Landmark-Based Qualitative Reference System - Semantic Scholar
Landmark-based Qualitative Reference System Xiaoming Wang , Yu Liu, Zhenji Gao and Lun Wu Institute of Remote Sensing and Geographic Information System Peking University Beijing, P.R. China [email protected] Abstract—It becomes more and more important for next generation of GIS to develop cognition-accordant data models which is properly guided by the way how human actually thinks about geographic space. Thus, a new method named landmarkbased qualitative reference (LBQR) system is introduced to express qualitative positional information in this paper. Qualitative position can be determined by one or several landmarks which are calculated adaptively according to the target object under LBQR framework. In LBQR framework, qualitative coordinates (QC) are used to represent the position of the target object. QC is defined based on cardinal direction relations between target object and one or several landmarks adjacent to it. At first, Voronoi model is used to determine the reference objects for each target object. Then cardinal direction relations are modeled by minimal bounding rectangle method or cone-based method according to the geometry type of each reference object respectively. Last, an experiment is carried out to evaluate whether the Voronoi model conforms to human spatial cognition. Keywords- qualitative spatial reasoning; landmarks; Voronoi diagram; landmark-based qualitative reference
I.
INTRODUCTION
Nowadays, knowledge about position in geographic space is commonly represented by the combination of orientation and distance relations between target objects and a given reference object in qualitative spatial reasoning (QSR) [1] [2] [3]. It becomes more and more important for GIS to develop cognition-accordant formal data models which is properly guided by the way how human actually thinks about geographic space [4] [5]. As argued in [6], computational perspective and cognitive perspective should be integrated . Landmark plays distinguished role for the acquisition and representation of commonsense spatial knowledge in everyday life [7] [8] [9]. Spatial knowledge acquisition often begins with landmarks knowledge [10]. Order information between landmarks, together with their locations relative to one other, consist of the foundation of spatial mental models [11]. Previous work on landmark-based qualitative positioning includes qualitative vector space (QVS) presented in [6]. Under QVS, the qualitative position of target object is modeled by the distance relations between it and each element of the reference framework, which is the set of landmarks. However, human usually use cardinal direction relations between target objects and one or several landmarks adjacent to it rather than QVS method to locate places. For example, we often say that
Vietnam is to the south of China, hardly say that Vietnam is near China and whilst far from U.S.A.. In this paper, a new method named landmark-based qualitative reference (LBQR) system is introduced. Compared with the QVS approach mentioned above, LBQR system provides a framework to position target object dynamically. Qualitative position can be determined by one or several landmarks which are calculated adaptively according to the target object in LBQR framework. Therefore LBQR is more natural and intuitive. Following the description of LBQR in §2, formal representation methods of LBQR are presented in §3. Cognitive experiment to evaluate the representing method is presented in §4. Finally, Conclusions and future works are discussed in §5. II.
DESCRIPTION OF LBQR SYSTEM
A. Definition of landmark There are three kinds of spatial knowledge: landmark knowledge, route knowledge and survey knowledge [10]. The term “landmark” forms the basis of theories of spatial cognition and wayfinding [9]. Anchor–point hypothesis assumes the existence of a set of landmarks [8]. The set of landmarks forms a reference system to represent the space in brief and locate non-landmark places in detail. Landmarks can serve as an organizing concept for space or as a navigational aid as elements of this reference system [12]. In organizing space, landmarks can represent a cluster of objects at a higher level of abstraction or scale and present an anchor for understand local spatial relations. In navigational aid, landmarks provide orientation cues and verification of route progress. Under this reference system, landmarks serve to define the location of adjacent places as reference objects (ROs) [7]; non-landmark places are target objects (TOs), which can be discriminated simply with reference to their locations relative to the ROs [6]. Landmarks are defined as prominent, identifying features in a geospatial environment, which provide a means for locating oneself and establishing goals in a space [9]. However, not all landmarks are singularities or prominences of spatial location in an environment, an element may also be a landmark based on its content, meaning, role, or historical and cultural significance [13]. Clearly, the selection of landmarks is dependent on context and personal preference.
