Spatial and spatio-temporal data models for GIS

Transcript Spatial and spatio-temporal data models for GIS

Spatial and Spatio-Temporal Data Models for GIS

Bart Kuijpers

Limburgs Universitair Centrum http://alpha.luc.ac.be/~lucp1265/ [email protected]

Overview

• Spatial data models in GIS – layers – raster model, vector model – specific models • Spatial database systems • Spatio-temporal data models – challenges and problems

What is the S in GIS?

• • • • 1980s: Geographic Information

Systems

– – – technology for the acquisition and management of spatial information software for professional users, e.g. cartographers Example: ESRI Arc/View software 1990s: Geographic Information

Science

– comprehending the underlying conceptual issues of representing data and processes in space-time – – the science (or theory and concepts) behind the technology Example: design spatial data types and operations for querying 1990s: Geographic Information

Studies

– understanding the social, legal and ethical issues associated with the application of GISy and GISc 2000s: Geographic Information

Services

– – Web-sites and service centers for casual users, e.g. travelers Service (e.g., GPS, mapquest) for route planning

GIS -- What is it?

No easy answer anymore!

• • Geographic Information – information about places on the earth’s surface – knowledge about “what is where when” (Don’t forget time!) Geographic Information

Technologies

– technologies for dealing with this information • Global Positioning Systems (GPS) • Remote Sensing (RM) • Geographic Information Systems (GIS)

Examples of GIS data

• • •

Urban Planning, Management

– – – Land acquisition Economic development Housing renovation programs – – Emergency response Crime analysis

Environmental Sciences

– – – Monitoring environmental risk Modeling stormwater runoff Management of watersheds, floodplains, wetlands, forests – – Environmental Impact Analysis Hazardous or toxic facility siting

Political Science

– Analysis of election results – Predictive modeling • • • • •

Civil Engineering/Utility

– – Locating underground facilities Coordination of infrastructure maintenance

Business

– – Demographic Analysis Market Penetration/ Share Analysis

Education Administration

– Enrollment Projections – School Bus Routing

Real Estate

– Neighborhood land prices – Traffic Impact Analysis

Health Care

– Epidemiology – Service Inventory

Older definitions of GISy

• The

common ground

between information processing and the many fields using spatial analysis techniques. (Tomlinson, 1972) • A powerful

set of tools

for collecting, storing, retrieving, transforming, and displaying spatial data from the real world. (Burroughs, 1986) • A computerised

database management system

for the capture, storage, retrieval, analysis and display of spatial (locationally defined) data. (NCGIA, 1987) • A

decision support system

involving the

integration

of spatially referenced data in a problem solving environment. (Cowen, 1988)

Definitions of GIS

“A system of hardware, software, and • • procedures designed to support the capture, management, • • manipulation, analysis, • • modeling and display of spatially referenced data (located on the earth’s surface) for solving complex planning and management problems.”

GIS Data Models Intuitive:

a map with a database behind it.

Purpose :

allows the geographic features in real world locations to be digitally represented and stored in a database so that they can be abstractly presented in map form, and can also be worked with and manipulated to address some problem.

GIS Data Model based on data layers or themes

Examples of layers or themes

• Data is organized by

layers

coverages

themes,

with each theme representing a common feature.

• Layers are integrated using explicit location on the earth’s surface,

thus geographic location is the organizing principal

Digital Elevation Models Watersheds Streams Waterbodies

An integrated view

• Layers are integrated using explicit location on the earth’s surface,

thus geographic location is the organizing principal

Example of layers or themes

roads Here we have three themes

- roads, layers

- hydrology (water), - topography (land elevation)

They can be related because precise geographic coordinates are recorded for each theme.

hydrology topography

How are layers described?

•Layers are comprised of two data • types:

spatial data

which describes location (where) •  stored in a

shape file attribute data

in ArcView specifing what, how much, when  stored in a database

table

roads hydrology GIS systems traditionally maintain spatial and attribute data separately, then “join” them for display or analysis (for example, in ArcView) topography

How are layers described?

