An ontology-driven approach for the extraction and description of geographic objects contained in raster spatial data

An ontology-driven approach for the extraction and description of geographic objects contained in raster spatial data

Expert Systems with Applications 39 (2012) 9008–9020 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal hom...

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Expert Systems with Applications 39 (2012) 9008–9020

Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

An ontology-driven approach for the extraction and description of geographic objects contained in raster spatial data Rolando Quintero ⇑, Giovanni Guzmán, Rolando Menchaca-Mendez, Miguel Torres, Marco Moreno-Ibarra Intelligent Processing of Geospatial Information Laboratory, Computer Research Center, National Polytechnic Institute, Mexico City, Mexico UPALM-Zacatenco, CIC Building, 07738 D.F. Mexico, Mexico

a r t i c l e

i n f o

Keywords: Raster data Semantics Ontology

a b s t r a c t In this paper, we present FERD, a methodology aimed to automatically identify, extract and describe relevant spatial objects contained in raster spatial datasets. Our objective is to provide a set of computational tools capable of finding landforms contained in the datasets that match human-friendly descriptions such as ‘‘In this model there is a mountain having a maximum altitude of 302 m, located between coordinates (19.09383°N, 99.85541°W) and (19.09393°N, 99.85554°W)’’. The proposed methodology is composed of three main stages: in the first stage (conceptualization), the knowledge domain is represented by means of ontologies. In the second stage (synthesis) a novel semantic decomposition algorithm is used to identify and extract relevant spatial objects from the spatial dataset. In the last stage (description), the geographic objects extracted in the second stage are mapped to concepts (objects of the knowledge domain) generated in the first stage. The final result is a set of metadata that describes the geomorphologic objects contained in the raster dataset. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays, geospatial information is becoming pervasive and people are applying this type of information in an increasing variety of disciplines, from personal leisure applications to large scale governmental systems. This broad spectrum of applications raises new challenges, such as the fact that people are not concerned about the complexity of the data, or the way that it is codified, but at the same time they are requiring more and better geospatial information. Projections, scales and datums are not meaningful to people, they are interested in places to have a lunch and how to get there. Thus, it is necessary to develop methods and algorithms to translate raw data into the type of information that people require. Raster spatial datasets (RSDSs) is a type of data that must be processed in order to transform raw information in something meaningful to a regular person. The process of mapping spatial objects to semantic objects is called semantic representation. In this paper, a methodology (FERD) for semantically extracting and describing objects contained in a RSDS is presented. It is based on three stages: conceptualization, synthesis and description. The goal of the proposed methodology is to build human-friendly representations of spatial objects based on the knowledge that people have cognitively about the geospatial domain.

⇑ Corresponding author. E-mail address: [email protected] (R. Quintero). 0957-4174/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2012.02.033

The conceptualization stage attempts to capture and organize common knowledge about the problem’s domain. In other words, in this stage we define concepts that people use when they talk or think about a specific domain (e.g., hydrology, landforms, transportation infrastructure, and so on). The stage consists of two tasks: (1) conceptualization of the geospatial domain and (2) conceptualization of the particular domain. In a previous work, we have proposed GEONTO-MET which is a methodology to create formal conceptualizations of the geographic domain (Torres, Quintero, Moreno-Ibarra, Menchaca-Mendez, & Guzman, 2011). GEONTO-MET is based on reducing the set of axiomatic relations of a conceptualization in order to obtain a reduced set of basic relations that can be used to define the remaining relations contained in the conceptualization. This way, we obtain more semantic richness. By using GEONTO-MET we developed an ontology (called Kaab) of the geographic domain that is based on the data dictionaries of the mexican National Institute of Statistics, Geography and Informatics (INEGI). Similarly, we used GEONTOMET and the dictionary of the International Standards Organization about the environmental data (ISO, 2005) to create an ontology (called Hunxeet) of the landforms domain. One of the main advantages of the ontologies created using GEONTO-MET is that the relationships among concepts are not predefined, but they are part of the conceptualization itself. The synthesis stage processes the raster spatial datasets (RSDSs) using three classical phases in digital image processing: pre-processing, processing and post-processing. This stage extracts and

