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Graphical Metric Spaces and Fixed Point Theorems
Published in Dhananjay Gopal, Praveen Agarwal, Poom Kumam, Metric Structures and Fixed Point Theory, 2021
Since E(G) ⊇ Δ, then we have x ∈ BG(x,ε) and so BG(x,ε)≠∅ for all x ∈ X and ε > 0. The collection B = {BG(x,ε) : x ∈ X,ε > 0} is a neighbourhood system for the topology τG on X induced by the graphical metric dG. Explicitly, a subset U of X is called open if for every x ∈ U there exists an ε > 0 such that BG(x,ε) ⊂ U. Of course, a subset C of X is called closed if its complement X \ C is open. Lemma 1. Every open ball in X is an open set.
Mixture Models for Image Analysis
Published in Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert, Handbook of Mixture Analysis, 2019
When the Zi are not independent, the interrelationship between sites can be modelled by a so-called neighbourhood system usually defined through a graph. Two neighbouring sites correspond to two nodes of the graph linked by an edge. The dependencies between neighbouring Zi are then modelled by further assuming that the joint distribution of Z1, …, Zn is a discrete Markov random field (MRF) on this specific graph defined by () p(z)=W−1exp(−H(z)),
Applications of Computer Vision
Published in Manas Kamal Bhuyan, Computer Vision and Image Processing, 2019
In literature, MRF is widely used as a tool for semantic segmentation [250], [77] and [54]. The classical MRF model used for segmentation is a pixel-based model [82] and [12]. An essential component of MRF is defining a neighbourhood system. A neighbourhood of rectangular lattice is chosen for classical pixel-based MRF and each site on the lattice is represented by a pixel.
A point cloud segmentation method for power lines and towers based on a combination of multiscale density features and point-based deep learning
Published in International Journal of Digital Earth, 2023
Wenbo Zhao, Qing Dong, Zhengli Zuo
In this study, training and testing datasets for power lines and towers were constructed using UAV LiDAR point data (with a total of six sections), and the density characteristics of these data were analysed. The density of the point clouds located on the basic structure of the object changed slightly after rotating at different angles. In contrast, the density of the point clouds in the details changed significantly, providing a theoretical foundation for the point segmentation of the power lines and towers. In terms of methods, a model combining multiscale density features and deep learning was proposed in this study. First, the point data are blocked, and the neighbourhood system is constructed. The subsequent operations are based on these neighbourhoods. Next, the point clouds are downsampled once to obtain the sparse point clouds. The point clouds before and after sampling are rotated, and their density is calculated. A direct mapping method is used to fuse the density information, and a lightweight network is constructed to train the features. Finally, the density information is concatenated with the local features provided by PointCNN, and the joint features are used to segment the point clouds.
Economic and ergonomic performance enhancement in assembly process through multiple collaboration modes between human and robot
Published in International Journal of Production Research, 2023
Anthony Quenehen, Nathalie Klement, Amine Mohamed Abdeljaouad, Lionel Roucoules, Olivier Gibaru
The metaheuristic goes through the space of solutions, considering lists Y of tasks, using a neighbourhood system V. Each considered list Y of tasks gives an assignment solution X thanks to the list algorithm L, whose cost is assessed using the overlap function described in Figure 4. Then, this solution is evaluated thanks to an objective function H. The metaheuristic then generates a new list from the current one, using the neighbourhood system V. In the developed method, a swap between two tasks is used as a neighbourhood system. The tasks of this new list , the neighbour, are then assigned thanks to the heuristic L, to give a solution . This solution is then evaluated using the objective function H. Finally both solutions (the current X and the neighbour ) are compared using the principle of the chosen metaheuristic. Algorithm 2 illustrates this hybridisation using the simulated annealing as a metaheuristic.
A new split-based hybrid metaheuristic for the reconfigurable transfer line balancing problem
Published in International Journal of Production Research, 2021
Y. Lahrichi, N. Grangeon, L. Deroussi, S. Norre
The neighbourhood system described in this subsection is used in Algorithms 2 and 4. We use a simple insertion neighbourhood: insert an operation in a different position of the giant sequence. This neighbourhood is applied in such way that the precedence constraints are respected. Given the giant sequence σ: a random neighbour is obtained by selecting a random operation . Once this operation selected, two operations must be identified and such that and Then a random position is selected between positions and (uniform selection in ) to (re)insert operation .