The spatial component of a layer may be represented in two ways: • in

raster (image)

as pixels format •in

vector

format as points and lines and areas (PLA-model)

1. Raster Model

• area is covered by grid sized cells with (usually) equal • cells often called pixels (picture elements); raster data often called

image

data • attributes are recorded by assigning each cell a single value based on the majority feature (attribute) in the cell, such as land use type corn wheat fruit fruit oats 6 7 8 9 3 4 5 0 1 2 0 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1 2 2 2 4 4 3 1 1 1 1 1 2 2 2 4 4 4 1 1 1 1 1 2 2 2 2 2 5 4 4 4 4 4 2 2 2 2 2 6 4 4 4 4 4 2 2 2 2 2 7 5 5 5 5 5 3 3 3 3 3 8 5 5 5 5 5 3 3 3 3 3 9 5 5 5 5 5 3 3 3 3 3

Raster Model: data structures

Runlength Compression (for single layer)

Full Matrix-162 bytes

111111122222222223 111111122222222233 111111122222222333 111111222222223333 111113333333333333 111113333333333333 111113333333333333 111333333333333333 111333333333333333

Run Length (row)-44 bytes

1,7,2,17,3,18 1,7,2,16,3,18 1,7,2,15,3,18 1,6,2,14,3,18 1,5,3,18 1,5,3,18 1,5,3,18 1,3,3,18 1,3,3,18

Raster Model: data structures

Quad-Tree Representation (for single layer)

Raster Model: data structures

Quad-Tree Representation (for single layer) 1 3 0 2

Raster Model: data structures

Quad-Tree Representation (for single layer)

Raster Model: data structures

Quad-Tree Representation (for single layer)

Raster Model: data structures

Quad-Tree Representation (for single layer) 1 0 3 2 4 5 0 1 7 6 3 2 13 12 8 9 15 14 11 10

Raster Model: data structures

Quad-Tree Representation (for single layer)

Raster Model: data structures

Quad-Tree Representation (for single layer)

Raster Model: data structures

Quad-Tree Representation (for single layer) 4 5 0 1 7 6 3 2 13 12 8 9 15 14 11 10

Raster Model: data structures

Quad-Tree Representation (for single layer) 0 5 4 7 6 12 9 8 11 10 4 5 0 1 7 6 3 2 13 12 8 9 15 14 11 10

Raster Model: data structures

Quad-Tree Representation (for single layer) 0 5 4 7 6 [0,2] white [12,2] blue 12 9 8 11 10 [4,1] blue [5,1] white [6,1] green [7,1] red [8,1] red [9,1] white [10,1] white [11,1] green

Raster Model

Raster data are good at representing continuous phenomena, e.g., • Wind speed • Elevation, slope, aspect • Chemical concentration • Likelihood of existence of a certain species • Electromagnetic reflectance (photographic or satellite imagery)

Raster Model

• much data comes in this form •images from remote sensing (LANDSAT, SPOT) •scanned maps • digital orthophoto

Raster Model

• best for continuous features: •elevation •temperature •soil type •land use • digital elevation model (DEM)

Raster Model: Pros and Cons

[+] Continuous (surface) data represented easily [+] Simple data structure, fast indexing [ –] Shape of discrete polygonal features generalized by cells [ –] Intersection of two lines

Raster Model: tesselations

•

Square grid

: equal length sides –4-connected neighborhood (

rook’s case

) •all neighboring cells are equidistant –8-connected neighborhood (

queen’s case

) •all neighboring cells

not

equidistant •

rectangular

•

triangular

(3-sided) and

hexagonal

(6-sided) –all adjacent cells and points are equidistant •

triangulated irregular network

(TIN): –

vector

model used to represent continuous surfaces (elevation) –more later under vector

2. Vector Model

The fundamental concept of vector GIS is that all geographic features in the real work can be • • • represented either as:

points or dots (nodes)

airports, cities : trees, poles, fire plugs,

lines areas (arcs):

streams, streets, sewers,

(polygons):

forest, rock type land parcels, cities, counties, Example: Because representation depends on shape, ArcView refers to files containing vector data as

shapefiles

Vector Model Points

: represent discrete point features each point location has a record in the table airports are point features each point is stored as a coordinate pair

Vector Model Lines

: represent linear features each road segment has a record in the table roads are linear features

Vector Model Lines

: fundamental spatial data model node vertex vertex vertex vertex node • Lines start and end at nodes • line #1 goes from node #2 to node #1 • Vertices determine shape of line • Nodes and vertices are stored as coordinate pairs

Vector Model Polygons

: represent bounded areas each bounded Polygon has a record in the table landforms and water are polygonal features

Vector Model Polygons

: fundamental spatial data model • Polygon #2 is bounded by lines 1 & 2 • Line 2 has polygon 1 on left and polygon 2 on right

Vector Model Polygons

: fundamental spatial data model • complex data model, especially for larger data sets • “arc-node topology,” only used for ArcInfo data sets

Vector Model

Shapefile polygon spatial data model • less complex data model • polygons do not share bounding lines

Vector Model

ArcInfo coverage spatial data model • Commonly found format (due to ArcInfo market dominance) • Coordinate data not editable in ArcView (but tabular data are editable in ArcView) • polygons share bounding lines

