Shape similarity measurement model for holed polygons based on position graphs and Fourier descriptors

Xu, Yongyang; Xie, Zhong; Chen, Zhanlong; Wu, Liang

doi:10.1080/13658816.2016.1192637

Cited by 31 publications

(22 citation statements)

References 28 publications

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“…The multilevel chord length [30] is adopted to construct complex functions to describe the geometric shape from entity to part, and the shape descriptor is based on the fast Fourier transform of the complex function [31]. This paper is an extension of our precedent work [25]. The main idea of this model is not characterized merely by the iterative approach of our previous work; the whole spatial distribution information of the holed-regions in the complex holed-region entity scenes is represented in our model, which is ignored in many previous studies.…”

Section: Introductionmentioning

confidence: 96%

“…Each edge of a shape is formed by two forces that have equal value but opposite direction [25]. As a result, a region can be described by a set of forces.…”

Section: Descriptive Measurement Of the Position Graphsmentioning

confidence: 99%

“…It is easily to see that the shape similarity and direction relationship similarity of solution 1 are all higher than those in solution 2 from Table 7. We can compute the matching completeness of the two solutions with Formula (24) and then substitute the results of matching completeness, shape similarity, and direction similarity into Formulas (23) and (25) to obtain the similarities of the two solutions, as shown in Table8. …”

Section: Inner Contour Similarity Measurement Of the Matching Lakesmentioning

confidence: 99%

“…When evaluating the consistency of the direction relationship between two holes in the micro-spatial-scenes R 2 and R' 2 , which are multi-hole regions, we should give the characteristic matrix of any pairs of holes in the scenes. A conceptual space of the F-Matrix is represented by the 4-D lattice [25]. The distance between two F-Matrixes on the 4-D lattice stands for the dissimilarity of the directions.…”

Section: Inner Contour Similarity Measurement Of the Matching Lakesmentioning

confidence: 99%

“…The hole distribution is considered as a constraint satisfaction problem (CSP) [24] that comprises the shape descriptors and the directional relationships of the holes. In addition, position graphs [25] describe the distribution of the micro-spatial-scene, and a force diagram [26,27] is used to measure the similarity between the graphs. The extended Hausdorff distance [28] represents the relationships between the holed-regions and the scene center.…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Model for the Similarity Measurement of a Complex Holed-Region Entity Scene

Chen

Zhu

Xie

et al. 2017

IJGI

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Abstract:Complex multi-holed-region entity scenes (i.e., sets of random region with holes) are common in spatial database systems, spatial query languages, and the Geographic Information System (GIS). A multi-holed-region (region with an arbitrary number of holes) is an abstraction of the real world that primarily represents geographic objects that have more than one interior boundary, such as areas that contain several lakes or lakes that contain islands. When the similarity of the two complex holed-region entity scenes is measured, the number of regions in the scenes and the number of holes in the regions are usually different between the two scenes, which complicates the matching relationships of holed-regions and holes. The aim of this research is to develop several holed-region similarity metrics and propose a hierarchical model to measure comprehensively the similarity between two complex holed-region entity scenes. The procedure first divides a complex entity scene into three layers: a complex scene, a micro-spatial-scene, and a simple entity (hole). The relationships between the adjacent layers are considered to be sets of relationships, and each level of similarity measurements is nested with the adjacent one. Next, entity matching is performed from top to bottom, while the similarity results are calculated from local to global. In addition, we utilize position graphs to describe the distribution of the holed-regions and subsequently describe the directions between the holes using a feature matrix. A case study that uses the Great Lakes in North America in 1986 and 2015 as experimental data illustrates the entire similarity measurement process between two complex holed-region entity scenes. The experimental results show that the hierarchical model accounts for the relationships of the different layers in the entire complex holed-region entity scene. The model can effectively calculate the similarity of complex holed-region entity scenes, even if the two scenes comprise different regions and have different holes in each region.

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Section: Introductionmentioning

confidence: 96%

“…Each edge of a shape is formed by two forces that have equal value but opposite direction [25]. As a result, a region can be described by a set of forces.…”

Section: Descriptive Measurement Of the Position Graphsmentioning

confidence: 99%