0-7803-9051-2/05/$20.00 (C) 2005 IEEE
B. Definition of LBQR system According to the cognitive description, TOs are usually positioned by near ROs in mental map. It is impossible and unnecessary to locate a TO by all ROs no matter they are near or far. Cardinal direction relations between a TO and one or several ROs nearby are used to qualitatively position the TO. Meanwhile, considering the complexity for selection of landmarks, ROs could be obtained through human-computer interaction in this study. Let P be the set of places P1, P2, …, Pn in a geographic space S. R is a subset of P and elements of R are landmarks selected from P to serve as candidate reference objects. N is the cardinality of R. T = P – R, is the set of non-landmark places that should be located by landmarks. Qualitative coordinate (QC) is applied to represent the qualitative position of the target object. QC is composed of at least one 2-tuples consisting of one reference object, the cardinal direction relation between the reference object and the target object. The number of the tuples equals to the number of reference objects.
A. Determing ROs by voronoi model The Voronoi model of space concords fairly with the perceptual and linguistic spaces of humans [14], and has been used to model the neighboring relationships in GIS [15]. Voronoi model divides the space into N regions called Voronoi polygons, each of which is associated with a generation seed. Any a point in a Voronoi polygon is closer to its generation seeds than to any other generation seeds. Considering the semiquantity and dynamical characteristic of nearness relationship [16], Voronoi model is used to determine the ROs of Ti. Landmarks in R are taken as seeds to generate Voronoi diagram in S, thus S is divided into N partitions with each landmark related to one Voronoi polygon. The partition related to Rj is denoted by V(Rj). Under this division, S is could be treated as a continuous medium filled with nearness fields generated by landmarks. As shown in Fig. 2, S consists of five Voronoi regions generated from five landmarks, where Ti is located in. R5
For each Ti∈T, its qualitative coordinates, denoted QC(Ti), is formally defined as
QC (Ti ) = {< R j , {CDR} >}
T5 R1
(1)
where R4
CDR is the cardinal direction relation between Ti and Rj and it is a nonempty subset of cardinal direction relation symbols {E, W, S, N, NE, NW, SE, SW, O}, where O means “same position”. The qualitative positional information can be described as the cardinal direction relations between TO and one or several ROs near by in (1). For example, the qualitative positional information of T1 in Fig. 1 could be QC (T1 ) = {< R1 , {SE} >, < R2 , { N , NE} >} . It means that T1 is near R1 and to the southeast of R1, at the same time, T1 is near R2 and to the North and Northeast of R2. R3
R1 T1 R2
R3
Figure 1. Example of qualitative coordinates
FORMAL REPRESENTATION METHODS OF LBQRS
In order to generate the qualitative coordinates for Ti, its ROs should be determined first, and then the CDR between Ti and Rj should be modeled.
T1
T2
Figure 2. Voronoi model and ROs determing method
Based on such Voronoi partition, for any Tj, its ROs can be one or several landmarks in R according to the topological relations between Ti and V(Rj). If the geometry type of Ti is point, its ROs can be determined according to the following three rules: •
If Ti is inside of V(Rj), only landmark Rj can be its RO. For example, R1 is the RO of T1 in Fig.2.
•
If Ti touches the boundary of two Voronoi regions, two landmarks could be its ROs. In this case, Ti touches each V(Rj) of the two ROs. For example, R1 and R3 are the ROs of T2 in Fig.2.
•
If Ti equals the vertex of three Voronoi regions, three landmarks is its ROs. In this case, Ti touches each V(Rj) of the three ROs. For example, R1, R2 and R3 are the ROs of T3 in Fig.2.
T2 R4
R2
T3
T6
Rj R, is a landmark calculated as a RO to locate Ti, which is adjacent to Rj ;
III.