5 4 3 2 1 0

Vector Model: illustration of polygon E A C B D

1 2 3 4 5 A 3 4 A 4 4 A 4 2 A 3 2 A 3 4 B 4 4 B 5 4 B 5 2 B 4 2 B 4 4 C 3 2 C 4 2 C 4 0

Data File

C 3 0 C 3 2 D 4 2 D 5 2 D 5 0 D 4 0 D 4 2 E 1 5 E 5 5 E 5 4 E 3 4 E 3 0 E 1 0 E 1 5

5 2 1 0 4 3

Vector Model: illustration of point & polygon 11 10 E 1 4 A 9 C 2 3 8 B D

1 2 3 4 5

5 12 6 7 Points File

1 3 4 2 4 4 3 4 2 4 3 2 5 5 4 6 5 2 7 5 0 8 4 0 9 3 0 10 1 0 11 1 5 12 5 5

Polygons File

A 1, 2, 3, 4, 1 B 2, 5, 6, 3, 2 C 4, 3, 8, 9, 4 D 3, 6, 7, 8, 3 E 11, 12, 7, 10, 11

1 I II Smith Estate A34 2 III Birch

Node/Arc/ Polygon and Attribute Data

A35

Relational Representation: DBMS required!

4 IV 3

Spatial Data

Cherry

Node Table

Node ID Easting Northing 1 2 126.5

218.6

578.1

581.9

3 4 224.2

129.1

470.4

471.9

Arc Table

I Arc ID From N To N L Poly R Poly 4 1 A34 II III IV 1 2 3 2 3 A35 4 A34 A34 A34

Polygon Table

Polygon ID A34 A35 Arc List I, II, III, IV III, VI, VII, XI

Attribute Data

Node Feature Attribute Table

Node ID Control Crosswalk 1 light yes 2 stop 3 yield 4 none no no yes ADA?

yes no no no

Arc Feature Attribute Table

I Arc ID Length Condition Lanes Name 106 good 4 II III IV 92 poor 111 fair 95 fair 4 Birch 2 2 Cherry

Polygon Feature AttributeTable

Polygon ID Owner Address A34 A35 J. Smith R. White 500 Birch 200 Main

Raster versus Vector Model

“

raster is faster but vector is corrector

” (Joseph Berry) From: Burrough, Peter A. and Rachael A. McDonnell. (1998).

Principles of Geographic Information Systems

. p 27.

Raster versus Vector Model

“

raster is faster but vector is corrector

” (Joseph Berry) •

Raster data model

– location is referenced by a grid cell in a rectangular array (matrix) – attribute is represented as a single value for that cell – much data comes in this form • images from remote sensing (LANDSAT, SPOT) • scanned maps • elevation data from USGS – features: best for continuous • elevation • temperature • soil type • land use •

Vector data model

– location referenced by x,y coordinates, which can be linked to form lines and polygons – attributes referenced through unique ID number to tables – much data comes in this form • DIME and TIGER files from US Census • DLG from USGS for streams, roads, etc • census data (tabular) – best for features with discrete boundaries • property lines • political boundaries • transportation

Variety of Vector Models

 Spaghetti model  Topological model (most common)  Triangulated irregular network (TIN)  Dime files and TIGER files  Network model  Digital Line Graph (DLG)  Shapefile (ArcView/ArcGIS; ESRI)  Others: HPGL, PostScript/ASCII, CAD/.dxf

Vector Model: Spaghetti

 information in n-dim. By m dim. hyperspaces (m

Introductory Geographical Information Systems

. p. 54.

Vector Model: Topological

Bernhardsen, Tor. (1999). 2 nd Ed.

Geographic Information Systems: An Introduction

. p. 62. fig. 4.12.

Topological Data Model

The topological data model is used, e.g., by the Census Bureau of the US: four relations  R1: every line has two endpoints  R2: every line has two areas  R3: every area is surrounded by lines  R4: every point is surrounded by areas and lines

Vector Model: Topological

 connections & relationships between objects are independent of their coordinates  overcomes major weakness of spaghetti model – allowing for GIS analysis (Overlaying, Network, Contiguity, Connectivity)  topological invariants

Topological Data Model

A database in the topological data model consists of a finite number of  labeled points  labeled lines  labeled areas p in

R 2

r  I E  C s v  D  A B  t J F H q

Topological Data Model

Give for each labeled point the circular list of all lines and areas that appear clockwise around it: List(p)=(  H  D  I) List(q)=(  J  F  H) … List(s)=(  C  B  E) lossless p 

= unbounded area

 r I E  C s v  D  A B  t J F H q

Vector Model: Dime files and TIGER files

Image Source: Demers, Michael. N. (2000). 2 nd Ed.

