A New Quadtree Histogram-based Spatial Modeling based on Cloud Model

Directional relations, topological relations and metric relations are the basic spatial constraint in the geometric space. The three kinds of spatial relations are not isolated and restrict each other. In this paper, we focus on the effect of topology and distance on the representation of directional relations and present a description mechanism of directional relations considering topology and distance. In this new model, (1)topological constraint is analyzed as the basis of directional relations categories; (2)distance relations is the other factor of representation of directional relations and distinguish the directional relations of different positions in the same ray line; (3)depending on the analysis of the capability of exiting directional relations models to represent the restraint from the topological relations and distance, a category mechanism based on the topological relations and distance is proposed to improve the accuracy of the directional description. This model combines the restraint from topological and distance relations and consummates the representation of directional relations. Experiments show excellent efficiency in view of directional description.

The spatial relations usually consist of topological, directional and measurement relations. It is not accurate to using single spatial relation to describe spatial scene. Double projections and interior-division matrix model in 3D space is proposed by dividing the reference object within interior rectangle box. The expression of direction relations is combined with interior, boundary and exterior direction relations. 11 transforming rules are proposed by the constraint between directional and topological relationships. Finally, the model is evaluated by Roop K.Goyal’s five required properties and the result shows the satisfaction.

5 - Geographic Relations

A concept of fuzzy three-dimensional Voronoi Diagram is presented for spatial relations analysis of real world three-dimensional geographical data, where it is an extension of well known two-dimensional Voronoi Diagram to three-dimensional representation with uncertain spatial relation information in terms of fuzzy set. It makes possible to analyze quantitatively complex boundaries of geographically intricate areas, to give human friendly fuzzy explanation of determining three-dimensional directions, and to express uncertain spatial relations by precise unified fuzzy description. It is applied to decide spatial direction relations of artificial geographicalmountain data, which includes 8 spatial directions with at most 60 relative direction relations, and it leads to detect threedimensional directions whereas the expression of traditional 4 directions and 12 relative directions indicate two-dimensional directions only. The proposed concept aims to discriminate neighbors’ class relations and spatial-temporal changes of specially appointed objects, and also aims to be a tool to achieve the intellective extraction and analysis of geographical data of a mountainous area located in northeast China.

The spatial relation model is an important technique for image indexing and retrieval in image or multimedia databases. 2D strings and its variants are proposed to support the representation of spatial relationships. A novel spatial knowledge representation model named “Two Dimension Begin-End boundary string” (2D Bε-string) is proposed. The 2D Bε-string represents an icon by its MBR boundaries. By applying a number of “dummy objects”, the 2D Bε-string can intuitively and naturally represent the pictorial spatial information without any spatial operator. In addition, an image similarity evaluation method based on the modified “Longest Common Subsequence” (LCS) algorithm is presented. By using the proposed evaluation method, not only can those images for which all the icons and their spatial relationships fully agree with the query image be sifted out, but also those images whose partial icons and/or spatial relationships are similar to the query image. It resolves the problems of query targets and/or spatial relationships not being certain. Our representation model and similarity evaluation also simplify the retrieval progress of linear transformations, including image rotation and reflection

The development of formal models of spatial relations is a topic of great importance in spatial reasoning, geographic information systems (GIS) and computer vision, and has gained much attention from researchers across these research areas during the past two decades. In recent years significant achievements have been made on the development of models of spatial relations between spatial objects with precisely defined boundaries. However, these models cannot be directly applied to spatial objects with indeterminate boundaries which are found in many applications in geographic analysis and image understanding. This article develops a method for approximately analyzing binary topological relations between geographic regions with indeterminate boundaries based upon previous work on topological spatial relations and fuzzy sets. In addition, examples are given to demonstrate the method and related concepts. It is shown that the eight binary topological relations between regions in a two-dimensional space can be easily determined by the method.

Fuzzy difference operators are used in different fields of decision making processes, image analysis and computer vision applications. Change detection in a spatial scene is the basic issue in modeling relative motion between object pair. Many approaches are adopted to change detection in a spatial scene and change in spatial relations is one of them. Separate methodologies are adapted to determine the change in topological, directional and distance relations. In this paper, a methodology for detection of a spatial change based on fuzzy matrix calculus is presented. Difference of combined fuzzy topological and directional relations matrices is determined by fuzzy difference operators. Experiments are performed to validate the proposed method and the promising results are obtained.

