Researches on Spatiotemporal

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1 Researches on Spatiotemporal modelling at the Geomatics Unit Roland Billen and Pierre Hallot (ULg) pril 19, 2013 Systems & Modeling seminar series Montefiore Institute, ULg

2 TOC Who are we? Definitions Well-known topological relationships model Projective relationships Spatio-temporal modeling

4 Cartographie -

5 Géodésie et GNSS Nouvelle constellation GLILEO Météorologie spatiale influençant la propagation des ondes électromagnétique Profil de densité électronique affectant la propagation des signaux GNSS 5

6 Télédétection Classification des bâtiments satellitaires stéréo à très haute résolution Projet LandSafe ES. Représentation du relief lunaire 6

7 SIG et analyse spatiale 7 Crime mapping analyse spatiale dans le cadre tueurs du Brabant»

8 Base de données spatiales et SIG Indoor LoD 1 Indoor LoD 2 Indoor LoD 3 Modélisation 3D utilisant CityGML enrichi Logiciel Web2GIS (ULg) de conception et gestion de SIG

9 géographique Modèle basé sur spatio-temporel Modèle de relations projectives ternaires 9 Modèle de relations topologiques 3D

10 Topométrie / lasergrammétrie Logiciel (ULg) de levé rapide topo-photographique Reconstitution 3D par Lasergrammétrie terrestre Cathédrale St-Paul Modèle 3D historique projet Virtual Leodium

11 Qualitative Spatial Reasoning

12 Definitions Saying that laska is km² is sufficiently exact quantitative information about size and distances in laska but very likely it is not meaningful in relation to the spatial knowledge of the average listener. On the other hand saying that laska alone is bigger than all the states of the East coast from Maine to Florida is cognitively more immediate

13 Definitions QSR is a branch of rtificial Intelligence (I), linked to Spatial Cognition, highly related to Geographical Information Science (GISc) and by extension to most aspects of geography. It is a particular (through its spatial component) subfield of Qualitative Reasoning (QR) and is often associated with Spatio-Temporal (Qualitative) Reasoning when time is considered.

14 Definitions Qualitative Reasoning is an approach for dealing with commonsense knowledge of the physical world without numerical computation. Its main goal is to make this knowledge explicit, so that given appropriate reasoning techniques, a computer could make predictions, diagnose and explain the behaviour of physical systems in a qualitative manner People natural language Formal models algorithmics GIS systems

15 Definitions the biggest challenge remains the development of calculi, allowing reasoning about objects in multidimensional space. The two main prevalent forms of qualitative reasoning are Composition Table (based on transitivity between relationships) and Conceptual Neighbourhood diagram (based on a continuity concept between relationships).

16 Background and Motivations Definition of many qualitative relations Topological: Lakes inside Scotland Projective: Cities between Glasgow and Edinburgh Lakes surrounded by mountains Shops on the right of the road Flags above the tree Metric: Edinburgh is east of Glasgow Edinburgh is not far from Glasgow

17 The 9-i model Boundary Interior Exterior

18 The 9-i model B B B B - B B B - disjoint - B B B - meet - B B B - - contains B B B - covers - B B B B B - - equal B B B B - overlap - B B B B - inside - B B B B - covered by

19 The 9-i model Conceptual neighbourhood diagram disjoint meet overlap coveredby cover inside equal contains

20 The 9-i model 33 line-line topological relationships

21 Dimensional Model l In 2002, we proposed a refinement of binary topological relations which could handle these types of configurations It was based on well-known concept of projective dimension is 0 geometry; the order of a point of convex set order 0 dimension is 2 order 1 order 1 order 2 l dimension is 1 order 0 order 1 order 0

22 Identified Relations inside contains disjoint equal

23 overlap Identified Relations coveredby cover meet 23

24 Conceptual Neighborhood Graph meet disjoint overlap disjoint inside coveredby equal cover contains meet overlap coveredby cover inside equal contains

25 Binary projective relations

26 Ternary projective relationships among points in R² Projective invariants Collinearity properties e.g., three points belong to the same line RO1 RO2 RO1 RO2 PO PO

27 Ternary projective relationships among points in R² Deriving other projective properties from collinearity U collinear aside rightside leftside inside outside between nonbetween before after

28 Ternary projective relationships among points in R² Partition of R² based on the two reference points Set of JEPD relationships (7) ls HP yz ou y z (, y ) y [ y, z ] z in bf bt yz ( z, yz ) af rs HP yz

29 Ternary projective relationships among regions in R² Still based on collinearity and reference objects shapes Set of JEPD relationships (34)

30 Ternary projective relationships among regions in R² Leftside(B,C) Before(B,C) Between(B,C) fter(b,c) Rightside(B,C) Inside(B,C) Outside(B,C) ls(,b,c) = ( ), bf(,b,c) = ( )