Fundamentals of Geographic Information Systems.

p. 113. fig 4.16.

Vector Model: Dime files and TIGER files

Image Source: Clarke, Keith C. (2001). 3 rd Ed.

Getting Started with Geographic Information Systems.

p 92.

Vector Model: DLGs

Digital Line Graphs Image Source: Clarke, Keith C. (2001). 3 rd Ed.

Getting Started with Geographic Information Systems.

p. 90

Vector Model: Network

Source: Heywood, Ian and Sarah Cornelius and Steve Carver.

An Introduction to Geographical Information Systems.

p. 60. fig. 3.14.

Vector Model: Topological data

 adding semantics  What kind of binary topological relations exist between spatial objects?

Vector Model: Topological

 adding semantics  What kind of binary topological relations exist between spatial objects?

 Based on region’s interior and boundary (and exterior)  Determines whether A o  A interior and boundary have (non-)empty interesection

Vector Model: Topological

 adding semantics  What kind of binary topological relations exist between spatial objects?

 Egenhofer and Randell Cohn C… A  o A B o  B     A o  A B o  B

Vector Model: Topological

   

disjoint

   

contains

   

inside

   

equal

   

meet

   

covers

       

coveredBy overlap

Disjoint Topological relationships Point/Point Line/Line Polygon/Polygon

Touches Topological relationships Point/Line Line/Polygon Point/Polygon Polygon/Polygon Line/Line

Crosses Topological relationships Point/Line Point/Polygon Line/Line Line/Polygon

Overlap Topological relationships Point/Point Line/Line Polygon/Polygon

Topological relationships Within/contains Point/Point Line/Line Point/Line Line/Polygon Point/Polygon Polygon/Polygon

Equals Topological relationships Point/Point Line/Line Polygon/Polygon

Topological relationships line-line relationships area-area relationships

adjacency island touch branching off

area-line relationships

cross intersect line in an area line ends at an area

point-line relationships

line ends in an area line is border of an area line intersects area line touches area

point-area relationships

point on line point beside a line point in area point on border of an area

TIN: Triangulated Irregular Network Surface Points

Node # 1 2 3 etc X 0 525 631 Y 999 1437 886 Z 1456 1437 1423

Polygons

Polygon Node #s Topology A 1,2,4 B,D B C 2,3,4 3,4,5 A,E,C B,F,G D etc 1,4,6 A,H

Attribute Info. Database

Polygons A B C D etc.

Var 1 1473 1490 1533 1486 Var 2 15 100 150 270 Elevation points (nodes) chosen based on relief complexity, and then their 3-D location (x,y,z) determined.

2 Elevation points connected to form a set of triangular polygons; these then represented in a vector structure .

Attribute data associated via relational DBMS (e.g. slope, aspect, soils, etc.) 1

A B

E 3 6

H 4 G

5 F

Vector Model: Shapefile (ArcGIS; ESRI)

This table represents examples of the shape types of geographic features in a data set for a shapefile Demers, Michael. N. (2000). 2 nd Ed.

Fundamentals of Geographic Information Systems.

p. 114. fig 4.17.

Vector Model:

Others …

HPGL, CAD/.dxf PostScript/ASCII

Source: Clarke, Keith C. (2001). 3 rd Ed.

Getting Started with Geographic Information Systems.

p. 89. fig. 3.12.

• •

Difference between GIS and Spatial Databases

GIS is a software to visualize and analyze spatial data using spatial analysis functions such as –

Search

Thematic search, search by region, classification – – – – –

Location analysis Terrain analysis Flow analysis Distribution

Buffer, corridor, overlay Slope/aspect, drainage network Connectivity, shortest path Change detection, proximity, nearest neighbor

Spatial analysis/Statistics

Pattern, centrality, autocorrelation, indices of similarity, topology: hole description –

Measurements

direction Distance, perimeter, shape, adjacency, GIS uses SDBMS – to store, search, query, share large spatial data sets

Difference between GIS and Spatial Databases

• • • SDBMS focusses on – Efficient storage, querying, sharing of large spatial datasets – – Provides simpler set based query operations Example operations: search by region, overlay, nearest neighbor, distance, adjacency, perimeter etc.

– Uses spatial indices and query optimization to speedup queries over large spatial datasets.

SDBMS may be used by applications other than GIS – Astronomy, Genomics, Multimedia information systems, ...

Will one use a GIS or a SDBM to answer the following: – – How many neighboring countries does USA have?

Which country has highest number of neighbors?

What is a Spatial DBMS?

