Related papers: Generalized $\beta$-skeletons
$\beta$-skeletons are well-known neighborhood graphs for a set of points. We extend this notion to sets of line segments in the Euclidean plane and present algorithms computing such skeletons for the entire range of $\beta$ values. The main…
A {\beta}-skeleton is a proximity graphs with node neighbourhood defined by continuous-valued parameter {\beta}. Two nodes in a {\beta}-skeleton are connected by an edge if their lune-based neighbourhood contains no other nodes. With…
The $\beta$-skeleton is a mathematical method to construct graphs from a set of points that has been widely applied in the areas of image analysis, machine learning, visual perception, and pattern recognition. In this work, we apply the…
A \beta-skeleton is a proximity undirected graph whose connectivity is determined by the parameter \beta. We study \beta-skeleton automata where every node is a finite state machine taking two states, and updating its states depending on…
A fractal construction shows that, for any beta>0, the beta-skeleton of a point set can have arbitrarily large dilation. In particular this applies to the Gabriel graph.
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also…
The choice of the representations is essential for deep gait recognition methods. The binary silhouettes and skeletal coordinates are two dominant representations in recent literature, achieving remarkable advances in many scenarios.…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
We generalize the notions of $\beta$- and $\lambda$-maps to general selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normality, extremal disconnectedness,…
Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…
Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural…
Gait recognition is a promising video-based biometric for identifying individual walking patterns from a long distance. At present, most gait recognition methods use silhouette images to represent a person in each frame. However, silhouette…
This paper investigates body bones from skeleton data for skeleton based action recognition. Body joints, as the direct result of mature pose estimation technologies, are always the key concerns of traditional action recognition methods.…
A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…
Gait recognition is a promising biometric with unique properties for identifying individuals from a long distance by their walking patterns. In recent years, most gait recognition methods used the person's silhouette to extract the gait…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
We discuss the skeleton as a probe of the filamentary structures of a 2D random field. It can be defined for a smooth field as the ensemble of pairs of field lines departing from saddle points, initially aligned with the major axis of local…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
A skeleton representation of the human body has been proven to be effective for this task. The skeletons are presented in graphs form-like. However, the topology of a graph is not structured like Euclidean-based data. Therefore, a new set…
A Deza graph with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$ vertices in which any two vertices have $a$ or $b$ ($a\leq b$) common neighbours. A Deza graph is strictly Deza if it has diameter $2$, and is not strongly regular. In…