InformatIon ScIence Reference Part 2 pdf

Querying GML Table Definition of predicates Domain Operator Topologically closed geometries Disjoint(a,b) ⇔ a ∩ b = ∅ a and b applies to the A/A, L/L, L/A, P/A and P/L groups of relationships Touches(a,b) ⇔ (I(a)∩I(b) = ∅) ∧ a and b applies to the P/L, P/A, L/L and L/A Crosses(a,b) ⇔ (dim(I(a) ∩ I(b)) < max(dim(I(a)), dim(I(b)))) ∧ (a ∩ b ≠a ) ∧ (a ∩ b ≠b) a and b applies to the A/A, P/A,L/A,L/L Within(a,b) ⇔ (a ∩ b = a) ∧ (I(a) ∩I(b) ≠ ∅) a and b applies to the A/A, P/A,L/A,L/L Contains(a,b) ⇔ Within(b,a) a and b applies to the A/A, P/A,L/A,L/L Intersects(a,b) ⇔ not.Disjoint(a,b) distances between spatial objects and calculating relative direction Some other forms of spatial predicates are realized as a set of functions The basic syntax of GML-QL is the same as that of XQuery, with added spatial functions The following are some examples of GML-QL queries Query 1: List the name, population, and area of each country for the file “country.XML” FOR $c I N d oc ument(“Cou nt r y.X ML”)  R ET UR N $c/ Na me/te xt( )  $c/pop  Area($c/sha pe) Query 2: The St Lawrence River can supply water to the cities which are within 300 km, if needed List the cities which can use water from the St Lawrence This query illustrates buffer analysis and spatial join operations FOR  $r I N d oc ument(“River.X ML”)            $c I N d oc ument(“Cit y.X ML”) W HER E  overla p( b uf fer($r/Sha pe ,30 0), $c/ Sha pe) == 1  R ET UR N                                  $c/ Na me                    16 (a ∩ b) ≠∅ Both queries use expressions similar to those of XQuery In the first example, document function opens the country XML document and binds the value of every country element in that document to variable $c Finally, the result is constructed as defined in the return clause The values obtained from the query, which is bound to the variable, can be used to construct new elements in the result if necessary In this example, a function, area(), is used to calculate the area of a country The second example illustrates buffer analysis and spatial joins operations by using overlap() and buffer() functions Although Vatsavai (2002) mentioned that spatial operators in this query language are implemented as a set of functions, the details of these functions were not given We therefore suppose that this query language has neither a particular application nor an implementation Nevertheless, it offered a novel and interesting approach to define a GML query language based on XQuery and OGC-SQL (Open Geospatial Consortium, 1999) spatial operators CXQuery (Constraint XML Query Language) CXQuery or Constraint XML Query Language (Chen and Revesz, 2002) is a declarative, Datalogstyle language for querying and updating XML documents It employs the syntax and semantics of constraint query languages (Kanellakis et al., Querying GML 1990) The input of a CXQuery is a set of XML documents The output of a CXQuery query is also an XML document When CXQuery is used to define views, the query result is not materialized A CXQuery expression contains a rule head and a rule body, with a “:-” symbol between them The rule body contains a set of predicates, which are separated by semicolons The semicolons stand for the logical operation “and” To simplify the CXQuery expression, it employs a subset of XPath functionality to navigate the hierarchical structure of XML documents and to avoid namespace conflicts Since most XML documents exchanged in e-Business have relatively restricted structures, CXQuery considers those XML documents that have internal DTD definitions or have external DTD definition connections Due to these difficulties, to date there is no query language proposal which supports querying spatial XML documents Since both CXQuery and many constraint query languages are based on Prolog, they can be easily combined Since constraint query languages can express spatiotemporal queries, the combination leads to a query language for XML documents that contain spatio-temporal data Moreover, combination can be easily implemented on top of a constraint database system Query shows a spatial query: Find all buildings located in citycampus and belonging to the Computer Science department citycampus(id,constraint): document(“citycampus.XML”), citycampus(id, departments, buildings, BoundedBy), constraint(x, y, BoundedBy); Building(name, dept, constraint): document(“campus.XML”), Building(name, dept, spatial), constraint(x, y, spatial); Building(name, dept, constraint): Building(name, constraint), citycampus(id, constraint), contains(citycampus/constraint,Building/ constraint), Building/dept = «Computer Science» The first two rules construct the constraint representation of the spatial data from the XML documents The third rule uses a spatial function contains() to test the spatial relation of two spatial objects One way in which CXQuery improves upon XQuery is by specifying schemas for the results of queries Chen and Revesz (2002) claim that query results without schemas are limited for defining views, integrating data, updating, and further querying XQuery can query the results of a query without a schema provided The main focus of this query language is to provide schema information in the query result Since CXQuery is derived from a constraint query language and the fact that constraint query languages can express spatial-temporal queries, the combination leads to a query language for XML documents that contains support for spatial-temporal data Gquery Gquery (Boucelma and Colonna, 2004) is yet another GML query language based on XQuery Unlike GML-QL, Boucelma and Colonna (2004) define a set of Gquery-specific spatial operators and basic data types Its data types are polygon, line and point, in the same way as the basic data types defined for GML The spatial operators can be classified into three groups: operators that return boolean type (equal, inside and cut), operators that return float type (distance, perimeter and length) and operators that return spatial type (convexhull, center, intersection) 17 Querying GML Query is an example It obtains the intersection point between a road and a river: for n in city return intersection(n/road, n/river) Gquery is designed for use in a particular mediator architecture It provides an integrated view of the data supplied by all sources, and Gquery makes it possible to access and manipulate integrated data C onc lus ion Currently, there is a large set of query languages over XML Although each one is based on different algebra and data models, all of them have the same aim: to query semi-structured data There are fewer query languages for GML documents Since GML is an XML encoding, the features of XML could be applied to GML With this, a GML query language should extend a query language over XML with spatial features In fact, in this chapter we have discussed four query languages over GML The first one is a novel extension of a previous query language over XML It is based on a robust data model and algebra and it offers all the features of an XML query language and a wide set of spatial operators Since it was the first approach in this area, it has inspired other query languages (Chung et al., 2004) The other three approaches are an extension of XQuery, with different aims and perspectives The first of these, GML-QL, was the first novel approach of a GML query language based on XQuery Since the literature about GML-QL is rather scarce, we suppose that this query language has neither a particular application nor an implementation Furthermore, details about spatial operators and functions were not given by Vatsavai (2002) 18 Although the second of these, CXQuery , is based on XQuery, it offers an interesting approach for a spatial query language over GML CXQuery allows to query and update XML documents using the syntax and semantics of constraint query languages This query language is currently the best approach over GML The last approach, Gquery, defines a set of spatial operators for GML It is a specific approach to be applied in a particular mediator architecture In conclusion, GML can represent database resources on the web, etc which can be queried with a specific query language Query languages over GML are a reality R eferences Abiteboul, S., Quass, S., McHugh, J., Widom, J., & Wiener, J (1997) The Lorel Query Language for Semistructured Data International Journal on Digital Libraries, 1(1), 68-88 Beech, D., Malhotra A., & Rys, M (1999) A Formal Data Model and Algebra for XML http://www-db.stanford.edu/dbseminar/Archive/ FallY99/ malhotra-slides/malhotra.pdf Boucelma, O., & Colonna, F (2004) Mediation for Online Geoservices In 4th International Workshop on Web and Wireless Geographical Information Systems W2GIS 2004 Korea Chen, Y., & Revesz, P (2002) CXQuery: A Novel XML Query Language In Proc of International Conference on Advances in Infrastructure for Electronic Business, Science, and Medicine on the Internet (SSGRR’02) Chung, W., Park, S., & Bae, H (2004) An Extension of XQuery for Moving Objects over GML ITCC Proc Of the International Conference on Information Technology: Coding and Computing IEEE Querying GML Córcoles, J E., & González, P (2001) A Specification of a Spatial Query Language over GML ACM-GIS 2001 9th ACM International Symposium on Advances in Geographic Information Systems Atlanta (USA) Deutsch, A., Fernandez, M., Florescu, D., Levy, A., & Suciu, D (1999) XML-QL: A Query Language for XML Computer Networks, 31, 11-16 Kanellakis, P C Kuper, G M., & Revesz (1990) P Constraint Query languages, Symposium on Principles of Database Systems Open Geospatial Consortium (1999) Simple Features Specification For SQL, 05-1341 Open Geospatial Consortium Retrieved 13th January, 2005, from http://www.opengeospatial.org Open Geospatial Consortium (2003) Geography Markup Language – GML Retrieved 13th January, 2005, from http://www.opengis.org/techno/ documents/02-023r4.pdf Robie, J (1998) The design of XQL Retrieved 13th January, 2005, from http://www.w3.org/style/ XSL/Group/1998/09/XQL-design.html Vatsavai, R (2002) GML-QL: A Spatial Query Language Specification for GML Retrieved 13th January, 2005, from http://www.cobblestoneconcepts.com/ucgis2summer2002/ vatsavai/ vatsavai.htm W3C (1998) XSL Retrieved 13th January, 2005, from http://www.w3 org/TR/REC-XML W3C (2001) XQuery: A Query Language for XML Retrieved 13th January, 2005, from http://www w3.org/TR/2001/WD-XQuery-20010215 W3C (2005) Extensible Markup Language – XML Retrieved 13th January, 2005, from http://www.w3c.org/XML/ key T er ms Feature: A feature is an application object that represents a physical entity, e.g a building, a river, or a person A feature may or may not have geometric aspects Markup Language: Language which combines text and extra information about the text The extra information is expressed using markup, which is intermingled with the primary text Query Language: Computer language used to make queries into databases and information systems Semi-Structured Data: Data with incomplete structure Data are directly described using a simple syntax, e.g XML, GML, etc 19 20 Chapter III Image Database Indexing Techniques Michael Vassilakopoulos University of Central Greece, Greece Antonio Corral University of Almería, Spain Boris Rachev Technical University of Varna, Bulgaria Irena Valova University of Rousse, Bulgaria Mariana Stoeva Technical University of Varna, Bulgaria Abstr act Image Databases (IDBs) are a kind of Spatial Databases where a large number of images are stored and queried In this chapter, techniques for indexing an IDB for efficiently processing several kinds of queries, like retrieval based on features, content, structure, processing of joins, and queries by example are reviewed The main indexing techniques used in IDBs are either members of the R-tree family (data driven structures), or members of the quadtree family (space driven structures) Although, research on IDB indexing counts several years, there are still significant research challenges, which are also discussed in this chapter IDBs and their indexing structures bring together two different disciplines (databases and image processing) and interdisciplinary research efforts are required Moreover, dealing with the semantic gap (successful integrated retrieval based on low-level features and high-level semantic features) and querying between images and other kinds of spatial data are also significant future research directions Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited Image Database Indexing Techniques INTRODUCT ION Image Databases (IDBs) are a special kind of Spatial Databases where a large number of images are stored and queried IDBs have a plethora of applications in modern life, for example in medical, multimedia, and educational applications In the framework of Geographical Information Systems (GIS), digital images (raster data) may represent changes in cultivations, sunny areas, and the discrimination between urban environments and country sides Apart from the raster format, GIS data may be stored in vector format (points, line segments, polygons, etc.) Each of these data formats has certain advantages making a choice between them a challenge Raster data leads to faster computing for several operations (e.g., overlays) and are well suited for remote sensing On the other hand, they have a fixed resolution leading to limited detail In this article, we focus on raster data (image databases) and their indexing techniques Since the start of the 1980s several structures for spatial objects have been proposed in the literature for efficient storage and retrieval of image collections Based on these methods, many kinds of useful queries on image data may be processed efficiently These include: • • • • Queries about the content of additional properties (descriptive information) that have been embedded for each image (e.g., which images have been used in the book cover of children’s books?) Queries about the characteristics/features of the images like color, texture, shape etc (e.g., find the images that depict vivid blue sky.) Queries for retrieving images with specified content (e.g., find the images that contain the sub-image of a specified chair.) Queries by example or sketch (e.g., a sample image is chosen, or drawn by the user and images similar to this sample are sought.) • • • • Structural queries (e.g., find the images that contain a number of specific objects in a specified arrangement.) Image Joins (e.g., find the cultivation areas that reside in polluted atmosphere areas.) Queries that combine regional data and other sorts of spatial data (e.g., find the cities represented by point data that reside within 5km from cotton cultivations.) Temporal Queries on sequences of evolving images (e.g., find if there has been an increase in the regions of wheat cultivations in this prefecture during the last two years.) The importance of image indexing and querying techniques led major Database Management Systems’ manufacturers to embed related extensions to the core engine of their products, (e.g., DB2 has embedded QBIC technology) (Flickner et al 1995) and Oracle provides Content-Based Image Retrieval (CBIR) based on Virage (Annamalai et al 2000) B ACKGROUND A digital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels In a binary image, each pixel can be either black, or white, while in a greyscale (color) image each pixel corresponds to a shade of gray (to a color), among a set of permitted greyscale (color) values Each image represents a scene containing objects and regions An IDB is an organized collection of digital images aiming at the management and the efficient processing of queries on this image collection There are numerous publications in the literature related to the processing of queries on image features like color (e.g., distribution of colors, dominant colors, and color moments), texture (the pattern of the image surface change, usually expressed by a combination of characteristics like coarseness, contrast, directionality, uniformity, regularity, 21 Image Database Indexing Techniques density, frequency, etc.) and shape (the physical structure of objects, or the geometric shapes present in the image) In several of these publications (emerging from the image processing/computer vision community) the term indexing refers to the features corresponding to each image and to the algorithm used for computing the similarity between them (the algorithm often works by an exhaustive comparison with all the images present in the databases) In this article, indexing is used in the context of databases and corresponds to the access methods (data structures) used to speed up query processing Several publications that contain review material have appeared in the literature Rui et al (1999) review numerous papers covering several aspects of CBIR, including multidimensional indexing, and identify open research issues Smeulders et al (2000) is another detailed review of CBIR techniques covering the research presented up to the year 2000 that includes also a subsection on storage and indexing