31 Ternary projective relationships among regions in R²

32 Reference Billen, R, & Van de Weghe, N. (2009). Qualitative spatial reasoning. In N., Thrift & R., Kitchin (Eds.), International Encyclopaedia of Human Geography (pp ). Elsevier. Billen, R, & Clementini, E. (2005). Semantics of Collinearity mong Regions. Lecture Notes in Computer Science, Billen, R, & Clementini, E. (2006). Projective relations in a 3D environment. Lecture Notes in Computer Science, 4197, Clementini, E, & Billen, R. (2006). Modeling and computing ternary projective relations between regions. IEEE Transactions on Knowledge and Data Engineering, 18(6), Billen, R, & Kurata, Y. (2008). Refining Topological Relations between Regions Considering Their Shapes. Lecture Notes in Computer Science, 5266/2008, Clementini, E, Skiadopoulos, S, Billen, R, & Tarquini, F. (2010). Reasoning System of Ternary Projective Relations. IEEE Transactions on Knowledge & Data Engineering, 22(2),

33 Spatiotemporal reasoning Example of identity across space and time. Pierre Hallot - 19 th of pril 2013

34 19/04/2013 Pierre Hallot 2

35 19/04/2013 Pierre Hallot 3

36 For our point of view, The cat exits The cat does not exist anymore 19/04/2013 Pierre Hallot 4

37 More about the cat Till when will the cat exist? - presence destroy its identity? If we remember the cat, is this relation sufficient to maintain its identity over time? 19/04/2013 Pierre Hallot 5

38 What about a geographical object? Does an object exist before its physical realisation? Does an objet exist after its physical destruction? What about the identity of an object which only appears once a while? 19/04/2013 Pierre Hallot 6

39 Does a geographical object may exist before after its physical realisation destruction? Study of identity across space and time 19/04/2013 Pierre Hallot 7

40 Outlines State- of- the- art review Objectives Object spatio- temporal state Relationships between spatio- temporal states Life and Motion Configuration LMC generalization Natural language interpretation 19/04/2013 Pierre Hallot 8

41 Identity 19/04/2013 Pierre Hallot 9

42 Objectives One object description Identity Spatiality Static Object identity modelling Objective 1 Data models Topology Projective Metric Dynamic Identity base change Objective 1 Shape evolution Spatial transformation Projections 19/04/2013 Pierre Hallot 10

43 Objectives Two objects relationships descriptions Relationship Object/Object Identity Space Objective 2 Static RCC 9- i CBM Dynamic Objective 3 Objective 4 QTC relative trajectories REMO 19/04/2013 Pierre Hallot 11

44 State of the art Objectives 3 Object spatio- temporal states Relationships between spatio- temporal states Life and Motion Configuration LMC generalisation Natural language interpretation 19/04/2013 Pierre Hallot 12

45 Workspace Defined as Visibility space Geographical space Conceptual space Mathematical space : 19/04/2013 Pierre Hallot 13

46 Workspace I B C H D G F E X 19/04/2013 Pierre Hallot 14

47 Workspace 19/04/2013 Pierre Hallot 15

48 Object spatio- temporal state Non- existent Non- present Present Transition 19/04/2013 Pierre Hallot 16

49 Conceptual representation forgot phase non- existence phase Ø existence phase transitions non- existence phase forgot phase 19/04/2013 Pierre Hallot 17

50 Conceptual representation E B np transition D p C phase de non- existence np p phase de non présence phase de présence 19/04/2013 Pierre Hallot 18

51 Conceptual representation Ø Ø B p r E D transition np C np p phase de non- existence phase de non présence phase de présence 19/04/2013 Pierre Hallot 19

52 Conceptual representation np p np p r t np p np p p np phase de non- existence phase de non présence np p phase de présence 19/04/2013 Pierre Hallot 20

53 Conceptual neighbourhood graph Existence Présence 19/04/2013 Pierre Hallot 21

54 Object spatio- temporal state t np t p 19/04/2013 Pierre Hallot 22

55 State of the art Objectives Object spatio- temporal states 4 Relationships between spatio- temporal states Life and Motion Configuration LMC generalisation Natural language interpretation 19/04/2013 Pierre Hallot 23

56 STS- i relationships 16 relationships between two objects Relationships between identity state of objects Possibility to take a spatial logic into account when objects are both present B, p B, np B, r r r r t B, pb, p pb, r r R = np pb, t pb, npb, B p npb, np npb, t npb, tb, p tb, np tb, t tb r r 19/04/2013 Pierre Hallot 24

57 B STS- i relationships B B B r r B t r B p r B np r B B B B B B B B r tb ttb ptb nptb B B B B r pb tpb ppb nppb B B B B r npb tnpb pnpb npnpb 19/04/2013 Pierre Hallot 25