T4
Applying similar method, the ROs can be determined when the geometry type of Tj is polygon. •
If Ti is within V(Rj), Rj is its RO, e.g. T4’s RO is R1 in Fig.2.
•
If Ti overlaps with 2 or 3 Voronoi regions, the corresponding landmarks can be its ROs, e.g., R1 and R3 are the ROs of T5 whilst R1, R4 and R5 are the ROs of T6 in Fig.2.
B. Modeling CDR between Ti and Rj Several methods have been presented to model cardinal direction relation (CDR), such as project-based method [17], cone-based method [18] [1] and MBR-based method [19] [20]. According to the geometry type of RO, Cone-based method or MBR-based is adopted respectively. Space can be divided into nine partitions corresponding to the nine symbols of cardinal direction relation by each method as shown in Fig.3. Especially pointed out, the “O” partition is itself when the geometry type of RO is point.
•
If Ti only intersects with the boundary of a partition of Rj when they are all polygons, the corresponding symbol can not be an element of CDR, e.g., CDR of T8 and R2 is {S, SE} in Fig.4.
C. Resulotion of LBQR system At last, we discuss the resolution problem of LBQR system in brief. Resolution is an important index to evaluate a reference system. For a LBQR system, it could be estimated coarsely. At first we assume the space size is S, there are n landmarks. An ideal case is that n Voronoi polygons partition the space near equally. Then the 9 CDR divide each polygon into 9 parts. So the average resolution of LBQR system is S/9n. This is much more acceptable than a pure place-name reference system. IV.
COGNITIVE EXPERIMENT BASED VALIDATION FOR
Figure 3. Cone-based method and MBR-based method
VORONOI MODEL
Based on the partitions mentioned above, CDR of TO and RO can be a nonempty subset of cardinal direction relation symbols according to the intersection status between TO and nine partitions of RO. Through the calculation of direction relation matrix, CDR can be obtained easily. For example, according to the direction relation matrixes shown in Fig.5 of T1 and R1, T6 and R2 in Fig.4, the CDR of T1 and R1, T6 and R2 are {W}, {NW, N, W, O} respectively.
The development LBQR system should accord to the developing framework of naive geography [4]. After the formalism of LBQR, the testing and analyzing should be carried out to assess how closely the formalizations match human performance. Since cone-based method and MBRbased method are popular in modeling cardinal direction relation, experiments focus on the validation for Voronoi model.
Figure 4. Example of CDR between Ti and Rj
∅ ∅ ∅ ¬∅ ∅ ∅ ∅ ∅ ∅
¬∅ ¬∅ ∅ ¬∅ ¬∅ ∅ ∅ ∅ ∅
Figure 5. Direction relation matrixes of T2 and R1(left), T6 and R2(right)
In these two methods, there are some special cases should be mentioned. •
If a point feature Rj is within Ti, it is inapposite if CDR includes all the nine symbols. The CDR can be usually {O} in this case. T3 and R1in Fig.4 is an example of this case.
•
If a point feature Rj touches Ti, the intersection status of Ti and “O” partition of Rj is ¬∅ elements. For example, CDR of T4 and R1 is {NE, E, SE, O} in Fig.4.
•
If Ti touches shared boundary of partitions of Rj when it is a point, the intersection status of Ti and partitions of Rj are all ¬∅ elements. For example, CDR of T2 and R1 is {SW, S}; CDR of T5 and R2 is {N, NE}; CDR of T7 and R2 is {W, O, SW, S} in Fig.4.