The last section of this paper presents the authors’ view on CBIR’s future trends Manolopoulos et al (2000) overview indexing for structural and feature based queries Veltkamp and Tanase (2001) performed a survey on numerous CBIR systems providing information that is available for each of them on several technical aspects, including the use of indexing structures One conclusion of this survey is that “Indexing data structures are often not used” Manouvrier et al (2005) present a detailed review of quadtree based indexing in the image domain ranging from image representation and storage to CBIR Price (2006) maintains an extensive Computer Vision bibliography (an invaluable tool for the researcher) that contains many references to image indexing MAIN FOCUS OF THE ART IC LE In this section, we review the main indexing techniques that have been proposed for image 22 databases These techniques are grouped and classified by the family of their structure The two main families are the R-tree family (data-driven structures) and the quadtree family (space-driven structures), (subsection 2.1.2 of chapter 6, Manolopoulos et al 2000) Chang (1987) proposed the use of 2-D strings for the structural representation of objects appearing in an image Using this technique, structural queries can be answered by exhaustive comparisons with all the images in the IDB Petrakis (1993) and Orphanoudakis (1996) used hash-based indexing to speed up processing 2D strings are an efficient representation of the “left/right” and “below/above” relationships Petrakis and Faloutsos (1997), Petrakis (2002) and Petrakis et al (2002) adopted Attributed Relational Graphs (ARG), the most general image structure representation method, where individual object, or regions are represented by graph nodes and their relationships are represented by edges between such nodes The method developed by Petrakis and Faloutsos (1997) achieves fast query processing by making certain assumptions on the presence of objects in each image Petrakis (2002) and Petrakis et al (2002) relax these assumptions All these ARG-based methods achieve high performance by indexing ARGs with the R-tree family structure An R-tree is a balanced multiway tree for secondary storage, where each node is related to a Minimum Bounding Rectangle (MBR), that represents the minimum rectangle that bounds the data elements contained in the node The MBR of the root bounds all the data stored in the tree Figure depicts some rectangles (MBRs of data elements) on the right and the corresponding R­tree on the left Dotted lines denote the bounding rectangles of the subtrees that are rooted in inner nodes The most widely used R-tee is the R*-tree; for more details refer to Gaede and Günther (1998) Papadias et al (1998) treat the problem of structural image queries as a Multiple Constraint Image Database Indexing Techniques Figure An example of an R­-tree A B C D F A K G E H B J I D E F G H I J K L Satisfaction (MCS) problem Both the images and the queries are mapped to regions in a multidimensional space and are indexed by structures of the R-tree family Query processing is treated as general form of spatial joins (multi-way spatial joins) QBIC (Flincker et al 1995) was one of the first systems that introduced multidimensional indexing to enhance performance of CBIR Color, shape and texture features are extracted from the images and are represented by points in high-dimensional spaces Karhunen Loeve Transform is used to perform dimension reduction of the feature data (in order to overcome the degradation of performance of multidimensional index structures as the dimensionality increases, a situation known as the “curse of dimensionality”, Lin et al 1994) and a structure belonging to the R-tree family (an R*-tree) is used as a multidimensional indexing structure Seidl and Kriegel (2001) present techniques for adaptable similarity search They use quadratic distance functions that are evaluated using multidimensional index structures of the R-tree family (and especially X-trees), dimensionality reduction and approximation techniques (for an introduction to X-trees, see Manolopoulos et al 2000) For efficient processing of queries in image databases, Quadtrees have also been extensively used as indexing mechanisms The Quadtree is a four-way unbalanced tree where each node corresponds to a subquadrant of the quadrant of its father node (the root corresponds to the whole space) These trees subdivide space in a hierarchi- M N N M C L cal and regular fashion They are mainly designed for main memory, however several alternatives for secondary memory have been proposed The most widely used Quadtree is the Region Quadtree that stores regional data in the form of raster images Figure depicts an 8x8 pixel array and the corresponding Quadtree Note that black/white squares represent black/white regions, while circles represent internal nodes (gray regions) The Linear Region Quadtree is an external memory version of the Region Quadtree, where each quadrant is represented by a codeword stored in a B+-tree; for more details refer to Samet (1990) Quadtrees have been used for CBIR (representation and querying by image features) by several researchers, as a mechanism for calculating image similarity by defining appropriate similarity measures Examples of such work follows In some research efforts, complete Quadtrees with a fixed number of levels are used, since they lead to precisely enough results Each node in the Quadtree stores the features that correspond to its quadrant, for example, a color histogram (Lin et al., 2001), or a combination of feature Figure An example of a Region Quadtree 23 Image Database Indexing Techniques histograms (Malki et al, 1999) De Natale and Granelli (2001) use unbalanced Quadtrees for image segmentation to dominant colors Each quadtree is modelled by a binary array representing its structure and a label array representing the dominant color associated to each node or leaf Ahmad & Grosky (2003) use unbalanced Quadtrees to decompose an image into a spatial arrangement of features points (extracted using image processing techniques) and to quantify image similarity, while providing geometric variance independence For search and retrieval, an indexing scheme based on image signatures and quadtrees is used Chakrabarti et al (2000), use Quadtrees to represent two-dimensional shapes and perform shape-based similarity retrieval The proposed representation is designed to exhibit invariance to scale, translation and rotation Overlapping has been applied to Linear Region Quadtrees (Tzouramanis et al 2004) In this and previous papers by the same authors, four different extensions of the Linear Region Quadtree are presented for indexing a sequence of evolving raster data Moreover, temporal window queries are defined and studied These queries relate to the evolution of regional data inside a window in the course of time Quadtrees have also been used for creating an IDB, where image retrieval, insertion, deletion, comparison and set operations can be applied A single quadtree is used for all images Its nodes are associated with the list of images that have information in the respective quadrants Vassilakopoulos & Manolopoulos (1995) proposed Dynamic Inverted Quadtrees, while Jomier et al (2000) proposed a version suitable for binary, gray scale or color images Corral et al (1999) combine two different kinds of data and two different kinds of indexing structures They present five algorithms suitable for processing join queries between point data stored in an R-tree and image data stored in a Linear Region Quadtree 24 Due to space limitations, the most prominent IDB indexing structures are reviewed in this article The choice of an indexing method among them depends on the application Each of the above techniques has been designed around a specific problem setting A qualitative comparison between them is an interesting direction for future work that lies beyond the scope and the size limit of this article Descriptions of several other Spatial Access Methods that have been used in IDBs can be found in Samet (1990), Gaede and Günther (1998) and Manolopoulos et al (2000) FUTURE TRENDS IDBs are related to two different scientific communities: database and image processing / computer vision researchers Multidimensional access methods as well as information retrieval techniques and their use for query processing, constitute the key meeting point of the two worlds Several of the techniques of the image processing community could make further use