the OGC spring. The domain of building construction also deals with things related to the Earth’s surface, but its standards have roots in CAD, leading to very different ways of specifying geometries. Then there the domain of 2D and 3D graphics, which also deals with spatial objects, but related to different reference systems: a sheet of paper, a computer screen or a virtual space, and is heavily focused on appearance. The transport domain has yet another focus: it is primarily concerned with network connectivity, leading to a graph-based view of spatial information. That is just mentioning a few domains that I am familiar with, probably there are more domains in IT and science that have developed their own ways of coding space.
>
> Different domain models and data formats may function well within their respective domains, but real life problems requiring sound solutions are likely not limited to a certain domain. The restrictiveness of domain standards has always existed, but comes to light more clearly now we have the means to work with data irrespective of their origin.
>
> Can Time set the pace for Space?
> As a data type, time has much in common with space. It is a universal reality that is always present in everyday life, and has therefore been described in many domain models. In a recent effort coordinated in the SDWWG, a universal model for time was made available: the Time Ontology in OWL <https://www.w3.org/TR/owl-time/>. It can be used to unify many different ways of how people have historically coded time instants and intervals. I think the Time Ontology could be an inspiration for a Space Ontology. Seemingly, it was possible to unify different ways of expressing information about time by going to the mathematical roots of the phenomenon. Mathematics is a truly domain-independent science and it is great for reducing everyday phenomena to their most basic and simple forms, using a language that all people on earth are able to speak, irrespective of their place of birth. I think going to the mathematical roots of space is what is required to come to a universal model for spatial information on the web.
>
> Doing the maths
> When looking at different ways spatial data are encoded, it seems to me that there are three basic ingredients needed. All of them can be expressed mathematically:
>
> 1) The notion of a spatial reference system. For geographers that will be some kind of model of the Earth’s surface. For astronomers some kind of model of the solar system, the galaxy or something even bigger. Physicists and chemists studying other phenomena might have a need for much smaller reference systems. For graphic designers an arbitrary 2D or 3D space needs to be agreed upon. For architects and engineers it could be a building plot or a building. The common ground seems to be that in order to define a spatial thing, first a frame of reference, a coordinate space, needs to be defined. Being able to do so using universal semantics would do a lot of good for data interoperability and transformation of spatial data between different reference systems.
> 2) The notion of coding the shape or spatial distribution of a thing in numbers. Related to this is the concept of spatial resolution, or the idea that when spatial data represent a real world phenomenon the numbers used will always be an approximation.
> 3) The notion of functions that work on numerical definitions of shapes or spatial distributions. One group of such functions would be topological relations between geometries. Other functions could define how to extrude a 2D shape to a 3D shape. Still other functions could be used to add or subtract shapes. And much more is needed and possible.
>
> These three ingredients depend on each other: a spatial reference system is needed to define shapes of things, and a way of defining shapes by numbers is needed to define functions working on those shapes. I hope it is possible to combine the three ingredients in a single model that is mathematical at its core, giving it the ability to be used at varying levels of complexity, with basic usage (e.g. defining a point location in a 2D space) being very simple.
>
> I can imagine that when such a shared model is in place it will be much easier to derive data types and data formats that are truly interoperable because they all have the same mathematical foundations. And probably we could do with far less data types and data formats too. That should be a great boost for developing software that can work with spatial data, on the web and elsewhere.
>
> Final words
> Ok, that is the idea I wanted to float. I hope it makes some kind of sense, but it would also be interesting to know if there are flaws in the reasoning. Of course, should people see the merit, a next question could how to make such a thing happen. Without going into detail about that issue, I just would like to note that a lot of what is needed already exists, and that the OGC-W3C combo seems to be just the right environment to make it happen.
>
> Regards,
> Frans
>
>
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Received on Friday, 26 October 2018 14:24:58 UTC

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