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labels the main spatial objects contained in the RSDS, by applying a novel semantic decomposition algorithm (Guzmán, Levachkine, Torres, Quintero, & Moreno, 2008). The aim of the labeling process is to associate a label of the adequate thematics to each region, taking only into account the primitive characteristics (i.e., raster values – RV) of the RSDS. Parts of the RSDS, called extracts, will be considered instances of a concept. The description stage consists of determining what an extract is (specialization), and building its semantic representation. The stage is conducted by the ontologies built in the conceptualization stage, in order to indicate which properties of an extract must be measured in order for considering it as an instance of a certain concept. For specializing each spatial object, a specialization algorithm that involves geometric and topologic relationships among geographic objects is proposed. Once the three stages are completed, the raw raster data has been augmented with semantic data, namely, human-like descriptions of the spatial objects contained in the RSDS. The rest of the paper is organized as follows: in Section 2 we present a summary of the previous work about semantic analysis of raster data. The proposed methodology for extracting and describing spatial objects contained in a RSDS is described in Section 3. Since the conceptualization stage was already presented in Torres et al. (2011), in this section we focus mainly on describing the synthesis stage where the Semantic Decomposition Algorithm is defined. Section 4 depicts experimental results obtained by applying the FERD methodology. Lastly, in Section 5 the conclusions of this work are presented.

2. Related work Extraction of features from RSDS is an important problem in many application domains. Current technologies for feature extraction from urban scenes (from remotely sensed imagery) rely on physical attributes as the basis for classification. Roads, railroads, rivers, buildings, lakes, and channels are typical examples of such features. Although this approach produces relevant information from imagery, low-level techniques for information extraction, classification and management limit both the analysis model and the quality and quantity of the information extracted from the image (Shekar & Xiong, 2008). In general, these techniques do not yield to a higher-level analysis, which allows for a better understanding of the role that individual and groups of features play in the processes related to human cognition. The reason for this failure is the gap between the representation used for features and the models defined for cognitive analysis (Shekar & Xiong, 2008). When RSDS are treated as images, the approaches used to extract relevant information can be classified in pixel-oriented and object-oriented. Pixel-oriented approaches are characterized by the fact that the information contained within the image is processed directly. One of the main disadvantages of these approaches is that they tend to eliminate semantic components (if any) from the images. Most of these approaches use well known image processing algorithms that are modified to adjust them to solve certain problems. For instance, Huang, Kumar, and Zabih (1998) proposed a method for making hierarchical classification of images using supervised knowledge. The core of such methodology is the extraction of low-level characteristics to iteratively make a reconfiguration of the space of such characteristics by applying singular value decomposition (SVD). The latter allowed the authors to eliminate noise and generate a hierarchical classification tree from training data. Once the tree has been generated, it can be used to classify new images. The methodology assumes that all the images are semantically similar; so, objects that can be classified are restricted to the domain of the training data. Also, authors do not

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explain what happen if an image with different semantics is classified. In Dorado and Izquierdo (2003) a technique for labeling images by combining texture and color with keywords is presented. By applying a conjunction of color similitude-based and texture analysis methods with data mining techniques, the authors map keywords from a reduced set of images to a large scale database. Other example is Zhang and Fu (2005), in which an architecture for semantic image labeling is outlined. In this architecture, a semantic network is used as a semantic representation model that is further used in conjunction with a combination of keywords, ontologies and low-level characteristics for querying labeled images. On the other hand, in Fung and Loe (1999) a semantic-based learning approach for classifying and querying digital images is described. This technique consists of dividing the image into matrices of regions of 32x32 pixels each. Then, their semantics is defined in two levels: (1) primitive semantics for a region, which focuses on the low-level characteristics, and (2) scene semantics, which is related to the identification of high-level characteristics at scene or image level by means of the association of primitive semantics. In Angulo and Serra (2003), three operators over the HSL (hue-saturation-lightness) color model are presented, namely, color gradient, top-hat and surface aperture operators. By combining these operators, specific characteristics of images are increased or decreased. Unfortunately, an algorithm to determine how to apply the operators for obtaining a specific characteristic is not defined. Although non-linear space and different operators are used, the proposed method is similar to well-known pattern recognition techniques such as segmentation and identification. The original aspect of this work is the use of a non-linear color space that replaces the lineal RGB model. The authors argue that significant improvements can be obtained by using a non-linear space over those approaches that use a linear color space. Unlike pixel-oriented approaches, object-oriented methodologies use additional information to perform image segmentation and classification. This type of methodologies usually define a set of criteria to manage information as objects instead of raw data. For example, in Mueller, Segl, and Kaufmann (2004) a methodology for extraction of regions focused on large geographic objects is outlined. It is based on applying basic digital image processing algorithms for growing, bordering and extracting regions. The main disadvantage of this methodology is that small objects are treated as parasite branches in the border of the regions with the consequent loss of potentially important information. Another objectoriented work is presented in Levachkine and Alexandrov (2003), in which a method for semantic image decomposition is proposed. This method is composed of an analysis and a synthesis stages. Its salient feature is that it allows the user to control the level of semantic decomposition. The approaches presented in this section attempt to improve the quality of the segmentation and extraction tasks, but the effort to describe the semantics of the results is weak. In these works, the training stage is performed a priori, and hence, only labels without information for further interpretations (e.g., topology and geometry) are obtained. Moreover, by applying image processing techniques to RSDS, the color space is limited to three bands. There are approaches that work over other types of RSDS, for instance, in the case of digital terrain models there are many proposals oriented towards flow analysis and extraction of drainage lines (Ackermann, 1993; Hodgson, 1995). Other efforts to characterize digital elevation models using a strong numeric component are presented in De Boer (1992) and Romstad (2001). In other areas related to landform analysis and processing; the geomorphometry has been deeply studied by researchers, but almost always with pure numeric approaches (Sulebak, Tallaksen, & Erichsen, 2000;