• • A SDBMS is a software module that – can work with an underlying DBMS – supports spatial data models, spatial abstract data types (ADTs) and a query language from which these ADTs are callable – supports spatial indexing, efficient algorithms for processing spatial operations, and domain specific rules for query optimization Example: Oracle Spatial data cartridge – – can work with Oracle 8i DBMS Has spatial data types (e.g. polygon), operations (e.g. overlap) callable from SQL3 query language – Has spatial indices, e.g. R-trees

Spatial database systems for GIS

• • • • Limitations of Relational Data Model Values are atomic, complex objects need to be unnested (first normal form) Only atomic types, no subtyping/inheritance, no encapsulation of operations with data, no OID No support for unstructured/heterogeneous data No support for infinite relations (spatial and spatio temporal data)

SSNr Name Salary

12345 Bart 50K 12346 12347 Sofie Bill 35K 500M

Spatial Data in the Relational Model

• • • Boundary representation No notion of spatial object/type Mismatch with query language, e.g. SQL (no arithmetic,…)

(0,1) Name

triangle1 triangle1 triangle1

0 0 1

1 0 0

(0,0) (1,0)

• • •

Extension of the Relational Model: ADT-approach

Relational model is augmented with ad hoc spatial data types: point, polyline, polygon SQL is also extended [G üting et al., 1990s]

• • •

Extension of the Relational Model: ADT-approach

Example: ADT – – – Polygon Constructors : Methods: containment, overlap, … Subtyping/Inheritance: Rectangle isa Polygon Query language: SQL [G üting et al., 1990s]

Beyond Relational: Constraint Databases

• • • [Kanellakis, Kuper and Revesz, PODS1990] Constraint tuple : finite combination of atomic constraints Constraint relation Semantics : finite set of generalized tuples : infinite point sets

T1 T2 C1

Color

green red yellow …

geometry

0  x  x  0  0  0  y  y  1  1  x+y y-x (x-1) 2 +(y -1) 2 = 1/9

Queries in constraint databases

• • In practice only linear constraints [DEDALE, DISCO, COSMOS] Natural query languages : FO+Poly, FO+While, FO+TC, Datalog with polynomial constraints • • Q(S) = {(x,y)  R 2 | S(x,y)  (  (   >0)(  x’)(  y’)((x-x’) 2 +(y y’) 2 <  2  S(x’,y’)))} Q 0  x  0  y  1  x+y 0  x  0  1  0  y = 0  y  1  x+y = 1) (x =

Query evaluation in constraint Databases

• • • • • Apply Q(S) = {(x,y)  R 2 | S(x,y)  (  (   >0)(  x’)(  y’)((x-x’) 2 + • (y y’) 2 <  2  Plugin: 0  (y y’) 2 <  2  S(x’,y’)))} on A given by 0 x 0   0 x’   y 0   1  y’  x+y 1   (  (    x’+y’ ))} x >0)(   0  x’)( y   1  x+y y’)((x-x’) 2 + Complexity is huge Tarski (1930) Collins’ CAD (1975): doubly exponential in #quantifiers 1990s: single exponential in #quantifier-alternations 0  x  0  y  1  x+y 0  x  0  1  0  y = 0  y  1  x+y = 1) (x =

From Spatial Data to Spatio-Temporal Data

• • • • Temporal databases – 1980s, one of the first special purpose database applications Spatial databases – well-studied area in GIS, – … in database theory during 1990s Spatio-temporal data : – studied in databases since mid 1990s, – – SSD’99 changes into SSTD’01 has its specific problems

Spatio-Temporal Data

Examples

• • • • • • • Transportation: truck or ship movement, airplane flights Meteorological: isobaric curves, temperature Climate: season, vegetation changes Natural disasters: forest fires, oil spills Ecology: species migration, vegetation changes, habitat and land cover changes Society and economy: urban growth, land use changes, epidemics Ownership or administrative changes

Spatio-Temporal Data

What is changing where and how?

• • • • What?

points

1D 2D 3D

lines regions volumes • • • • How?

continuous continuous evolution movement discrete evolution birth, death, split, merge • • • Where?

on in in

1D 2D 3D

line plane space

Spatio-Temporal Data

What is changing where and how?

• • • • What?

points

1D 2D 3D

lines regions volumes • • • • How?

continuous continuous evolution movement discrete evolution birth, death, split, merge • • • Where?

on in in

1D 2D 3D

line plane space In combination with classical alpha-numerical data.

