Topological relations between a directed line and a directed region

2020 ◽  
Vol 24 (2) ◽  
pp. 526-548
Author(s):  
Jingwei Shen ◽  
Yang Huang ◽  
Min Chen
2020 ◽  
Vol 22 (4) ◽  
pp. 497-518
Author(s):  
Jingwei Shen ◽  
Kaifang Shi ◽  
Min Chen

2021 ◽  
Vol 5 (1) ◽  
pp. 1-20
Author(s):  
Isabelle Bloch

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.


Author(s):  
Xiongnan Jin ◽  
Sungkwang Eom ◽  
Sangjin Shin ◽  
Kyong-Ho Lee ◽  
Chaoqun Hong

2014 ◽  
Vol 602-605 ◽  
pp. 3104-3106
Author(s):  
Shao Hua Liu ◽  
Jia Hua Zhang

This paper introduced points and directed line segment relation judgment method, the characteristics of generation and Graham method using the original convex hull generation algorithm of convex hull discrete points of the convex hull, an improved algorithm for planar discrete point set is proposed. The main idea is to use quadrilateral to divide planar discrete point set into five blocks, and then by judgment in addition to the four district quadrilateral internally within the point is in a convex edge. The result shows that the method is relatively simple program, high computational efficiency.


2007 ◽  
Vol 10 (4) ◽  
pp. 293-298
Author(s):  
Min Deng ◽  
Zhilin Li ◽  
Guangqiang Li ◽  
Xuesong Zhang

Author(s):  
YUE LU ◽  
CHEW LIM TAN ◽  
PENGFEI SHI ◽  
KEHUA ZHANG

In this paper, we illustrate a method to segment handwritten Chinese characters from destination addresses of mail pieces. Fast Hough transform is utilized to detect the reference lines preprinted on the mail piece. In the segmentation, subassemblies of Chinese characters are merged based on the structural features of Chinese characters and the subassemblies' topological relations, viz. upper–lower, inside–outside and left–right relations. The width of subassemblies and the spacing between neighboring subassemblies in the whole image of the destination address are analyzed to guide the merging of the left–right subassemblies. Experimental results with real mail piece images show that the proposed approach has achieved a promising performance for segmenting handwritten Chinese characters.


2004 ◽  
Vol 127 (3) ◽  
pp. 502-505 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Yi Zhang ◽  
Ruj Bunduwongse

A point-line refers to a rigid combination of a directed line and an endpoint along the line. To trace a point-line trajectory, one must control not only the trajectory of the endpoint (the directrix) but also the direction of the point-line (the indicatrix). This paper addresses three issues on point-line trajectories. First of all, by considering the relationship between the point trajectory and the corresponding point-line direction, it offers the complete characterization of point-line trajectories. It presents the coordination of the point-line axis with a free point trajectory and also with a point trajectory constrained on a free form surface. The issue of maintaining an invariant orientation relationship between the point-line axis and the point trajectory is also addressed.


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