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Weibel & DeLotto, 1988). Some proposals have used ‘‘categories’’ or ‘‘classes’’ for making analysis (Evans, 198; Romstad, 2001). Recently, proposals such as (Sikder, 2009; Lee, Yang, & Wang, 2011), have gone beyond pure numerical analysis and have used knowledge-based systems to enhance the geographical applications. We believe that in order to obtain the semantics of a RSDS, it is necessary to have more information that is not contained in the image. In particular, we propose the use of concepts such as ‘‘island’’ which is defined as ‘‘portion of land surrounded by a ‘‘water body’’ or ‘‘lake’’ which means ‘‘water body inside of the land’’ in order to improve the effectiveness of our algorithms. This is the knowledge (the objects and relationships between them) that we humans use to determine the contents of the visual information that we process by means of our cognitive system (Fonseca, Egenhofer, Davis, & Câmara, 2002). Consequently, we believe that in order to completely solve this type of problems, it is necessary to move towards non-numeric processing approaches that are based on semantic analysis.

3.1.2. Concepts They are a collection of abilities and properties with a unique existence. There are four types of concepts:  Relational concepts (verbs). They are defined as elements denoting an action or operation over other concepts. CR represents the set of concepts–R.  Standard concepts (nouns). They are defined as elements belonging to a class. All their abilities and properties are abstract. CE denotes the set of concepts–E.  Class concepts. They are concepts–E that allow us to define partitions of CR and CE. They are described by CL (concepts–L).  Instance concepts. They are concepts whose abilities and properties are concrete. 3.1.3. Properties They are concepts aggregated or associated with other concepts by means of a belonging relation (has). Properties can be either abstract or concrete.

3. Methodology for feature extraction from raster data (FERD) In Torres et al. (2011) we have stated that the semantics of a set of geographic objects is given by the definition and/or description of these objects according to the conceptualization of the domain in which the objects have been processed. This seems to strongly suggest that it is necessary to specify a conceptualization for each particular case study. Accordingly, we propose a methodology to make a semantic representation of geospatial data which is composed of three stages: conceptualization, synthesis and description. In the following sections we describe each of these stages. 3.1. Conceptualization The main objective of the conceptualization stage is to generate two ontologies, namely, a high-level ontology that describes the whole geographic domain with its relationships and phenomena; and a domain ontology that provides a more detailed description of the application domain (i.e., the domain of the landforms). In Torres et al. (2011) we proposed a methodology, called GEONTOMET, for conceptualizing the geographic domain. The salient feature of this methodology is that it was designed with the goal of minimizing the number of axiomatic relations that are used to define concepts and relationships. In that work, we proposed a set of three fundamental axiomatic relations, namely (is,has and does), and a set of auxiliary relations based on the prepositions. The focus of the methodology consists of conceptualizing the geographic domain through these sets. GEONTO-MET states that to conceptualize the geographic domain, it is necessary to define the following components: 3.1.1. Relations They are elements used to link concepts. There are two types:  Simple: aqb 2 RKS , where a, b 2 C, q 2 A1, C is the set of concepts, A1 = {is, has, does} is the set of axiomatic relations and RKS is the set of simple relations for the conceptualization K.  Complex: aqbpc 2 RKC , where a, b, c 2 C, q 2 A1, p 2 A2, A1 = {is, has, does} is the set of axiomatic relations, A2 is the set of prepositions as defined by Eq. 1 and RKC is the set of complex relations for the conceptualization K.   to; before; under; with; against; of; from; in; between; towards A2 ¼ until; for; by; since; on; after; behind; beside; near; through