A. Cognitive experiment The experiment was based on the scenario presented in Fig.2. In order to avoid the influence of Voronoi partitions, they are removed in the questionnaire. The purpose of cognitive experiment was to validate whether the Voronoi model conforms to human spatial cognition. Fifty human subjects were chosen. They are students from department of geography of Peking University. The heading instructions are given below: “When is it true to say that a non-landmark place is near a landmark place in the scenario? We are interested in your view of the matter. Please indicate, by ticking the sentence below, for which of the following sentences is it true to say that a nonlandmark place is near a landmark place.” According to the calculation by Voronoi method, twelve sentences are given. The sequences are random to ensure that no explicit cross-referencing could be made. Subjects were asked not to deliberate too long in any a sentence. B. Analysis of results Eight sentences were ticked by all subjects. Sentences “T2 is near R3”, “T3 is near R2”, “T6 is near R5”, “T6 is near R1” were ticked by 48 subjects, 41 subjects, 37 subjects and 35 subjects respectively. The overall ticked ratio is 93.5%. From the results, we can conclude that the Voronoi model is practicable in most cases. But the exceptional cases should be analyzed further. By discussions with human subjects, our views on exceptional cases are below.
•
Vision distortion is probably the main reason for sentence “T2 is near R3” is not ticked by two subjects
•
Sentence “T3 is near R2” is not ticked by nine subjects is because geometry type of R2 is polygon and some subjects measured from the center of R2.
•
Most partition of T6 is located in V(R4) is the main reason for sentences “T6 is near R5” and “T6 is near R1” are not ticked by some subjects. In this case, minimum distance between T6 and R4is shorter than minimum distance between T6 and R5 or T6 and R1. V.
CONCLUSIONS AND FUTURE RESEARCH
Landmark plays distinguished role for acquisition and representation of commonsense spatial knowledge. The aim of this paper is to present qualitative positional representation based on landmarks which is cognition-accordant. Definition and representation methods of LBQR system is presented based on landmark definition in this paper. At last, cognitive experiment is presented to prove our formalizations match human spatial cognition. Based on the work of this paper, qualitative descriptions emphasizing on landmarks of local survey knowledge could be made. However, pieces of landmark centered survey knowledge need to be integrated to global knowledge in some cases. The future work is to explore how local knowledge can be integrated to global knowledge.
[7]
[8]
[9]
[10]
[11]
[12]
[13] [14]
[15]
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A. U Frank, “Qualitative spatial qeasoning about distances and directions in geographic space,” Journal of Visual Languages and Computing., vol. 3, pp. 343-371, 1992 K. Zimmermann, “Enhancing qualitative spatial reasoning- combining orientation and distance,” In Spatial Information Theory: A Theoretical Basis for GIS, A.U Frank, I. Campari eds, Lecture Notes in Computer Science, vol. 716, Berlin: Springer-Verlag, pp. 69-76, 1993 E. Clementini. P. Felice, D. Hernandez, “Qualitative representation of positional information,” Artifical Intelligence, vol. 95, pp. 317-356, 1997 M. Egenhofer, D M. Mark, “Naive geography,” In Spatial Information Theory - A Theoretical Basis for GIS, A. Frank, W. Kuhn eds, Lecture Notes in Computer Science, vol. 988, Berlin: Springer-Verlag, pp. 1-15, 1995 M. Egenhofer, J. Glasgow, O. Gunther, et al, “Progress in computational method for representing geographical concepts,” INT. J. Geographical Information Science, vol. 13, pp. 775-796, 1999 M. Duckham, M. Worboys, “Computational structure in three-valued nearness relations,”. In Spatial Information Theory - Cognitive and