Abstract Spatio-Temporal Objects

• Time is isomorphic to the reals R • n-dimensional abstract spatio-temporal object O  R n  R • It should satisfy – slice regularity , i.e., O t0 ={(x 1 ,…,x n ) | (x 1 ,…,x n ,t 0 )  O} should be a familiar object (point, square, triangle, polygon) – – f(t)=O t should be piece-wise continuous closure properties

Closure Properties

• A class of spatio-temporal objects

is closed under an operation

if for all O 1 ,…, O k 

(of arity k) , also op(O 1 ,…, O k )  C • • Relevant operations: – intersection, union, difference – temporal/spatial selection – temporal/spatial projection Closure properties are easy to obtain for spatial objects, more difficult for natural classes of spatio temporal objects

The ADT-approach [G üting et al., TODS 2000]

• Spatial objects : points, polylines, polygons • Operations : – Set theoretic: intersection, union, difference – Aggregation: min, max, avg, center, area, volume – Metrical: distance – Topological: containment, adjacency, …

The ADT-approach: Temporal Lifting

• Temporal lifting of spatial type   (  with domain D  ) consist of partial functions R  D  E.g.,  (points),  (polylines),  (polygons) : • Temporal lifting of spatial operation op:  1  …   k op  :  (  1 )    0 …   (  k )   (  0 ) • E.g.  : polygons    polygons  polygons :  (polygons)   (polygons)   (polygons) (p 1 , p 2 )  {(t, p 1 (t)  p 2 (t))| t  R}

Example of SQL3 Query • “Find all pairs of airplanes that came closer than 500 meters during their flight” SELECT A.id, B.id

FROM Flights A,Flights B WHERE A.id <> B.id

AND minvalue(distance(A.route,B.route))<500 • Example of spatio-temporal join

Concrete Representation [Forlizzi et al., SIGMOD 2000]

• • Spatial objects : region (=finite set of polygons with holes ) Spatio-temporal (evolving) objects : – finitely many spatial slices (=time intervals) – coordinates are linear functions of time on each slice – segments may degenerate but cannot rotate within a slice – spatio-temporal object is a polyhedron .

The ADT-approach: Conclusion

• • • • Change : both continuous and discrete Closure : – for union: trivial, – for intersection, difference, selection, projection: depends on properties of polyhedra.

Object-orientation : – – – object types, operation signatures object easy to implement in object-relational DB no natural restriction on movement guarantees polyhedral structure Queries : – – – good integration with SQL3, e.g., aggregation expressiveness: difficult to establish notoriously hard to optimize

Spatio-Temporal Data in the Constraint Model

One extra time variale: t t=0

Name

MT1

Color

white

geometry

0  x-t  0  y-t  t+1  x+y  0  t  4

Spatio-Temporal Data in the Constraint Model

One extra time variale: t t=1

Name

MT1

Color

white

geometry

0  x-t  0  y-t  t+1  x+y  0  t  4

Spatio-Temporal Data in the Constraint Model

One extra time variale: t t=2

Name

MT1

Color

white

geometry

0  x-t  0  y-t  t+1  x+y  0  t  4

Spatio-Temporal Data in the Constraint Model

One extra time variale: t t=3

Name

MT1

Color

white

geometry

0  x-t  0  y-t  t+1  x+y  0  t  4

Spatio-Temporal Data in the Constraint Model

One extra time variale: t t=4

Name

MT1

Color

white

geometry

0  x-t  0  y-t  t+1  x+y  0  t  4

Spatio-Temporal Data in the Constraint Model

• • • • • • Closure guaranteed Natural query languages : FO+Poly, FO+While, Datalog with Constraints Theoretically appealing and suited to study e.g., expressiveness of query languages but few implementations (mostly with linear constraints [DEDALE, DISCO,COSMOS]) Representation problem: a plane circles at constant speed More restricted models: – – parametric spatio-temporal objects implementations (MLPQ, PReSTO [Revesz, SIGMOD 2000])

Spatio-Temporal Data : Representation problem

An airplane circles at constant speed.

z=constant x=x 0 +r.cos t y=y 0 +r.sin t

Spatio-Temporal Query Languages

•First-order logic over the reals : relational calculus extended with polynomial (in)equalities.

“ Do plane1 and plane2 collide at 5 o’clock above position (0,0)?“ (  x)(  y)(  z)(  t)(Plane 1 (x,y,z,t)   Plane 2 (x,y,z,t) x = 0  y = 0  t = 5) •Extension of FO with a while loop : finite sequence of statements & while loops.