The technological progress in the field of artificial intelligence (AI) has brought new opportunities and challenges to the intelligent development and innovative research in fuzzy spatial relations, fuzzy theory is the basic theory of intelligent information processing, and the paper gives a brief analysis of fuzzy calculation method in spatial analysis and spatial relation calculation. In particular, the spatial relations of fuzzy objects are more difficult to express and describe accurately. This paper proposes a method to calculate the topological relations between fuzzy objects with 4-Intersection model and 9-Intersection model, in the analysis of spatial relations, the extension from deterministic entity to uncertain entity is realized with fuzzy set theory, the fuzzy space matrix is constructed, then fuzzy topological relations and fuzzy membership are calculated and output, the model simplifies many complex relations, and it can describe eight topological relations including disjoint, meet, overlap, covers, contains, covered-by, inside and equal. In practical application, the position of spatial objects can be controlled and adjusted according to topological relations. Through analysis of algorithm and fuzzy membership calculation, the model is effective in theory.

To solve the disadvantages of high difficulty and complexity in studying the spatial topological relation method on different resolution remote sensing images, this paper proposes a spatial topological relationship model based on GeoSOT, which is one of the global subdivision grids. To express spatial objects on different resolution remote sensing images, this paper introduces the spatial objects subdivision location identification. Then, the model calculates spatial topological relation by comparing location identifications in combined table. At last, test shows that it is feasible to analyze the spatial objects topological relations based on GeoSOT and it has high efficiency operation significantly, especially for complicated spatial objects.

Modeling of image content based on chromatic arrangement includes representation of the spatial relationship between complex sets of pixels. We propose a model of spatial directional relationship between extended sets. This involves the same computational and programming complexity as that of conventional representations based on centroids, but it is able to account for the overall sets of pixels without reducing them to a single representative point or to a bounding rectangle. The gain in effectiveness is evaluated in a user-based comparison with a representation based on mutual centroid orientation.

Models of spatial relations are a key component of geographical information science (GIS). Efforts have been made to formally define spatial relations. The foundation model for such a formal presentation is the 4-intersection model proposed by Egenhofer and Franzosa (1991). In this model, the topological relations between two simple spatial entities A and B are transformed into pointset topology problems in terms of the intersections of A's interior and boundary with B's interior and boundary. Later, Egenhofer and Herring (1991) extended this model to 9-intersection by addition of another element, i.e. the exterior of an entity, which is then defined as its complement. However, the use of its complement as the exterior of an entity causes the linear dependency between its interior, boundary and exterior. Thus such an extension from 4- to 9-intersection should be of no help in terms of the number of relations. This can be confirmed by the discovery of Egenhofer et al. (1993). The distinction of additional relations in the case where the co-dimension is not zero is purely due to the adoption of definitions of the interior, boundary and exterior of entities in a lower dimensional to a higher dimension of space, e.g. lines in 1-dimensional space to 2-dimensional space. With such adoption, the topological convention that the boundary of a spatial entity separates its interior from its exterior is violated. It is such a change of conventional topological properties that causes the linear dependency between these three elements of a spatial entity (i.e. the interior, boundary and exterior) to disappear, thus making the distinction of additional relations possible in such a case (i.e. the co-dimension is not zero). It has been discussed that the use of Voronoi-regions of an entity to replace its complement as its exterior in the 9-intersection model would solve the problem (i.e. violation of topological convention) or would make this model become more comprehensive. Therefore, a Voronoi-based 9-intersection model is proposed. In addition to the improvement in the theoretical aspect, the Voronoi-based 9-intersection model (V9I) can also distinguish additional relations which are beyond topological relations, such as high-resolution disjoint relations and relations of complex spatial entities. However, high-resolution disjoint relations defined by this model are not purely topological. In fact, it is a mixture of topology and metric.