58 CND 1 change, pb p, np, t,,tb,npb t,tb np,tb t,pb p,tb t,npb p,pb np,pb np,npb p,npb 19/04/2013 Pierre Hallot 26

59 CND 2 change, t,,tb np, pb p,,npb t,tb t,pb p,tb np,tb t,npb np,npb np,pb p,npb p,pb 19/04/2013 Pierre Hallot 27

60 CNDs combination pb, p, CND STSi- R np, t,,tb,npb t,tb np,tb t,pb p,tb t,npb p,pb np,pb np,npb p,npb Identity Based Change CND 9- i cover contain equal disjoint touch overlap covered CND QTC in 19/04/2013 Pierre Hallot 28

61 STS- i relationships, pb p, B np, t,,tb,npb t,tb np,tb t,pb p,tb t,npb p,pb np,pb np,npb p,npb 19/04/2013 Pierre Hallot 29

62 State of the art Objectives Object spatio- temporal states Relationships between spatio- temporal states 5 Life and Motion Configuration LMC generalisation Natural language interpretation 19/04/2013 Pierre Hallot 30

63 Life and motion configuration Formalization of identity relationships evolution between two objects Formal language Visual language Exhaustive computation of possible change LMC( n( R ( STS i)) n avec n N B 19/04/2013 Pierre Hallot 31

64 LMC LMC(B)={ppB d,ppb e,tpb,nppb, nppb,tpb,ppb e,ppb e} 3D temporal space t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 temps t B espace identitaire ppb d ppb e tpb nppb nppb tpb ppb e ppb e LMC(B)={ppB d,ppb e,,ppb d, tpb, pb} y Formalization t 1 t 2? t 3 t 4 t 5 B ppb d ppb e ppb d tpb pb x espace identitaire 19/04/2013 Pierre Hallot 32

65 LMC Visual language B W() W() W(B) W(B) ppbe ppbd ppbe R(B)=e 19/04/2013 Pierre Hallot 33

66 LMC Visual language ppbe tpb nppb B W() W() W(B) W(B) R(B)=e 19/04/2013 Pierre Hallot 34

67 Life and motion configuration B 19/04/2013 Pierre Hallot 35

68 Life and motion configuration time space space 19/04/2013 Pierre Hallot 36

69 State of the art Objectives Object spatio- temporal states Relationships between spatio- temporal states Life and Motion Configuration 6 LMC generalisation Natural language interpretation 19/04/2013 Pierre Hallot 37

70 LMC Generalization 9- i CBM 9- i+ Generalization condition LMC B, ppbe LCM (2,..., n 1) R B /04/2013 Pierre Hallot 38

71 Impossible relationships 8 topological relationships do not generalize life and motion configurations Impossible relationships in a spatio- temporal context Negative spatio- temporal condition: /B 0 - /B 0 - R {, } (,B) B 0 B B 0 B B - B - 19/04/2013 Pierre Hallot 39

72 State of the art Objectives Object spatio- temporal states Relationships between spatio- temporal states Life and Motion Configuration LMC generalisation 7 Natural language interpretation 19/04/2013 Pierre Hallot 40

73 Natural language interpretation Relationships Matrix configuration Natural language interpretation of 25 generalized relationships Repetitions Non- univocal definitions Lot of remaining information Complex description leur phase de présence ensemble. Les objets et B apparaissent, se rencontrent et disparaissent ensemble. 19/04/2013 Pierre Hallot 41

74 Natural language interpretation Relationships Matrix configuration More efficient interpretation Natural French language prepositions Rencontre Croisement Génération Capture Égalité Ignorance /B 0 - /B 0 - R {, } (,B)= B 0 B R {, } (,B)= B 0 B B - B - 19/04/2013 Pierre Hallot 42

75 Natural language interpretation Relationships Matrix configuration Spatial reasoning LMC interpretation /B 0 - /B 0 - R {, } (,B)= B 0 B R {, } (,B)= B 0 B B - B - 19/04/2013 Pierre Hallot 43

76 Natural language interpretation Spatio- temporal «meeting» 9- i CBM Projective 19/04/2013 Pierre Hallot 44

77 Natural language interpretation Relationships Matrix configuration Spatial reasoning LMC interpretation /B 0 - /B 0 - R {, } (,B)= B 0 B R {, } (,B)= B 0 B B - B - 19/04/2013 Pierre Hallot 45

78 Conclusions 4 research objectives completed Definition of identity across space and time - Modelling identity spatio- temporal state of one object - Definition of possible cases of existence and presence Study of spatio- temporal identity relationships between two objects - Spatio- temporal identity states relationships model - CNDs Decision trees 19/04/2013 Pierre Hallot 46

79 Conclusions 4 research objectives completed Study the temporal evolution of spatio- temporal identity relationship - Life and motion configuration model - Formal and iconic representation - Framework for spatio- temporal reasoning LMC applications - Generalization of spatio- temporal relationships - Natural language interpretation Useful for ontological spatio- temporal information definition 19/04/2013 Pierre Hallot 47