ð1Þ

3.1.4. Abilities They are concepts that define actions and/or operations associated with other concept (using the does relation). Abilities describe the interaction between concepts and properties. Abilities can be either abstract or concrete. As result of this stage, two ontologies were built. Ontology OG that represents the conceptualization of the geographic domain, and the ontology OD that describes the specific domain. These two ontologies are mapped to each other, and hence there exist relations between concepts in OD and concepts in OG. In order to establish such relations, we define the genealogy of a concept as the set of concepts having an existence relation. It is expressed n o as follows: GðaÞ ¼ bjaðisÞb 2 RKR [ GðbÞ, where a, b 2 C and RKR is the set of real or concrete relations for the conceptualization K. So, if a 2 OD, b 2 G(a) and c 2 OG then 8a9c; bðisÞc 2 RKR . This means that all the concepts of OD are not only directly related with OG, but they are also inherited by some concept in OG. The latter is shown in Fig. 1. 3.2. Synthesis In the synthesis stage, a set of extracts that are consistent with the conceptualization are obtained from the RSDS. The proposed extraction process follows an strategy similar to the one used for clustering objects, namely, it applies different criteria to different clusterization levels. For example, in an set that contains classroom furniture, we first try to classify the different objects into broad classes of furniture such as chairs, tables and blackboards. In the next level of clusterization we can apply a different set of criteria to each type of furniture to create more specific classes of objects by classifying chairs by their color, tables by their use and blackboards by their state. 3.2.1. Semantic decomposition algorithm We propose the semantic decomposition algorithm (SDA) as our extraction method. SDA quantifies different characteristics of the RSDS in an isotropic space of a segment set, which is represented by means of a dynamic tree (hierarchical segments) as in Adams and Williams (2003). The initial precondition is that the number of segments is equal to the number of discretional elements (pixels) of the RSDS. This condition is necessary, because there is no prior knowledge about the structure or form of the geographic objects contained in the RSDS. By means of quantifying geometric properties, an iterative process is carried out, where two segments

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Fig. 1. Genealogy.

are merged if some property is within a similitude range, and the segments satisfy the adjacency condition. A new node is created and associated with the involved segments in the dynamic tree to represent the fusion of the segment. The selection of the criteria that governs the segment fusing process is restricted by a set of characteristics that is computed for each segment in the fusion process. The segment characteristics are classified in two groups: attributes and properties. The attributes are a primary set of segment characteristics, which are dynamically estimated and stored in the dynamic tree for each segment at any level of its representation. The properties are quantitative characteristics and are selected considering the processing stage and the context of the problem. The set of characteristics for our context is sorted according to the order of complexity: global characteristics (for all RSDS), local characteristics (inside the neighborhood of a segment), integral raster values (IRV, sum of all RVs), number of pixels, first and second order moments (computed with respect to the center of the segment), non-additive perimeter and description of adjacent segments using a binary relation. This list represents the geometric and RV-related properties. In order to determine the numerical expressions needed to quantify the segment properties, it is necessary to work on a different space, and hence we apply a space transformation to convert regular objects into their isotropic counterparts (Levachkine, Velázquez, Alexandrov, & Kharinov, 2002). Isotropic objects have the advantage of being invariant to the rotation and translation (orientation and position) of the region that describes the geographic object. The latter simplifies the process of computing the homogenized quantitative parameters of an image. The transformation is performed as follows: we first determine the orientation of the individual objects contained in the RSDS, and define a new adequate coordinate system to it. By using this new coordinate system, an equalization of the axis scale is carried out. In this coordinate system, the real objects are described by an invariant parameter equal to the media square root of their size. Given a set of points that define an object in the original coordinate system (x, y), we compute the vectors (u, v) which are the basis of the new vectorial space, namely, the isotropic space (see Fig. 2). Then, the second order moments (computed relative to the center of inertia of an object) are obtained as the scalar products Ix  (u  u), Iy  (v  v), Ixy  (u  v), where isotropic objects (invariant

figures) are represented by two orthogonal vectors of the same length Ix = Iy, Ixy = 0. This way, any non-isotropic object is transformed into an isotropic one by means of a linear transformation, denoted by W (Eq. 2).