The integration of the raster data cube alongside another form of geospatial data (e.g., vector data) raises considerable challenges when it comes to managing and representing it using knowledge graphs. Such integration can play an invaluable role in handling the heterogeneity of geospatial data and linking the raster data cube to semantic technology standards. Many recent approaches have been attempted to address this issue, but they often lack robust formal elaboration or solely concentrate on integrating raster data cubes without considering the inclusion of semantic spatial entities along with their spatial relationships. This may constitute a major shortcoming when it comes to performing advanced geospatial queries and semantically enriching geospatial models. In this paper, we propose a framework that can enable such semantic integration and advanced querying of raster data cubes based on the virtual knowledge graph (VKG) paradigm. This framework defines a semantic representation model for raster data cubes that extends the GeoSPARQL ontology. With such a model, we can combine the semantics of raster data cubes with features-based models that involve geometries as well as spatial and topological relationships. This could allow us to formulate spatiotemporal queries using SPARQL in a natural way by using ontological concepts at an appropriate level of abstraction. We propose an implementation of the proposed framework based on a VKG system architecture. In addition, we perform an experimental evaluation to compare our framework with other existing systems in terms of performance and scalability. Finally, we show the potential and the limitations of our implementation and we discuss several possible future works.

Due to the vagueness of spatial direction relations and the limitation of current models, a fuzzy description model of direction relations based on adaptive sampling is presented. According to fuzzy theory, a new membership function is proposed as the reference model which is a basic fuzzy description model of 4 directions. And two objects are adaptively partitioned and sampled, thus the detailed fuzzy description of direction relations between two objects and the cardinal direction relations are obtained by calculating the direction relations between two sample point sets. At last, the validity of this model is verified by an illustration. Moreover, the direction relations between overlapping and contained region can also be effectively described using this model.

Handling the deformations of the lung tissues in successive chest computed tomography (CT) scans of a patient is a vital step in any computer-aided diagnostic (CAD) system for lung cancer diagnosis. In this paper, we propose a new nonrigid registration methodology for the segmented lung region from CT data that involves two steps. The first step globally aligns the target-to-reference CT scans using an affine transformation based on ascent maximization of the estimated mutual information of the calculated distance map using the fast marching level sets method inside the segmented lung for both the target and reference objects. The second step is the local alignment of the target lung object in order to correct for intricate relative deformations due to breathing and heart beats. The local deformations are handled based on displacing each voxel of the target over evolving closed equi-spaced surfaces (iso-surfaces) to closely match the reference object. In order to displace the voxel on the iso-surfaces of the target lung object, the initial voxel-to-voxel match between target and reference lung objects is estimated by solving the 3D Laplace equation between each two corresponding iso-surfaces on the reference and target objects. Finally, the estimation of voxel-to-voxel match is refined through iterative energy minimization using a generalized Gauss-Markov random field (GGMRF) model. Qualitative and quantitative results demonstrate the promise of the proposed nonrigid registration framework.

This research proposes an advanced approach that improves the efficiency of skyline query processing by significantly reducing the computational cost on object comparisons, i.e., dominance tests between objects. Our solutions are based on two novel concepts. The skyline query over Minimum Bounding Rectangles (MBRs) receives a set of MBRs and returns the MBRs that are not dominated by other MBRs. In the dominance test for MBRs, the detailed attribute values of objects in the MBRs are not accessed. Moreover, the dependent group of MBRs reduces the search space for dominance tests. Objects in an MBR are only compared with the ones in the corresponding dependent groups of the MBR rather than with the entire dataset. Our solutions apply the two concepts to the R-tree in order to use its hierarchical structure in which every node is a natural abstraction of an MBR. Specifically, given the R-tree index of an input dataset, we first eliminate unqualified objects by utilizing the skyline query over MBRs (i.e., intermediate nodes in the R-tree). Subsequently, we generate dependent groups for the skyline MBRs. Two dependent group generation methods that rely on either the sorting technique or the R-tree index are developed. Further, we apply an existing skyline algorithm to every dependent group, and the results of the original skyline query are the union of skyline objects in the dependent groups. In addition, we also analyze the cardinality of the two new concepts based on a probabilistic model, which enables us to analyze the computational complexity of the proposed solutions. Our experimental results show that the proposed solutions are clearly more efficient than the state-of-the-art approaches.