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Computational Foundations of Geographic Information Science, D.R. Montello eds, Lecture Notes in Computer Science, vol. 2005, Berlin: Springer-Verlag, pp. 76-91, 2001 E.K. Sadalla, W.J. Burroughs, and L.J. Staplin, “Reference points in spatial cognition,” Journal of Experimental Psychology : HumanLearning and Memory, vol.6(5), pp. 516-528, 1980 H. Couclelis, R.G. Golledge, N. Gale, et al, “Exploring the anchor–point hypothesis of spatial cognition,” Journal of Environmental Psychology, vol. 7, pp. 99-122, 1987 E.S. Molly, C. H.Stephen, “The Natures of landmarks for real and electronic space,” In Spatial Information Theory - Cognitive and Computational Foundations of Geographic Information Science, C. Freksa, D.M. Mark eds, Lecture Notes in Computer Science, vol. 1661, Berlin: Springer-Verlag, pp. 37-50, 1999 D.R. Montello, “Spatial cognition,” In International Encyclopedia of the Social & Behavioral Science, N.J. Smelse, P.B. Baltes eds, Oxford: Pergamon Press, pp. 14771-14775, 2001 B. Tversky, “Cognitive maps, cognitive collages,and spatial mental models,” In Spatial Information Theory - A Theoretical Basis for GIS, A. Frank, I.Campari eds, Lecture Notes in Computer Science, vol. 716, Berlin: Springer-Verlag, pp. 14-22, 1993 R.G. Golledge, “Human wayfinding and cognitive maps,” In Wayfinding Behavior: Cognitive Mapping and Other Spatial Processes, R.G. Golledge eds, Baltimore, Maryland: Johns Hopkins University, pp. 5-45, 1999 D. Appleyard, “Why buildings are known,” Environment and behaviro, vol. 1, pp. 131-156, 1969 G. Edwards, “The voronoi model and cultural space: applications to the social science and humanities,” In Spatial Information Theory - A Theoretical Basis for GIS, A. Frank, I.Campari eds, Lecture Notes in Computer Science, vol. 716, Berlin: Springer-Verlag, pp. 202-214, 1993 C.M. Gold, “The meaning of “Neighbor,” In Theory and Methods of Spatial-Temporal Reasoning in Geographical Space, A.U. Frank, I. Campari, and U. Formentini eds, Lecture Notes in Computer Science, vol. 639, Beilin: Springer Verlag, pp. 220-235, 1992 M. Gahegan, “Proximity Operators for Qualitative Spatial Reasoning,” In Spatial Information Theory - A Theoretical Basis for GIS, A. Frank, W. Kuhn eds, Lecture Notes in Computer Science, vol. 988, Berlin: Springer-Verlag, pp. 31-44, 1995 D. Papadias, T. Sellis, “Qualitative representation of spatial knowledge in two-dimensional space,” Very Large Data Bases Journal, Special Issue on Spatial Database, vol. 3(4), pp. 479-516, 1994 C. Hernandez, Qualtiative Representation of Spatial Knowledge, Lecture notes in Artificial Intelligence, vol. 804, New York: Springer Verlag, 1994. R. Goyal, M.J. Egenhofer, “Similarity of cardinal directions,” In Advances in Spatial and Temporal Databases, C.S. Jensen, M. Schneider, B. Seeger, V.J. Tsotras eds, Lecture Notes in Computer Science, vol. 2121, Berlin: Springer Verlag, pp. 36-55, 2001. S. Skiadopoulos, M. Koubarakis, “Composing cardinal direction relations,” In SSTD-2001, C.S. Jensen, M. Schneider, B. Seeger, V.J. Tsotras eds, Lecture Notes in Computer Science, vol. 2121, Berlin: Springer Verlag, pp. 299-317, 2001
I.