• Statement: R := {(x,y,t)|  (x,y,t)}; • While-loop: while  do P;

Queries in the Constraint Model

• Closure : naturally available in the model • problems with aggregation, distance, … • no object-oriented features • Query langauges : • FO + extensions, • simple semantics, • expressiveness well-studied, • implementation requires constraint engine

Parametric Spatio-Temporal Objects

• • An atomic geometric object – spatial reference object consists of: S (in R 2 ) – – reference time transformation function f: R 2 xR  R 2: I (interval in R) (x,y;t)  parameterized by time, i.e., (x’,y’)=f(x,y;t) A molecular geometric object atomic objects consists of a finite number of Example: S=[0,1]x[0,1], I=[1,5], f(x,y;t)=(tx,ty) t=0 t=5

Parametric Spatio-Temporal Objects

Example database: ID “classical” pict time interval from to dept Spatio - temporal arr Referentie object Route functie 1 A D 2h00 2h30 f 1 (x,y,t) 2 B C 1h30 2h30 f 2 (x,y,t)

Parametric Spatio-Temporal Objects

Semantics of an atomic geometric object {(x,y;t)| t  I  ((  x’)(  y’)(x’,y’)  S  (S,I,f) is (x,y)=f(x’,y’;t))}, e.g.: ( , I, f(x,y,t) ) Semantics of an molecular geometric object is union of semantics of its atomic objects 3D figure is always a semi-algebraic set y t x And it is viewed as:

Reference Objects

arbitrary Poly Trax sides parallel to coordinate axes Rect

Transformation Functions

• Affinities : (x,y;t)  a(t) b(t) x c(t) d(t) y + e(t) f(t) • Scalings : (x,y;t)  a(t) 0 x 0 d(t) y + e(t) f(t) • Translations : (x,y;t)  • Identity 1 0 x 0 1 y + e(t) f(t) with a(t), b(t), c(t), d(t), e(t), f(t) linear, polynomial rational or

Transformation Functions

• Affinities : (x,y;t)  a(t) b(t) x c(t) d(t) y + e(t) f(t) observe an passing object under an angle circling airplane • Scalings : (x,y;t)  a(t) 0 x 0 d(t) y + e(t) f(t) observe an object that you are walking away from/to, oil spill, forest fire • Translations : (x,y;t)  wind, transport 1 0 x 0 1 y + e(t) f(t) • Identity spatial data with a(t), b(t), c(t), d(t), e(t), f(t) linear, polynomial rational or

Closure Properties under Boolean Operations

Object O 1 : (the immediate proximity) of a ship Object O 2 : another ship (or a natural hazard) Object O 1  O 2 : danger zone Query: “Is there any danger of collision?”

Parametric Spatio-Temporal Objects

Example database: ID “classical” pict time interval from to dept Spatio - temporal arr Referentie object Route functie 1 A D 2h00 2h30 f 1 (x,y,t) 2 B C 1h30 2h30 f 2 (x,y,t)

Closure Properties under Boolean Operations

C A D B

Closure Properties under Boolean Operations

C A D B

Closure Properties under Boolean Operations

C A D B

Closure Properties under Boolean Operations

A D B

Closure Properties under Boolean Operations

A D B

Closure Properties under Boolean Operations

A D B

Closure Properties under Boolean Operations

A D

Closure Properties under Boolean Operations

A D

Closure Properties under Boolean Operations

A D B

Closure Properties under Boolean Operations

Which classes are closed under  ,  ,

A class (

S,F

) is closed under of (the semantics) of any two molecular geometric objects from the class (

S,F

 iff the intersection ) can be described as a geometric object from (

S,F

Property: A class (

S,F

) is closed under  closed under  iff it is for atomic objects.

Closure Properties under Boolean Operations

Which classes are closed under  ?



Affinity Scaling Translation

Rat Pol Lin Rat Pol Lin Rat Pol Lin

Id Poly + + + + + + + + + + Tr + + + + + + + + + + TraX + + + + + + + + + + Rect + + + + + + + + + +

Closure Properties under Boolean Operations

Which classes are closed under  

\ Affinity Scaling

Rat Pol Lin Rat Pol Lin ,

Translation

Rat Pol Lin

Id Poly + - - - - - - - - + Tr + - - - - - - - - + TraX + - - - - - - - - - Rect + - - + + + - - - +

Property

A class is closed under  iff it is closed under

Closure Properties under Boolean Operations

    

Closure Properties under Boolean Operations

Example : A :rectangle B :rectangle A: (x,y)  (x-t,y-t)

B: (x,y)



(x,y-t)

Assume that both objects have the same time interval

Closure Properties under Boolean Operations

Different shapes of A  B  The intersection of two translating objects is a

SCALING

object that cannot be described as a union of translating objects (translation preserves length + area).

Closure Properties under Boolean Operations

This result is very intuitive, see example:

Closure Properties under Boolean Operations

The movement of the intersection can be described by a scaling.