of access methods or/and adapt to their properties, leading to more efficient processing of image related queries Related to the previous research direction is the further development of systems able to retrieve (and, in general, process queries) from image collections existing in different sources, including the WWW (Rui et al 1999) and indexing techniques are expected to play a dominant role in them In Zhao and Grosky (2002) one of the first techniques for integrated image retrieval based on low-level features and high-level semantic features of images is presented Mojsilovic et al (2004) present a methodology for semantic-based image retrieval based on low-level image descriptors However, neither of these works is based on indexing structures Since image retrieval based on both these kinds is features is crucial for the usefulness of CBIR systems (for a discussion of the semantic gap see subsection 2.4 of, Smeulders et al 2000) and still remains one of the big chal- Image Database Indexing Techniques lenges for researchers, indexing structures could be used in this context for calculating the correlations between low-level features and high-level concepts efficiently In Mao et al (2005) distance-based tree structures are used for computing the similarity of images, which are represented by features reflecting their structure, texture and color Although the high dimensionality of the feature space suggests that distance-based indexing techniques are outperformed by sequential scan (curse of dimensionality), the authors show that the intrinsic dimensionality of real data is low and can apply distance-based indexing that is specifically designed to reflect the intrinsic clustering of real data The design and study of more generalized techniques in this direction is another research challenge Despite the extensive research performed in spatial / spatio-temporal databases, storing a large database of (possibly evolving) images, or of regional data sets and being able to efficiently answer queries between these data and other sorts of spatial/spatiotemporal data, or queries involving the notion of time is still a big research challenge For example, being able to efficiently answer queries like: find the boats (moving points) that were inside the storm (changing regional data) during this morning (a time interval) CONC LUS ION In this paper, we have reviewed techniques related to indexing an image database as a means for efficiently processing several kinds of queries, like retrieval based on features, content, structure, processing of joins, and queries by example Although, research in this scientific area counts several years, there are still significant research challenges Image databases and their indexing structures bring together two different disciplines (databases and image processing) and developing a true Image Database System requires interdisciplinary research efforts Nevertheless, the semantic gap is alive and querying between images and other kinds of spatial data has not attracted enough attention yet R eferences Ahmad, I., & Grosky, W I (2003) Indexing and retrieval of images by spatial constraints Journal of Visual Communication and Image Representation, 14(3), 291-320 Annamalai, M., Chopra, R., DeFazio, S., & Mavris, S (2000) Indexing images in oracle8i In Proc SIGMOD’00, 539-547 Chakrabarti, K., Ortega-Binderberger, M., Porkaew, K., Zuo, P., & Mehrotra, S (2000) Similar Shape Retrieval in MARS In Proc IEEE Int Conf on Multimedia and Expo (II), 709-712 Chang, S K., Shi, Q Y., & Yan, C W (1987) Iconic indexing by 2-d strings IEEE Trans Pattern Anal Machine Intell., 9, 413-427 Corral, A., Vassilakopoulos, M., & Manolopoulos, Y (1999) Algorithms for Joining R-trees and Linear Region Quadtrees In Proc of SSD’99, LNCS 1651, 251-269 Spinger Verlag De Natale, F G B., & Granelli, F (2001) Structured-Based Image Retrieval Using a Structured Color Descriptor In Proc Int Workshop on Content-Based Multimedia Indexing (CBMI’01), 109-115 Flickner, M., Sawhney, H., Ashley, J., Huang, Q., Dom, B., Gorkani, M., Hafner, J., Lee, D., Petkovic, D., Steele, D., & Yanker, P (1995) Query by Image and Video Content: The QBIC System IEEE Computer 28(9), 23-32 Gaede, V., & Günther, O (1998) Multidimensional Access Methods ACM Computing Surveys, 30(2), 170-231 25 Real-Time Extraction of the Road Geometry • • • • independence from the cellular provider who can grant routable but highly expensive SIM cards, free choice of format and throughput, multicasting of the reference corrections to groups of rovers, user-friendly development of add-in software for the server The custom server-based RTK computation was tested kinematically in a suburban environment where many bridges and buildings block the GPS signals and a highway section “mistreats” the wireless link (surroundings of the EPFL near Lake Geneva, Switzerland) Complete loss of lock occurred on 4% of the 30-km-long journey In such a challenging test (Figure 2), the percentages of RTK fixed, RTK float, and code solutions from the custom server (32%, 36%, and 32%, respectively) closely resemble those of a GPS correction reference service named “Networked Transport of RTCM messages via Internet Protocol” However, at a speed of 80 km/h and beyond, the GPRS link to the custom server either fails to deliver the RTK corrections, or postpones the correction transfer; hence a significant degradation of the positioning accuracy arises (Weber et al., 2003) The second subsystem involves autonomous image grabbing and preprocessing that is achieved by a vertical camera with an embedded PC Triggered by a GPS pulse to guarantee accurate synchronization, the vision sensor captures frames via logarithmic CMOS pixels Previous road surveys with CCD sensors showed that most automatic algorithms for centerline detection are deceived by varying light conditions (Gilliéron et al., 2001) In fact, using fast low-level filtration techniques, such as binarization, rejects under-exposed pixels of shadowed areas or promotes over-saturated pixels in direct sunlight Due to its logarithmic response to illumination, a specific CMOS sensor allows the reproduction of the outdoor scenes largely without any imperfections such as blooming, smearing, or time lag (Figure 3) Preprocessed frames are sent to the host computer via an Ethernet link Figure Trajectory results obtained by the NTRIP streaming system and by the custom server 53 Real-Time Extraction of the Road Geometry Figure Light and shadow on the same frame, as seen by CCD (left) and CMOS (right) cameras R e al-t ime georeferenc ing To implement our real-time georeferencing algorithms, we chose the open-source Xenomai project that is well-established in the academic community (Lewis, 2005) This complementary Linux kernel accomplishes real-time performance by monitoring device drivers, the use of interrupt disabling and virtual memory operations that are sources of unpredictability In fact, the Xenomai interface lies between the standard Linux kernel and the hardware, whereas the standard Linux kernel sees the real-time layer as the actual hardware Theoretically, the user can introduce and set priorities to every thread Consequently, we can achieve correct timing for the processes by deciding on the scheduling algorithms, priorities and frequency of execution (Yodaiken, 1999) Data storage and visualization of the trajectory and the heading of Photobus are given a lesser priority than pixel georeferencing while the data synchronization with GPS time is completed first (Figure 4) Pixel georeferencing is automated via an opensource vision library called TLIB written at EPFL for real-time object tracking (Grange et al., 2003) TLIB implements Tsai’s algorithm as a conventional approach of camera calibration that relies on accurate 3D coordinate measurements with regard to a fixed reference Once the calibration 54 is performed, the georeferencing allows relating the individual pixels with world coordinates with centimeter accuracy Here, the pixels of interest belong to the road centerline and are automatically selected by using topological constraints on the bright blobs of the captured frames The quality of the extraction is confirmed offline by using the computationally-demanding pattern recognition module of TLIB future invest ig at ions To ensure a use of the real-time mapping platform under poor GPS coverage, an inertial measurement unit (IMU) should be integrated into the subsystem in charge of positioning Add-in software in the relay server should automatically remove outliers