INTRODUCTION
Nowadays, knowledge about position in geographic space is commonly represented by the combination of orientation and distance relations between target objects and a given reference object in qualitative spatial reasoning (QSR) [1] [2] [3]. It becomes more and more important for GIS to develop cognition-accordant formal data models which is properly guided by the way how human actually thinks about geographic space [4] [5]. As argued in [6], computational perspective and cognitive perspective should be integrated . Landmark plays distinguished role for the acquisition and representation of commonsense spatial knowledge in everyday life [7] [8] [9]. Spatial knowledge acquisition often begins with landmarks knowledge [10]. Order information between landmarks, together with their locations relative to one other, consist of the foundation of spatial mental models [11]. Previous work on landmark-based qualitative positioning includes qualitative vector space (QVS) presented in [6]. Under QVS, the qualitative position of target object is modeled by the distance relations between it and each element of the reference framework, which is the set of landmarks. However, human usually use cardinal direction relations between target objects and one or several landmarks adjacent to it rather than QVS method to locate places. For example, we often say that
Vietnam is to the south of China, hardly say that Vietnam is near China and whilst far from U.S.A.. In this paper, a new method named landmark-based qualitative reference (LBQR) system is introduced. Compared with the QVS approach mentioned above, LBQR system provides a framework to position target object dynamically. Qualitative position can be determined by one or several landmarks which are calculated adaptively according to the target object in LBQR framework. Therefore LBQR is more natural and intuitive. Following the description of LBQR in §2, formal representation methods of LBQR are presented in §3. Cognitive experiment to evaluate the representing method is presented in §4. Finally, Conclusions and future works are discussed in §5. II.
DESCRIPTION OF LBQR SYSTEM
A. Definition of landmark There are three kinds of spatial knowledge: landmark knowledge, route knowledge and survey knowledge [10]. The term “landmark” forms the basis of theories of spatial cognition and wayfinding [9]. Anchor–point hypothesis assumes the existence of a set of landmarks [8]. The set of landmarks forms a reference system to represent the space in brief and locate non-landmark places in detail. Landmarks can serve as an organizing concept for space or as a navigational aid as elements of this reference system [12]. In organizing space, landmarks can represent a cluster of objects at a higher level of abstraction or scale and present an anchor for understand local spatial relations. In navigational aid, landmarks provide orientation cues and verification of route progress. Under this reference system, landmarks serve to define the location of adjacent places as reference objects (ROs) [7]; non-landmark places are target objects (TOs), which can be discriminated simply with reference to their locations relative to the ROs [6]. Landmarks are defined as prominent, identifying features in a geospatial environment, which provide a means for locating oneself and establishing goals in a space [9]. However, not all landmarks are singularities or prominences of spatial location in an environment, an element may also be a landmark based on its content, meaning, role, or historical and cultural significance [13]. Clearly, the selection of landmarks is dependent on context and personal preference.
0-7803-9051-2/05/$20.00 (C) 2005 IEEE
B. Definition of LBQR system According to the cognitive description, TOs are usually positioned by near ROs in mental map. It is impossible and unnecessary to locate a TO by all ROs no matter they are near or far. Cardinal direction relations between a TO and one or several ROs nearby are used to qualitatively position the TO. Meanwhile, considering the complexity for selection of landmarks, ROs could be obtained through human-computer interaction in this study. Let P be the set of places P1, P2, …, Pn in a geographic space S. R is a subset of P and elements of R are landmarks selected from P to serve as candidate reference objects. N is the cardinality of R. T = P – R, is the set of non-landmark places that should be located by landmarks. Qualitative coordinate (QC) is applied to represent the qualitative position of the target object. QC is composed of at least one 2-tuples consisting of one reference object, the cardinal direction relation between the reference object and the target object. The number of the tuples equals to the number of reference objects.