The intersection of two

linear

is a (union of)

linear

scaling rectangles scaling rectangle(s) …

Closure Properties under Boolean Operations

Proof sketch: It can be shown that if  

x y

    

1 (

) 0 0

1 (

)    

x y

    

1 (

t t

) )   and  

x y

    

2 (

) 0

2 0 (

)    

x y

    

e f

2 2 ( (

t t

) )   are the transformations of the original objects, the intersection’s transformation is described as:  

x y

      

1 (

)

x ul



(

)

ul x





x lr

1 (

) 

2 (

)      ( (

b a

2 2 ( (

t t

) )  

b a

1 1 (

(

)) ))

y x ul ul x y x lr ul lr

  

y ul



y f e x lr

1 1

( (

t t

) )

x lr y lr

 

2 (

)

x ul f

2 (

)

y ul

    0

1 (

)

y ul



2 (

)

y ul y





y lr f

1 (

)  linear

2 (

)      

x y

 

Closure Properties under Boolean Operations



Poly Tr TraX Rect \ Affinity Scaling

Rat Pol Lin Rat Pol Lin

Translation

Rat Pol Lin

Id + - - - - - - + - - - - - - + - - - - - - + - - + + + - - - - - - + - + - - - +

The only class of transformations that can be used for Boolean operations.

MLPQ/PReSTO System [Revesz et al., SIGMOD 2000]

• MLPQ: linear constraints • GIS: operations special to GIS objects • PReSTO (STDB): spatio-temporal database system • RECURSIVE 

\ Affinity Scaling Translation Id

Rat Pol Lin Rat Pol Lin Rat Pol Lin

Poly + - - - - - - - - + Tr + - - - - - - - - + TraX + - - - - - - - - - Rect + - - + + + - - - +

Rectangle based system

PReSTO Example: Cloud over US

PReSTO (STDB): spatio-temporal database system

PReSTO

Data definition in PReSTO: Nebraska() :- i=1, x1=550, y1=340, x2=570,y2=355, t>=0,t<=300,p=-1, s = 0.

clouds(h) :- i=1,x1 - t = 80, y1 - 0.5t = 100, x2 - 1.1t = 220, y2 - 0.6t = 200, t >=0, t<=300, p = -1, s = 0, h = 0.

Available operations/queries in PReSTO: •Union, intersection, difference, complement; •Projection, selection

Parametric Spatio-Temporal Objects: Conclusion

•Closure : for union trivial; for intersection and difference in some cases •Solution : restrict to polygons or work with Boolean combination of atomic objects (AND-OR-NOT trees, see CSG) •Advantage: - closure in definition - easier to construct more complicated objects (polygons with holes…) a a d b c a  b  c  d b a

Representing Spatio-Temporal Phenomena using ADTs or Constraints

Problem with real spatio-temporal data: (A) data comes with discrete observations •Within a snapshot (TINs) •In different snapshots (B) data lacks clearly identifiable and delineated objects (C) modeled movement/evolution is often irregular (D) Data does not have regular (polyhedral) 3D structure Solution to (A), (C) and (D): •Convert each snapshot to a set of polygons •Interpolate/approximate between the snapshots

Other Challenges

Data models: • type system • representing uncertainty • integrating different representations • resolving inconsistencies Query languages and interfaces: • multi-dimensional aggregation (ST OLAP) • visualization • animation: explicit representations (ADTs) are more suitable than implicit ones (constraints)

Moving Objects Databases (MOD) [Wolfson et al., 1997, Su et al., 2001]

Data model: • point moving in nD plane (e.g., n=2) • finite chain of infinitely differentiable functions p:R  R 2 • MOD = finite set of moving objects Operations: • vel(p), acc(p), • moving direction =vel(p)/||vel(p)|| • speed =||vel(p)|| • distance = dist(p,q)= min t ||p(t)-q(t)|| • same direction

Moving Objects Databases (MOD) [Wolfson et al., 1997, Su et al., 2001]

Query languages: • SQL3 [Forlizzi et al, SIGMOD 2000] • relational calculus with built in functions [Su et al., SSTD 2001] • temporal logic [Wolfson et al, ICDE 1997] Expressiveness: • vel(p), acc(p), moving direction, speed , distance are enough to express all temporal and topological queries • PTIME languages •precision/uncertainty/probability

Final Look

Bottum-up: • adding spatio-temporal constructs to existing spatial/GIS systems to cope with application demands • closure problems, interoperability Top-down: • develop a general model (e.g., a constraint model) with clean semantics, properties and query languages • will it be used?

More information at:

http://alpha.luc.ac.be/~lucp1265/ [email protected]

Spatial and spatio-temporal data models for GIS

Transcript Spatial and spatio-temporal data models for GIS

Spatial and Spatio-Temporal Data Models for GIS

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