by a spline modeling of the obtained trajectories It may also exploit the continuous knowledge of the rover location to virtually move the reference station Moreover, the adoption of a mobile CMOS-stereovision strategy will diversify the data collected by our mapping platform, and Matlab calibration toolbox for camera by Heikillä (2000) provided promising results for this purpose However, substantial transcription needs to be carried out for the real-time exploitation of this toolbox Real-Time Extraction of the Road Geometry Figure Real-time algorithmics for georeferencing the road centerline conc lus ion The update of road databases is a crucial stake for the maintenance and the security of the road network A real-time mobile-mapping system represents a technological solution that is simple, productive and economic It may also contribute to the wide spreading of geomatics engineering in society R eferences Abbott, D (2003) Linux for Embedded and Real-time Applications Newnes, pp 117–146 Burlington, MA Cannon, M E., Basnayake, C., Syed, S., & Crawford, S (2003) A Precise GPS Sensor Subsystem for Vehicle Platoon Control Proceedings of the ION GPS-03 Conference, Portland, September 9-12 Ellum, C., & El-Sheimy, N (2002) Land-based Integrated Systems for Mapping and GIS Applications Survey review, 36(283), 323-339 Gilliéron, P.-Y., Skaloud J., Merminod B., & Brugger D (2001) Development of a Low Cost Mobile Mapping System for Road Database Management Proceedings of the 3rd Symposium on Mobile Mapping Technology, Cairo, Egypt, January 3-5 Gontran, H., Skaloud, J., & Gilliéron, P.-Y (2004) Photobus: Towards Real-time Mapping The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Istanbul, 35(B), Grange, S., Fong, T., & Baur, C (2003) TLIB: A Real-Time Computer Vision Library for HCI Proceedings of 7th Digital Image Computing: Techniques and Applications, Sun C., Talbot H., Ourselin S and Adriaansen T (Eds.), Dec 10-12, Sydney, Australia Heikkilä, J (2000) Geometric Camera Calibration Using Circular Control Points IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(10),, 1066-1077 Lewis, Q (2005) Hard Real-Time in User Space Project Report, University of Houston, Houston TX, Mather, P M (1999) Computer Processing of Remote-Sensed Images John Wiley and Sons, New York, NY 55 Real-Time Extraction of the Road Geometry Weber, G., Dettmering, D., & Gebhard, H (2003) Networked Transport of RTCM via Internet Protocol International Union of Geophysics and Geodesy General Assembly, Sapporo, Japan, June 30-July GPRS: General Packet Radio Service (GPRS) is a mobile data service available to users of wireless mobile phones It provides moderate speed data transfer, by using unused radio channels in the cellular network Yodaiken, V (1999) The RTLinux manifesto Proceedings of the 5th Linux Expo, May 18-22, Raleigh, NC NTRIP: Networked Transport of RTCM via Internet Protocol is an open, non-proprietary method that encodes the RTK corrections for highly-efficient transmission over the Internet It calls upon a substantial array of servers that allows the simultaneous connection of thousands of users key T er ms CCD: A Charge-Coupled Device is a sensor for recording images, consisting of an integrated circuit containing an array of linked, or coupled, capacitors Under the control of an external circuit, each capacitor can transfer its electric charge to one or another of its neighbors CMOS: The Complementary Metal-Oxide Semiconductor is a major class of integrated circuits whose chips include a microprocessor, microcontroller, static RAM, and other digital logic circuits CMOS devices use little power and allow a high density of on-chip logic functions Distributed Computing: This computing methodology is based on the fact that the process of solving a problem can be divided into smaller tasks, which may be carried out simultaneously with some coordination FGDC: The Federal Geographic Data Committee is an interagency committee that promotes the coordinated development, use, sharing, and dissemination of geospatial data The FGDC develops geospatial data standards for implementing the American spatial data infrastructure GDF: Geographic Data File stands for a European standard file format for geographic files It also gives rules about capturing, describing and linking data Although its primary use is for automotive navigation systems, GDF is widely used in transport and traffic applications 56 Real-Time Mapping: This expression refers to a process of map making for a level of computer responsiveness that a user senses as sufficiently immediate or that enables the computer to keep up with the georeferencing process Real-Time OS: Dedicated to real-time applications, this class of operating system uses specialized scheduling algorithms in order to provide the developer with the tools necessary to produce deterministic behavior in the final system RTK GPS Receiver: This class of GPS receiver exploits relative positioning based on the interferometric principle of exploiting precise carrier-phase measurements in real-time The attainable accuracy is at the centimeter level provided that the reference station measurements are transmitted timely and reliably to the rovers and the integer ambiguities can be resolved correctly Xenomai: This technology aims at helping application designers relying on traditional RTOS to move as smoothly as possible to a GNU/Linuxbased execution environment, without having to rewrite their application entirely Section II Mapping and Visualization 58 Chapter VIII Cognitive Maps Stephen Hirtle University of Pittsburgh, USA Abstr act Cognitive maps are the representations that individuals use to understand, process, and navigate environments The term cognitive map should not be taken as a literal metaphor as the internal representation will often violate principles of two-dimensional geometry, will rarely be either continuous or complete, and will often include non-spatial attributes, such as sights, sounds, or even aesthetic qualities, of a location Research on cognitive mapping as made important contributions to both theory and application of geoinformatics by demonstrating how spatial information is acquired, structured, accessed, and schematized by the human information processing system Theories of cognitive mapping have been expanded by through new frameworks, such as naïve geography, synergetic inter-representation networks, and geocognostics Together, this body of research has provided a framework for the development of the next generation of user-centered geographic information systems introduct ion Geographic information systems have greatly facilitated the use of geographic information by both experts in the field and the general public through Web-based interfaces The increased use of geographic information systems by all users will be facilitated through an understanding of human spatial reasoning (Kitchin & Blades, 2001; Slocum et al., 2001) In this article, the state-of-theart of understanding the representation of spatial knowledge, or cognitive maps, will be reviewed Much of this literature has been reviewed in several recent papers and books In particular, the reader is invited to read Golledge (1999), Peuquet (2002), and Portugali (1996) for foundational readings on cognitive mapping Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited Cognitive Maps The term “cognitive map” is one that is not without controversy The term was coined by E C Tolman (1948) when he argued that rats in a maze had an internal representation or, cognitive map, of the environment, which would lead to the use of shortcuts in finding food These maps were assumed to be used by humans as well and research over the years has attempted to delineate the nature of these representations The term was further expanded in the classic work by Lynch (1960) and by Downs and Stea (1973) The next 30 years has seen an explosion in empirical research on the topic of cognitive mapping Some have argued that the term “cognitive map” is misleading, as it might be taken to be imply a particularly kind of two-dimensional or pictorial representation Alternative terms, such as cognitive collage (Tversky, 1993) or cognitive atlas (Kuipers, 1982), have been introduced as a replacement to the term cognitive map to highlight a particular characteristic, such as the notion of multi-media (in a cognitive collage) or multiple scales or reference frames (in a cognitive atlas) The use of the term cognitive map in this article should not be taken a literal metaphor, but rather a useful