A. Determing ROs by voronoi model The Voronoi model of space concords fairly with the perceptual and linguistic spaces of humans [14], and has been used to model the neighboring relationships in GIS [15]. Voronoi model divides the space into N regions called Voronoi polygons, each of which is associated with a generation seed. Any a point in a Voronoi polygon is closer to its generation seeds than to any other generation seeds. Considering the semiquantity and dynamical characteristic of nearness relationship [16], Voronoi model is used to determine the ROs of Ti. Landmarks in R are taken as seeds to generate Voronoi diagram in S, thus S is divided into N partitions with each landmark related to one Voronoi polygon. The partition related to Rj is denoted by V(Rj). Under this division, S is could be treated as a continuous medium filled with nearness fields generated by landmarks. As shown in Fig. 2, S consists of five Voronoi regions generated from five landmarks, where Ti is located in. R5
For each Ti∈T, its qualitative coordinates, denoted QC(Ti), is formally defined as
QC (Ti ) = {< R j , {CDR} >}
T5 R1
(1)
where R4
CDR is the cardinal direction relation between Ti and Rj and it is a nonempty subset of cardinal direction relation symbols {E, W, S, N, NE, NW, SE, SW, O}, where O means “same position”. The qualitative positional information can be described as the cardinal direction relations between TO and one or several ROs near by in (1). For example, the qualitative positional information of T1 in Fig. 1 could be QC (T1 ) = {< R1 , {SE} >, < R2 , { N , NE} >} . It means that T1 is near R1 and to the southeast of R1, at the same time, T1 is near R2 and to the North and Northeast of R2. R3
R1 T1 R2
R3
Figure 1. Example of qualitative coordinates
FORMAL REPRESENTATION METHODS OF LBQRS
In order to generate the qualitative coordinates for Ti, its ROs should be determined first, and then the CDR between Ti and Rj should be modeled.
T1
T2
Figure 2. Voronoi model and ROs determing method
Based on such Voronoi partition, for any Tj, its ROs can be one or several landmarks in R according to the topological relations between Ti and V(Rj). If the geometry type of Ti is point, its ROs can be determined according to the following three rules: •
If Ti is inside of V(Rj), only landmark Rj can be its RO. For example, R1 is the RO of T1 in Fig.2.
•
If Ti touches the boundary of two Voronoi regions, two landmarks could be its ROs. In this case, Ti touches each V(Rj) of the two ROs. For example, R1 and R3 are the ROs of T2 in Fig.2.
•
If Ti equals the vertex of three Voronoi regions, three landmarks is its ROs. In this case, Ti touches each V(Rj) of the three ROs. For example, R1, R2 and R3 are the ROs of T3 in Fig.2.
T2 R4
R2
T3
T6
Rj R, is a landmark calculated as a RO to locate Ti, which is adjacent to Rj ;
III.
T4
Applying similar method, the ROs can be determined when the geometry type of Tj is polygon. •
If Ti is within V(Rj), Rj is its RO, e.g. T4’s RO is R1 in Fig.2.
•
If Ti overlaps with 2 or 3 Voronoi regions, the corresponding landmarks can be its ROs, e.g., R1 and R3 are the ROs of T5 whilst R1, R4 and R5 are the ROs of T6 in Fig.2.
B. Modeling CDR between Ti and Rj Several methods have been presented to model cardinal direction relation (CDR), such as project-based method [17], cone-based method [18] [1] and MBR-based method [19] [20]. According to the geometry type of RO, Cone-based method or MBR-based is adopted respectively. Space can be divided into nine partitions corresponding to the nine symbols of cardinal direction relation by each method as shown in Fig.3. Especially pointed out, the “O” partition is itself when the geometry type of RO is point.
•
If Ti only intersects with the boundary of a partition of Rj when they are all polygons, the corresponding symbol can not be an element of CDR, e.g., CDR of T8 and R2 is {S, SE} in Fig.4.
C. Resulotion of LBQR system At last, we discuss the resolution problem of LBQR system in brief. Resolution is an important index to evaluate a reference system. For a LBQR system, it could be estimated coarsely. At first we assume the space size is S, there are n landmarks. An ideal case is that n Voronoi polygons partition the space near equally. Then the 9 CDR divide each polygon into 9 parts. So the average resolution of LBQR system is S/9n. This is much more acceptable than a pure place-name reference system. IV.
COGNITIVE EXPERIMENT BASED VALIDATION FOR
Figure 3. Cone-based method and MBR-based method
VORONOI MODEL
Based on the partitions mentioned above, CDR of TO and RO can be a nonempty subset of cardinal direction relation symbols according to the intersection status between TO and nine partitions of RO. Through the calculation of direction relation matrix, CDR can be obtained easily. For example, according to the direction relation matrixes shown in Fig.5 of T1 and R1, T6 and R2 in Fig.4, the CDR of T1 and R1, T6 and R2 are {W}, {NW, N, W, O} respectively.