Wfug ¼ eh ðu cos /  v sin /Þ Wfv g ¼ eh ðu sin /  v cos /Þ

(

 )

If xy ¼ 0 e Ix ¼ Iey

ð2Þ

The transformation of vectors u and v is a function of the angle / which also determines the orientation of the axis for non-isotropic objects according to the initial configuration. Angle / is defined by Eq. 3.

( /:

sin 2/ ¼ r cosd c c cos 2/ ¼ r sinh d

;r  1

ð3Þ

In Eq. 4, the parameter c is related to the second order moments and represents the angle between the vectors that comprise the basis of the isotropic space. (Fig. 2). The parameter / is the angle

Fig. 2. Transformation to an isotropic space.This figure illustrates the geometrical meaning of the parameters c and /; and that of the vectors u and v. The shadowed region represents the area of a non-isotropic object with four vertices.

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between the semi-axis of the isotropic space and the x-axis of the original system (Fig. 2). By using these parameters, it is possible to compute d (Eq. 5). Please note, that for isotropic objects the value of d equals 0.

c:

8 Ixy ffi > < cos c ¼ pffiffiffiffiffi Ix Iy > : sinh c ¼  1

qffiffiffi

2



Ix Iy

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 cos2 c þ sinh c



qffiffiffi Iy Ix

ð4Þ

ð5Þ

The parameter h describes, in a logarithmic scale, the linear dimension ratio of the isotropic figures, it is computed using Eq. 6.



1 r ln lh; r ¼ 1; 2

ð6Þ

where l and h are the width and height of the object, respectively. The dimensions of the objects are computed independently of their orientation by using the average square of the distance of the figure to the main axis. They are computed using Eqs. 7 and 8, where n is the number of pixels of a given segment.

pffiffiffiffiffiffiffi Ix Iy l ¼ ðcosh c  dÞ n pffiffiffiffiffiffiffi Ix Iy 2 h ¼ ðcosh c þ dÞ n 2

ð7Þ ð8Þ

As shown in Eq. 9, the area (a) of an isotropic object equals the square of its linear size invariant (sz). This is related with the area of the initial object (non-isotropic) and is equal to the product l times h.

pffiffiffiffiffiffiffi Ix Iy j sinh cj s2z ¼ a ¼ n

ð9Þ

The number of points (n), area (a), height (h), width (l), the object invariant (s), as well as the trigonometric and hyperbolic parameters are computed for the whole RSDS in the fusion process. Lastly, the set of characteristics and parameters are composed of: raster value (I), average raster value (avgI), distance (d), length (l), width (w), size (sz), area (a), sinc, cos 2c and sin 2c. This set of parameters characterize, in an isotropic space, the objects extracted from an RSDS. Under this characterization it is possible

to use multiple dimensions to compare objects, which improves the process of combining objects because many of these characteristics can not be quantified in the original space. 3.2.2. Analysis The analysis stage consists of iteratively applying the semantic decomposition algorithm (SDA) to generate semantically decomposed RSDSs. As we have mentioned, the input of SDA is the source RSDS and the result is a RSDS in which the (raster value) RV for each pixel is normalized, according to the value of the segment to whom the pixel belongs to. The specific characteristics or parameters used in the execution of SDA determine when two segments have to be merged, and hence, the association between segments may be different with respect to other characteristics or parameters. In fact, the user needs to choose the adequate parameters in order to obtain a semantically decomposed RSDS that produces the best results. Generally, after the execution of the first iteration of the algorithm, the desired simplification is not obtained. This is due to the complexity of the geographic objects. So, in general it is necessary to apply the merging process once again, using as input the selected semantically decomposed RSDS. The goal is to execute the SDA until each main geographic object is described by a uniform pixel value. In order to control the execution of the algorithm, it is necessary to determine a semantic decomposition string as follows:

S ¼ fðk1 ; t 1 Þ; ðk; t2 Þ; . . . ; ðk; tn Þg

ð10Þ

where:  (ki, ti) are the parameters used in the ith iteration.  ti denotes the similitude threshold used in the ith iteration.  ki is the characteristic or parameter employed to simplify the RSDS Ri1 (used at the ith iteration). In Algorithm 1 the SDA is outlined. The function merge(s1, s2) is used to fuse segments s1 = {p1, p2, . . . , pn} and s2 = {q1, q2, . . . , qm} into merge (s1, s2) = {p1, p2, . . . , pn} [ {q1, q2, . . . , qm}. The SDA uses the function called compute(k, s), to evaluate the property k of the segment s. This function is defined by Eq. 11.