catch phrase for the underlying representation of spatial memory F ound at ion al Issues The research over the past thirty years has highlighted the importance of cognitive maps in geographic communication, acquisition and use of geographic information, wayfinding, planning, and urban design (Evans, 1980; Kitchin, 1994) From constructing user-centered in-car navigation systems that impose minimally attentional demands on a driver to constructing urban parks that encourage public use, research on cognitive mapping can suggest appropriate parameters to consider in the design process Most important are a number of foundational issues that have emerged over years of research (Mark et al, 1999) Knowledge Acquisition In early research on cognitive mapping with humans, Siegel and White (1975) argued that the acquisition of spatial knowledge starts with landmark recognition, followed by the learning of routes between known landmarks With enough experience, one will eventually acquire survey knowledge in which the relative location of landmarks is fully understood Further research on spatial cognition has indicated two problems with the initial conceptualization First, it is clear that the acquisition sequence is not strictly linear (Allen, 1999) Second, survey knowledge is often never acquired despite years of experience For example, Moeser (1988) found that student nurses lacked survey knowledge of a large hospital, even after working in the building for over three years, and instead continued to rely on directional signs and known landmarks to navigate through the space In a recent in-depth study, Ishikawa & Montello (2006) found that that accurate metric knowledge was either gained in the first session or never learned, calling into question the learning parameters in the original conceptualization Despite these caveats, the distinction between landmark, route and survey knowledge remains a useful starting place Most navigation systems are designed to support either route or survey knowledge In the simplest case, point by point written directions, such as those provided by Mapquest (www.mapquest.com) and similar web-based mapping systems, are designed to support route knowledge, whereas floor plans are designed to support survey knowledge Hierarchical Structuring While automated navigation systems often provide directions using street nodes (e.g, turn left at Main St; Go 3.4 km), humans often talk in terms of neighborhoods and landmarks (e.g., when you get downtown, turn left at the Starbucks) Neighborhoods form one of the basic organizing 59 Cognitive Maps principles of cognitive maps A neighborhood is conceptually coherent region that is used to organize space Neighborhoods are nested in a semi-lattice (Hirtle, 1995), which leads to hierarchical clustering like effects on judgments of distance and orientation Stevens and Coupe (1978) demonstrated that subjects misalign cities using the superordinate relationships For example, Montreal is judged mistakenly to be northeast of Seattle, as Canada is north of the United States Tversky (1981) showed alignment effects between regions, which lead to judgments of North America being preceived directly north of South America Hirtle and Jonides (1985) demonstrated that fuzzy neighborhoods within a city result in similar biases The hierarchical structure is a fundamental principle of cognitive mapping In addition to their role in denoting routes, landmarks can also be thought of as notable locations that are used to organize space (Presson & Montello, 1988; Sorrows & Hirtle, 1999) A landmark may indicate the centroid of a neighborhood or the boundary between two neighborhoods Thus, the symbiotic relationship between landmarks and neighborhoods provides two distinct ways of structuring space into regions, which in turn influences the perception of that space Locations within the same neighborhood are judged closer than identically distant locations between neighborhoods Distances are often asymmetric with the distance to a landmark judged to be shorter than the distance from a landmark map), as well as the critical linear ordering of stations along a specific route Beck’s map replaced a more geographically accurate, but less useful, rendition of the same information In fact, it is becoming clear that photographs, virtual reality, immersive environments and other photo-realistic settings by themselves are not particularly useful as navigation aids (Darken & Peterson, 2002; Freksa, 1999) Researchers have explored the schematization of geographic knowledge to better understand what information is important to maintain and what information is less important This research has lead to automatic schematization Freksa (1999) argues the need for multiple levels of abstraction based on the principles of cognitive mapping This can be done by seeking a cognitive correspondence between the environment and the schematic representation by first extracting the conceptually critical entities for the task at hand In this way, schematic map design is seen as solving a representation-theoretic optimization problem In further work, Klippel et al (2005) review several cognitively based schemes for schematization of spatial information, including wayfinding choremes, which capture the inherent structure of intersections, and focus maps, which direct a viewers attention to critical regions of interest In a more applied domain, Agrawala and Stolte (2001) have automated the sketch map creation process Their Linedrive algorithm is available at www.mapblast.com and has been incorporated into the MSN direction-giving website S chematization of G eographic K nowledge Altern ate F r ameworks Why is the London Underground map seen as ideal communicator of one kind of spatial information? The map designed in 1931 by Harry Beck extracts useful information, organizes that information in a colorful and pleasing display, while keeping relative directional information intact (e.g., northern stations are at the top of the 60 While traditional approaches have been useful in understanding the nature of cognitive mapping, they are limited in their ability to account for the interactions of multiple criteria A number of researchers have explored several alternative frameworks for the development of cognitive maps Three of these approaches are reviewed below Cognitive Maps Naïve Geography Naïve Geography is an approach based on work in artificial intelligence in the 1970’s on Naïve Physics to model common-sense knowledge of objects and motion in the world (Hayes, 1979) Egenhofer and Mark (1995) introduced the concept of Naïve Geography to capture everyday reasoning about geographical space Naïve Geography include a number of interesting principles from assuming a space is two-dimensional, even though it is not, to asserting that boundaries are sometimes entities and some not For example, if a boundary is always taken as a mathematical object of having length but no width, then the common notion of leaving one’s country before entering another country would be impossible Reasoning about boundaries in such situations, including the legal standing, would follow the principles of Naïve Geography and not the underlying mathematical principles Geographical Information Systems (GISs) that ignore the principles of Naïve Geography might prove difficult to use These limitations are particularly worth noting for community-based or public participation GISs Synergetic Inter-Representation N etwork Portugali (1996) has taken another interesting approach to the problem of representation and cognitive maps In an influential book, he argues the value of considering the links between internal representation and the external environment, which necessarily influence each other Using the mechanics of self-organizing systems, he introduces the notion of a Synergetic Inter-Representation Network (SIRN) The importance of the SIRN model is on the interplay between perception and cognition, which is a fundamental principle of cognitive science To be concrete about how a SIRN might be implemented, consider an American visiting a European city for the first time One might quickly integrate a familiar symbol, such as a McDonald’s sign, into the internal representation of the city and would use it as a future landmark in navigation and orientation The same visitor might find themselves perplexed by a local sign with unfamiliar markings even if they are plentiful and common in the region Few theories of cognitive mapping make this interplay between external and internal as