The development LBQR system should accord to the developing framework of naive geography [4]. After the formalism of LBQR, the testing and analyzing should be carried out to assess how closely the formalizations match human performance. Since cone-based method and MBRbased method are popular in modeling cardinal direction relation, experiments focus on the validation for Voronoi model.
Figure 4. Example of CDR between Ti and Rj
∅ ∅ ∅ ¬∅ ∅ ∅ ∅ ∅ ∅
¬∅ ¬∅ ∅ ¬∅ ¬∅ ∅ ∅ ∅ ∅
Figure 5. Direction relation matrixes of T2 and R1(left), T6 and R2(right)
In these two methods, there are some special cases should be mentioned. •
If a point feature Rj is within Ti, it is inapposite if CDR includes all the nine symbols. The CDR can be usually {O} in this case. T3 and R1in Fig.4 is an example of this case.
•
If a point feature Rj touches Ti, the intersection status of Ti and “O” partition of Rj is ¬∅ elements. For example, CDR of T4 and R1 is {NE, E, SE, O} in Fig.4.
•
If Ti touches shared boundary of partitions of Rj when it is a point, the intersection status of Ti and partitions of Rj are all ¬∅ elements. For example, CDR of T2 and R1 is {SW, S}; CDR of T5 and R2 is {N, NE}; CDR of T7 and R2 is {W, O, SW, S} in Fig.4.
A. Cognitive experiment The experiment was based on the scenario presented in Fig.2. In order to avoid the influence of Voronoi partitions, they are removed in the questionnaire. The purpose of cognitive experiment was to validate whether the Voronoi model conforms to human spatial cognition. Fifty human subjects were chosen. They are students from department of geography of Peking University. The heading instructions are given below: “When is it true to say that a non-landmark place is near a landmark place in the scenario? We are interested in your view of the matter. Please indicate, by ticking the sentence below, for which of the following sentences is it true to say that a nonlandmark place is near a landmark place.” According to the calculation by Voronoi method, twelve sentences are given. The sequences are random to ensure that no explicit cross-referencing could be made. Subjects were asked not to deliberate too long in any a sentence. B. Analysis of results Eight sentences were ticked by all subjects. Sentences “T2 is near R3”, “T3 is near R2”, “T6 is near R5”, “T6 is near R1” were ticked by 48 subjects, 41 subjects, 37 subjects and 35 subjects respectively. The overall ticked ratio is 93.5%. From the results, we can conclude that the Voronoi model is practicable in most cases. But the exceptional cases should be analyzed further. By discussions with human subjects, our views on exceptional cases are below.
•
Vision distortion is probably the main reason for sentence “T2 is near R3” is not ticked by two subjects
•
Sentence “T3 is near R2” is not ticked by nine subjects is because geometry type of R2 is polygon and some subjects measured from the center of R2.
•
Most partition of T6 is located in V(R4) is the main reason for sentences “T6 is near R5” and “T6 is near R1” are not ticked by some subjects. In this case, minimum distance between T6 and R4is shorter than minimum distance between T6 and R5 or T6 and R1. V.
CONCLUSIONS AND FUTURE RESEARCH
Landmark plays distinguished role for acquisition and representation of commonsense spatial knowledge. The aim of this paper is to present qualitative positional representation based on landmarks which is cognition-accordant. Definition and representation methods of LBQR system is presented based on landmark definition in this paper. At last, cognitive experiment is presented to prove our formalizations match human spatial cognition. Based on the work of this paper, qualitative descriptions emphasizing on landmarks of local survey knowledge could be made. However, pieces of landmark centered survey knowledge need to be integrated to global knowledge in some cases. The future work is to explore how local knowledge can be integrated to global knowledge.
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