Fig. 3. Methodology for specializing extracts.

R. Quintero et al. / Expert Systems with Applications 39 (2012) 9008–9020

8 I > > > > > > avgI > > > > > > > d > > > > > > > 2 > > >l > > > < 2 computeðk; sÞ ¼ w > > > > > > > sz > > > > >a > > > > > sinh c > > > > > > > cos 2c > > : sin 2c

sI Rni¼1 sI n

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 cos2 c þ sin c pffiffiffiffiffiffi Ix Iy ðcosh c  dÞ n pffiffiffiffiffiffi Ix Iy ðcosh c þ dÞ n qp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffi Ix I y j sinh cj n pffiffiffiffiffiffi Ix Iy j sinh cj n sinh c

ð11Þ

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The RSDS obtained as output of the SDA is composed of a set of uniform raster values (RVs), which are further used in the recognition task. In this algorithm, the original pixel-values of geographic objects are used to process these objects and, in the next phase, to assign them to a concept in the ontology OD. Basically, we need to use a mapping function to extract each region within the original RVs. The result of this process is a list of regions called extracts, where the number of regions is equal to the different RVs obtained by the SDA. The algorithm retrieve all the homogeneous regions that were assigned to the ith-extract with i = {1, 2, . . . , ccss}. By using these regions, a new RSDS, denoted by IT i (in terms of Eq. 12) is generated.

IT i ¼ fðx; yÞ 2 IA jNc ðx; yÞ ¼ ig

ð12Þ

cos 2c sin 2c

where Nc(x, y) is a function that determines the number of extracts to whom the pixel p(x, y) belongs to. In consequence, the range of

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Fig. 4. Methodology for specializing extracts (cont.).

Fig. 5. Methodology for specializing extracts (cont.).

Fig. 6. Methodology for specializing extracts (cont.).

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Fig. 7. Methodology for describing extracts.

Fig. 8. Fragment of the Kaab ontology.

Range (Nc(x, y)) is {1, 2, . . . , nrcs}. Thus, the algorithm outputs a total of nrcs RSDSs denoted by IT ¼ fIT 1 ; IT 2 ; . . . ; Inrcs g, where each RSDS describes all extracts that can be assigned as an instance of a concept in OD. 3.2.3. Description The description stage consists of identifying and describing the extracts that have been obtained during the previous stage. One of the main objectives of this stage is to generate a mapping between the extracts and the concepts in the ontology OD. In addition to the mapping, some extra elements such as properties and measurements must be defined in order to achieve the identification of the extracts. The latter is performed using either the spectral signatures or a set of training RSDSs that were previously mapped

to key concepts. For instance, if the concept ‘‘water body’’ is defined in OD, then a set of known RSDSs of ‘‘water bodies’’ must be provided in order to train a learner that will be in charge of identifying objects of this type. This way, a classification process can be applied to the extracts in order to map them to a concept in OD. However, it is not always possible to link an extract to the best concept of a conceptualization; for example, if we assign an extract to the concept ‘‘mountain’’ or to the concept ‘‘hill’’, we must be able to differentiate between these two concepts. Let us review the definitions of such concepts: Mountain: ‘‘great natural elevation of land’’. Hill: ‘‘natural elevation of land lower than a mountain’’. Therefore, in the description stage we have to analyze the properties and relationships of the concepts in order to improve the

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Fig. 9. Fragment of the Hunxeet ontology.

Fig. 10. Fragment of the integrated ontology Kaab–Hunxeet.

mapping process (from extracts to concepts in the ontologies OD and OG). In the previous example, it can be understood that mountains have higher elevation than hills, so the value of the property ‘‘altitude’’ is considered from the RSDS to identify the extract as a mountain or as a hill. Additionally, the use of application domain

ontologies (Borst, 1997; Corcho, Fernandez-Lopez, & Gomez-Perez, 2002), in which the relationships between the spatial objects are computed by means of a set of digital image processing operators is proposed to obtain a better characterization of the most interesting geographic objects.