80 Outlook Composition table Completion of reasoning model Knowledge inference Take into account a complex objects spatiality Integration of spatial reasoning models to LMC 9- i CBM D- Workspace Perceived space Egocentric workspace definition Psychological perception of space Presence history Formal Semantic Practical Spatio- temporal footprints Study of spatio- temporal footprints relationships 19/04/2013 Pierre Hallot 48

81 Outlook Formal Semantic Practical Spatial cognition LMC interpretation Model cognitive value User panel perception of spatio- temporal information Interpretation of panel predicates FNRS research project 19/04/2013 Pierre Hallot 49

82 Outlook Formal Semantic Practical Practical implementation Prototype of LMC automatic computation Management of existence and presence CND collaboration Use of CND as spatio- temporal reasoning model selection 19/04/2013 Pierre Hallot 50

83 Thanks for the time interval shared together ppb d pnpb Even if for now, p B relationship between you and my presentation, I hope it will be for a long time. pnpb No cats was injured during this research. 19/04/2013 Pierre Hallot 51

84 Space Geometry Set theory Topology Projective Metric 19/04/2013 Pierre Hallot 52

85 Space Geometry Set theory Topology Projective Metric 19/04/2013 Pierre Hallot 53

86 Space Geometry Set theory Topology Projective Metric 19/04/2013 Pierre Hallot 54

87 Space Geometry Set theory Topology Projective Metric 19/04/2013 Pierre Hallot 55

88 Time Instant Interval xiomatization Galton Ligozat McDermott 19/04/2013 Pierre Hallot 56

89 Time Instant Interval xiomatization llen ctions Events Situation Calculus 19/04/2013 Pierre Hallot 57

90 Spatio- temporal reasoning Identity Combination Mereology Existent Visible Invisible ctive actor spy Inactive scenery camouflage Non- existent ctive ghost fable Inactive mirage myth Hornsby, K. and Egenhofer M. (2000) Campos, J. et al. (2003) 19/04/2013 Pierre Hallot 58

91 Spatio- temporal reasoning Identity Combination Mereology I : X DC, EC Y, I : Y TPP Z, J: X PO Y, J: Y DC Z Claramunt, C. and Jiang, B (2001) Gerevini,. and Nebel, B. (2002) 19/04/2013 Pierre Hallot 59

92 Spatio- temporal reasoning Identity Combination Mereology Muller, P. (1999) Van de Weghe et al. (2006) 19/04/2013 Pierre Hallot 60

93 Research objectives 1. Formalization of identity spatio- temporal states 2. Spatio- temporal reasoning model based on identity state evolution across space- time. 3. Study of identity spatio- temporal states relationships. 4. Definition of a visual language describing spatio- temporal information evolution. 19/04/2013 Pierre Hallot 61

94 Research assumptions No backward in time time No instantaneous movement time No resurrection space? 19/04/2013 Pierre Hallot 62

95 Dominance theory Espace qualitatif y Conceptual representation Espace qualitatif y Espace qualitatif de présence x Espace qualitatif de présence x Dominance theory Dominance space Existence >< Holds, i Lim t, i Holds at 0, t 0 Holds, i Lim t, i Holds at 0, t 0 + +,>< donc Holds, i Lim t, i Holds at 0, t 0 et 0,>< S Y 0 ou 0 -,>< 19/04/2013 Pierre Hallot 63

96 Dominance theory (once again) Objet B - >< +>< 0>< >< - ><,- >< - ><,+>< - ><,0>< - ><,- 0 - ><,+0 - ><,00 S B,,0, 0, 0,00,,,0, 0, 0,00, 0, 0,0 0, 00, 00,000, 0, 0, 0 0, 0 0, 0 0, 00 0, 0, 0, 0 0, 0 0, 0 0, 00 0, 00, 00, 0 00, 000, 000, >< ><,- >< +><,+>< +><,0>< +><,- 0 +><,+0 +><,00 0>< 0><,- >< 0><,+>< 0><,0>< 0><,- 0 0><,+0 0><,00-0,- >< - 0,+>< - 0,0>< - 0,- 0-0,+0-0,00 +0,- >< +0,+>< +0,0>< +0,- 0 +0,+0 +0, ,- >< 00,+>< 00,0>< 00,- 0 00,+0 00,00 19/04/2013 Pierre Hallot 64

Spatio-temporal configurations of dynamics points in a 1D space

Spatio-temporal configurations of dynamics points in a 1D space Pierre Hallot 1, Roland Billen 1 1 Geomatics Unit, University of Liège, Allée du 6 Août, 17 B-4000 Liège Belgium {P.Hallot@ulg.ac.be, rbillen@ulg.ac.be}