explicit and as a result would have trouble accounting for such cultural differences in the creation of cognitive maps G eocognostics In a related approach, Edwards (1997) developed a framework called geocognostics In this approach, he argues for the need to combine two representational structures, one for views, which is the typical focus of cognitive maps, and another for trajectories, or one’s path through the space This latter approach of using trajectories through space was also the focus of work by Hutchins (1995) in explaining the representations of Polynesian sailors who could not depend on traditional landmarks in their navigation tasks Geocognistics gets its name from the combination of geometrical and cognitive principles that are needed to account for a rich set of empirical findings C onc lus ion Cognitive mapping is proven to be rich source of both empirical findings and theoretical research In addition, it is argued that cognitive mapping is important for many areas of geoinformatics The acceptance of public GIS projects, the ability to provide useful feedback to planners, the use of navigation systems, and the modeling of emergency management evacuation plans depend in part on understanding how humans process spatial information (Frank et al.,2001; Gero & Tversky, 1999; Portugali, 2006) 61 Cognitive Maps In part, cognitive mapping provides the framework for developing user-centered GISs A navigation system working only in longitude and latitude would be accurate but worthless as an in-car navigation system While this example may seem obvious, the reality is that multiple coordinate systems are already in use and emergency call operators are faced with translating from a caller’s natural language information to a GIS to a rescue vehicle’s code, resulting in a large number of possible confusions or miscommunications (Goodchild, 2000) Users of public participation GIS might have simple needs that are easy to express in language, such as “List the property assessments of all my neighbors” or slightly more complex “List the property assessments of all my neighbors who also live alone” to see if the assessment values are in line Yet the system built on other parameters might find these queries impossible to generate, especially when giving a vague concept such as “my neighbors” (Montello et al, 2003) Cognitive mapping provides the necessary concepts that can be encapsulated into future information systems to make them usable with regard to human information processing tasks Darken, R P., & Peterson, B (2002) Spatial orientation, wayfinding, and representation In K Stanney (Ed.), Handbook of Virtual Environment Technology (pp 493-518) Mahway, NJ: Erlbaum R eferences Freksa, C (1999) Spatial aspects of task-specific wayfinding maps A representation theoretic perspective In J S Gero & B Tversky, (Eds.) Visual and spatial reasoning in design (pp 1532) Sydney: Key Centre of Design Computing and Cognition Agrawala, M., & Stolte, C (2001) Rendering effective route maps: Improving usability through generalization In E Fiume (Ed.), Siggraph 2001 Proceedings of the 28th Annual Conference on Computer Graphics, Los Angeles, California, USA (pp 241-250) ACM Press Allen, G L (1999) Spatial abilities, cognitive maps, and wayfinding: Bases for individual differences in spatial cognition and behavior In R Golledge (Ed.), Wayfinding behavior: Cognitive maps and other spatial processes (pp 46-80) Baltimore: Johns Hopkins University Press 62 Downs, R J., & Stea, D (1973) Cognitive Maps and Spatial Behavior Image and Environment Chicago: Aldine Publishing Company Edwards, G., (1997) Geocognostics: A new framework for spatial information theory In A.U Frank and S Hirtle (Eds.) Spatial information theory A theoretical basis for GIS, LNCS 1329 (pp 455-471) New York: Springer-Verlag Egenhofer, M J., & Mark, D M (1995) Naïve geography In A.U Frank & W Kuhn (Eds.), Spatial information theory A theoretical basis for GIS, LNCS 988 (pp 1-15) Berlin: Springer Evans, G W (1980) Environmental cognition Psychological Bulletin, 88, 259-297 Frank, A U., Bittner, S., & Raubal, M (2001): Spatial and cognitive simulation with multi-agent systems In D R Montello (Ed.), Spatial Information Theory: Foundations of Geographic Information Science, Lecture Notes in Computer Science, 2205, 124-139 Berlin: Springer-Verlag Gero, J S., & Tversky, B (Eds.) (1999) Visual and Spatial Reasoning in Design Sydney: Key Centre of Design Computing and Cognition Golledge R G (Ed) (1999) Wayfinding Behavior Baltimore: John Hopkins University Press Goodchild, M F (2000) GIS and transportation: Status and challenges GeoInformatica, 4, 127-139 Cognitive Maps Hayes, P J (1979) The naïve physics manifesto In D Michie (Ed.), Expert Systems in the Microelectronic Age (pp 242-270) Edinburgh: Edinburgh University Press Hirtle, S C (1995) Representational structures for cognitive space: Trees, Ordered Trees, and Semi-lattices In A V Frank & W Kuhn (Eds.), Spatial information theory: A theoretical basis for GIS LNCS 988 (pp 327-340) Berlin: SpringerVerlag Hirtle, S C., & Jonides, J (1985) Evidence of hierarchies in cognitive maps Memory and Cognition, 13, 208-217 Hutchins, E (1995) Cognition in the wild Cambridge, MA: MIT Press Ishikawa, T., & Montello, D R (2006) Spatial knowledge acquisition from direct experience in the environment: Individual differences in the development of metric knowledge and the integration of separately learned places Cognitive Psychology, 52, 93-129 Kitchin, R M (1994) Cognitive maps: What are they and why study them? Journal of Environmental Psychology, 14, 1-19 Kitchin, R M., & Blades, M (2001) Cognition of geographic space London: IB Taurus Klippel, A., Tappe, H., Kulik, L., & Lee, P U (2005) Wayfinding choremes: A language for modeling conceptual route knowledge Journal of Visual Languages and Computing, 16, 311-329 Kuipers, B (1982) The map in the head metaphor Environment and Behavior 14, 202-220 Lynch, K (1960) The Image of The City Cambridge, MA: MIT Press Mark, D M., Freksa, C., Hirtle, S C., Lloyd, R., & Tversky, B (1999) Cognitive models of geographical space International Journal of Geographical Information Science, 13, 747-774 Moeser, S D., (1988).  Cognitive mapping in a complex building.  Environment and Behavior, 20, 21-49.  Montello, D R., Goodchild, M F., Gottsegen, J., & Fohl, P (2003) Where’s downtown? Behavioral methods for determining referents of vague spatial queries Spatial Cognition & Computation, 3, 185-204 Peuquet, D J (2002) Representations of space and time New York: Guilford Portugali, J (1996) The construction of cognitive maps, Dordrecht: Kluwer Presson, C C., & Montello, D R (1988) Points of reference in spatial cognition: Stalking the elusive landmark British Journal of Developmental Psychology, 6, 378-381 Siegel, A.W., & White, S H (1975).  The development of spatial representation of large-scale environments.  In H.W Reese (Ed.), Advances in Child Development and Behavior (pp 9-55).  New York:  Academic Press.  Slocum, T A., Blok, C., Jiang, B., Koussoulakou, A., Montello, D R., Fuhrmann, S., & Hedley, N R (2001) Cognitive and usability issues in geovisualization Cartography and Geographic Information Science, 28, 61-75 Sorrows, M E., & Hirtle, S C., (1999) The nature of landmarks for real and electronic spaces In Freksa, C.; Mark, D (Eds.), Spatial Information Theory, LNCS 1661 (pp 37-50) Berlin: Springer Stevens, A., & Coupe, P (1978) Distortions in judged spatial relations Cognitive Psychology, 10, 422-437 Tolman, E C (1948) Cognitive maps in rats and men Psychological Review, 55, 189-208 Tversky, B (1981) Distortions in memory for maps Cognitive Psychology, 13, 407-433 63 Cognitive Maps Tversky, B (1993) Cognitive maps, cognitive collages, and spatial mental models In A U Frank & I Campari (Eds.), Spatial information theory: A theoretical basis for GIS LNCS 716 (pp 14-24) Berlin: Springer-Verlag key T er ms Cognitive Map: Internal representation of the environment used for orientation, wayfinding and navigation Landmark: A notable building or location used in navigation to help orient oneself 64 Landmark Knowledge: Recognition and recall of landmarks in the environment Route Knowledge: Ability to navigate along a route without getting lost Schematization: Abstraction of spatial relationships, such as connectivity and connectedness, from a Euclidean representation Survey Knowledge: Knowledge of the orientation and distance between locations in the environment Wayfinding: The ability to navigate within an environment or from one