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To determine the best specialization of an extract, we follow a clustering approach. For example, Fig. 3 shows an extract that was mapped to a concept in OD, which is associated with three properties (prop1, prop2 and prop3). The concept also has three children concepts (A, B and C). As it is shown in Fig. 4, the values of the properties given by the conceptualization must be obtained (1). Please note that these values are obtained from the relevant extract (2) and as result, the properties of the extract with their values are obtained (3). Fig. 5 illustrates the next step in the process, in which the reference values for the properties are obtained (4). This will allow us to determine to which of the children concepts the extract must belong to. The reference values are obtained from the conceptualization (a priori knowledge) or by means of a training process (5). With these reference values, the extract is classified (6) and assigned to the most appropriate concept (7). In the next step (Fig. 6), the ‘‘is’’ relation (8) between the extract and the best concept is assigned (B, in the example). Now, additional properties of the new concept can be measured (9). As in the previous steps, measurements are taken from the RSDS (10). As a result, all the properties of the extract contain the assigned values (11). To build the description1 of an extract, we first obtain the extract mapped to the concept (1), see Fig. 7. The procedure is carried out by visiting the nodes of the extracts in the B tree. Once the extract is found, it can be described (2). At this point, the relationship that an extract has to the concept in OD is followed to obtain its existence information (2.1). Additionally, the label of the concept, as well as its properties and abilities are found (2.2 and 2.3). Once the description of an extract is made, the next extract to be described is searched for (3). The description process (2) is repeated until no more extracts are found in the B tree (4). 4. Results We used FERD to semantically represent geospatial objects contained in a set of RSDSs. Particularly, we applied the proposed methodology to extract and describe water and land bodies. The set of results presented here, are just a representative sample of the series of experiments that we have performed using our proposed methodology. 4.1. Conceptualization The conceptualization was performed in two parts: conceptualization of the geographic domain, and conceptualization of the specific domain (land and water bodies). Fig. 8 shows an extract of the Kaab2 ontology that contains the main classes defined for conceptualizing the geographic domain. Detailed descriptions of each class, as well as all the remaining concepts can be found in Quintero (2007) (in spanish3). For this conceptualization, we have used the topographic 1:50000 vector data dictionary from Mexico INEGI (1996), where more than 70 topographic features are defined. An extract of the Hunxeet4 ontology, which is used for conceptualizing the domain of land and water bodies is also depicted in Fig. 9. It includes concepts like ‘‘continent’’, ‘‘ocean’’, ‘‘lake’’, among others. These concepts are also taken from ISO (2005). As we have already mentioned, the Kaab ontology was devel1 The description of an extract consist of a declaration of existence and a characterization by means of its properties. 2 From the mayan word kaab, that means Earth. 3 http://sites.google.com/site/rolandoquintero/home/formacion-academica/ TesisDoctoral.pdf. 4 From mayan voice hunxet’ lu’um, that means landscape.

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Fig. 11. RSDSs used for test purposes: Mexico.

oped using the GEONTO-MET methodology described in Torres et al. (2011). Such methodology establishes the use of seven partitions to provide meaning to the concepts in the geographic domain. These partitions are as follows:  Sayab, (nature) used to distinguish between real and imaginary objects. Examples: hills are real, magnetic field lines are imaginary.  Ixco, (position) distinguishes objects according to their position in the land. Examples: sewers are sub-superficial, streets are superficial and electric lines are super-superficial.  Utskin (matter) classifies the objects into water, ground or air. Examples: reefs are water objects, rails are land objects and air routes are air objects.  Xuul, (boundary) classifies objects according to their boundary type: bona-fide or fiat. Based on the definitions proposed in Smith and Varzi (1997).  Moots, (origin) distinguishes objects according to their origin: natural, such as forests; and artificial, such as buildings.  Pakaat, (sense) represents perceivable objects (their effects can be perceived or measured) such as air flows; and non-perceivable, such as country boundaries.  Chuuk, (scope) describes the scope associated to the objects. There are regional objects, such as volcanoes; national objects, such as seas or gulfs; and international objects, such as oceans. The ontologies developed in this stage have been integrated with each other to enrich the described knowledge. Fig. 10 shows the integration of the Kaab ontology with the Hunxeet ontology by means of the association of the main classes of theHunxeet ontology with their corresponding classes in the Kaab ontology.

4.2. Synthesis In this section, we depict the results obtained with the semantic decomposition algorithm (SDA). Different semantic decomposition strings were used for the RSDS with similar results. The latter is important because it indicates that the SDA is not very sensitive to the selection of the semantic decomposition string. Fig. 12 presents the results of applying the SDA to the RSDS of Fig. 11 using the decomposition string S = {(I, 21.5), (I,2.5), (I, 1.5), (d, 90)} that produced the best results for this test. This particular decomposition string indicates that in its first three iterations, the SDA fuses segments based on the intensity or height (‘‘I’’) of the different regions (please remember that initially every pixel is considered a region). The latter is necessary because in these early iterations

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Fig. 12. RSDSs obtained when applying the semantic decomposition string to the test RSDS. (a) First iteration: result of using (int, 21.5) to the original RSDS; (b) second iteration, result of using (int,2.5); (c) third iteration, result of using (int,1.5); (d) fourth iteration, result of using (d, 90).