location to another 65 Chapter IX Map Overlay Problem Maikel Garma de la Osa University of Havana, Cuba Yissell Arias Sánchez University of Havana, Cuba Abstr act Maps usually contain data from different sources (e.g., population, natural resources, cities, roads, infant mortality rate, etc.) When all the information is complied it is almost impossible to distinguish a certain type of data from the rest Geographic Information Systems (GIS) usually organize maps into layers, each representing an aspect of the real world (de Hoop et al 1993) Layers form thematic maps of a single type of data, allowing users to query each one separately INTRODUCT ION The main purpose of a GIS is to analyze geographic data As map information is organized into layers, it is necessary to overlay the thematic maps involved whenever we need to query data that relates to various layers (e.g., which regions with population larger than one million have infant mortality rate lower than a certain value?) Each thematic map can be seen as a partition of the plane into regions determined by points and lines Overlaying two or more maps generates a Copyright © 2009, IGI Global, distributing in print or electronic forms without written permission of IGI Global is prohibited Map Overlay Problem new map containing information about the relationship between them Thus, overlaying is one of the most important analysis operations in GIS, allowing complex queries that can not be applied to the original layers separately Applications There are many uses derived from overlaying subdivisions of the map, such as: • • • • • Overlaying layers of geographical data in order to perform queries involving several layers Area interpolation: given the population of a region A that overlaps a region B, estimate B’s population, assuming that it is proportional to the area of A that is covered by B Boolean operations among polygons: union, intersection, difference Windowing: operation for which a window is overlaid over the map and everything outside of the window is eliminated Buffering: it is made around points, lines and polygons If the combined buffer of several elements is needed, it is done as a polygon overlay PROB LE M DESCR IPT ION The Map overlay problem is the overlay of several input maps into a single output map A map is a 2D spatial data structure, which is compounded by nodes (2D point where two or more lines intersect), chains (connected set of segments that start and end on two nodes), and regions (connected subset of the plane with polygonal boundary) that create a plane subdivision The output map contains all the nodes in the input maps plus the nodes generated by the intersections of the chains of both maps together The chains of the input maps are interrupted at the intersection points creating 66 the output map’s chains; hence, the output map contains new regions defined by the intersections of the input regions The map overlay problem consists of generating and relating the structures of the output map (Wu, 2005) The process of obtaining the output map can be divided into four steps (Wu, 2005): Determine the new nodes at the intersection points of the input chains Form the new chains by splitting the chains at the new nodes Form the new regions, and solve the containment of boundaries Determine the overlay relationships between the regions of the output map and those of the input maps The first step is the most time consuming In order to improve its performance, many algorithms based on spatial analysis and computational geometry techniques, have been developed ST ATE OF THE ART A Brief History A naive algorithm for overlaying maps would take each segment of one map and compare it with all the segments of the other looking for intersections If each input maps have Ο(n ) segments, the algorithm runs in Ο( ) time But, this is low n performance for the most typical input sizes (over 100,000 points) To improve the time it is convenient to follow a local processing principle, which means not checking for intersections between segments of distant regions because they not intersect It has been proven that a lower bound for the problem of finding all the intersection points between a set of n segments is Ω(n ∗ log n + k ), where k is the number of intersections, and it can be achieved using Ο(n ) space Map Overlay Problem Bentley and Ottman (1999) were first at applying the local processing principle for reporting segment intersection through the plane sweep algorithm Their algorithm takes Ο(n ∗ log n + k ∗ log n ) time and Ο(n + k ) space In 1988 Chazelle and Edelsbrunner created the first algorithm that runs in Ο(n ∗ log n + k ) time and uses Ο(n + k ) space (Chazelle & Edelsbrunner, 1992) Balaban (1995) developed the first optimum algorithm with respect to time and space complexity, which also works for curves For some cases the segment intersection problem can be easier than the general problem In the map overlay problem, as the maps are a planar subdivision of the space, all intersections will occur between a segment of the first map with a segment of the second one This particular problem is also known as the red-blue line intersection problem, and a solution was found by Mairson and Stolfi (1998), before the general problem was optimally solved, taking Ο(n ∗ log n + k ) time and Ο(n ) space In the case of maps as connected subdivisions, Finke and Hinrichs (1995) showed that it can be done in Ο(n + k ) time • Vector Algorithms Spatial Partitioning Algorithms divide the plane in disjoint regions, distribute the segments between the regions they intersect and determine the intersections in each region (using the naive technique or a local processing principle) Some examples are (Andrews et al 1994): • Uniform Grid: On a grid g x g, the algorithm has a running time Ο( ), and space Ο(g ∗ n ) n (Franklin et al 1989) Usually, it does not need a pre-processing step, although segments could be assigned to the grid cells As a counterpart, it assumes the segments are uniformly distributed However, it runs faster when the segments are small and scattered over the plane Then, it divides the • plane by a uniform grid, and assigns each chain segment to the grid cell in which it is included This way, it only needs to compare segments in the same grid cell to check for an intersection Moreover, only cells containing segments of different subdivisions have to be checked n Quadtree: It has a running time Ο( ) in the worst case and space Ο(n ) (Shaffer et al 1990) Basically, it divides the plane hierarchically into rectangles A bounding box of the segments of one subdivision (red segments) is taken and divided into four equally sized rectangles, which are the children of the original box node Each time a red segment is completely inside of a rectangle, it is stored in the associated tree If a segment overlays more than one rectangle, then it is stored in the parent rectangle node This process is repeated until the number of segments associated with the rectangle is too small or the tree depth is too large In order to compute the intersections between a blue segment and each red segment, only those red segments contained in the paths from the root to the leaves whose bounding box intersect the blue segment need to be checked Binary Space Partition requires Ο( )runn ning time and space complexities However, van Oosterom proved a better behavior for the average case (van Oosterom, 1990) The time and space depends on the strategy for partitioning the plane BSP trees store in each node a line that divides its associated space into half planes: the regions to the left and to the right of the line Each half plane is then associated with a child of the node The children are recursively partitioned by partitioning lines The red and blue segments are stored in the leaves of the tree All the blue and red segments are compared against the line stored at the root The segments that 67 ... 14(1-3), 23 5 -24 6 Crist, E P., & Cicone, R C (1984b) A physically-based transformation of Thematic Mapper data-the TM tasseled cap IEEE Transactions on Geoscience and Remote Sensing, 22 (3), 25 626 3... Cognitive Science, 14 (2) , 179 -21 2 Fischer, G., & Ostwald, J (20 01) Knowledge management: problems, promises, realities, and challenges IEEE Intelligent Systems, 16(1), 60 72 Franklin, C (19 92) An introduction... Oosterom, P v (20 06, 20 -22 April, 20 06) Semantic and Syntactic Service Descriptions at Work in Geo-Service Chaining Paper presented at the 9th AGILE Conference on Geographic Information Science, Visegrád,