Fig. 13. Result of the SDA applied to the test RSDS.

of the algorithm, no geometry has been detected. Once the geometry of the different regions has begun to emerge, SDA performs a last iteration based on the isotropic distance as defined by Eq. 5. The RSDSs generated after applying the extraction algorithm are depicted in Fig. 13. As it is shown in Fig. 12a, after the first iteration of the SDA, there are many segments sharing an intensity, which is within 21.5 units of difference. Although it is apparent (for the human eye) that the main extracts have been found in this first iteration, it will be necessary to iterate two more times (varying the intensity threshold) to clearly obtain the final extracts. In the last iteration, the unconnected segments with the same intensity are differentiated by their isotropic distance (parameter d). The latter is shown in Fig. 12c and Fig. 12d.

4.3. Description The labels obtained in the recognition and specialization algorithms are T I0 ¼ fwater body; land massg and SI0 ¼ fsea; land; islandg. It is important to mention that only one instance of the

Fig. 14. Semantic description of RSDS.

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Fig. 15. (a) Original RSDS ‘island01’. (b) Result of synthesis stage by using the string S = {(I, 50), (avgI, 50), (sin 2c, 50), (l, 50), (sinc, 50)}.

Fig. 16. Semantic description of the RSDS from Fig. 15.

Fig. 18. Semantic description of the RSDS from Fig. 17.

same concept is described. In the test RSDS, we have two water bodies, but only one label appeared. Lastly, we semantically represent the extracts obtained by matching the labels to concepts as previously described. In Fig. 14 the result of the description stage is presented for the RSDS shown in Fig. 11.

resulting image is shown in Fig.17(b) and the result of the description stage is presented in Fig. 18.

4.4. Additional results In this section, we present the results of two more experiments in which we applied FERD to the RDSDs shown in Fig. 15(a) and Fig. 18(a). In the first of these experiments, we used the decomposition string S = {(I, 50), (avgI, 50), (sin 2c, 50), (l, 50), (sinc, 50)} as input of the SDA. The latter indicates that in the first iteration, SDA fuses segments based on the intensity of the pixels (‘‘I’’), in the second iteration it uses the average intensity (‘‘I’’), in the third iteration it uses the sin 2c as defined by Eq. 4, in the fourth it uses intensity (‘‘I’’), and in the last iteration it uses the sinc as defined by Eq. 4. The resulting image is shown in Fig.15(b) and the result of the description stage is presented in Fig. 16. For the RDSD of the Fig. 18(a) we used the decomposition string S = {(I, 21.5), (I, 22.5), (a, 22.5), (a, 22.5)} as input of the SDA. This indicates that in the first two iterations, SDA fuses segments based on the intensity of the pixels (‘‘I’’), and in the third and fourth iterations it uses the isotropic area (‘‘a’’) as defined by Eq. 9. The

5. Conclusions In this work, we have presented a methodology composed of three stages (conceptualization, synthesis and description) for making semantic descriptions of RSDSs. A semantic description of a RSDS consist of the identification of the types of spatial objects contained in the dataset, as well as the characterization of these objects by means of their individual properties. In the conceptualization stage, we propose to use only three axiomatic relations, which allow us to translate the ‘‘classic’’ relations into concepts that are also part of the conceptualization, enriching the semantics of the ontology. As a case study, we developed the Kaab ontology for the conceptualization of the geographic domain and the Hunxeet ontology for the conceptualization of water and land bodies. The synthesis stage was conducted by applying the semantic decomposition algorithm (SDA), which is a general decomposition method to obtain the meaningful geographic objects contained in a raster spatial dataset. SDA employs a new transformation to an isotropic space that serves to quantify relevant attributes and geometric properties of the segments. The main goal of the stage is to generate a series of semantic decomposition strings that are used to simplify the RSDS. The algorithm is applied until

Fig. 17. (a) Original RSDS ‘island01’. (b) Result of synthesis stage by using the string S = {(I, 21.5), (I, 22.5), (a, 22.5), (a, 22.5)}.

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