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We present a method that allows for the discovery of communities within graphs of arbitrary size in times that scale linearly with their size. This method avoids edge cutting and is based on notions of voltage drops across networks that are…
This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…
Representing 3D shape is a fundamental problem in artificial intelligence, which has numerous applications within computer vision and graphics. One avenue that has recently begun to be explored is the use of latent representations of…
Visual object recognition in unseen and cluttered indoor environments is a challenging problem for mobile robots. This study presents a 3D shape and color-based descriptor, TOPS2, for point clouds generated from RGB-D images and an…
3D convolutional networks is a good means to perform tasks such as video segmentation into coherent spatio-temporal chunks and classification of them with regard to a target taxonomy. In the chapter we are interested in the classification…
In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A…
We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances…
In this paper, we address the challenging problem of spatial and temporal action detection in videos. We first develop an effective approach to localize frame-level action regions through integrating static and kinematic information by the…
Geometric 3D scene classification is a very challenging task. Current methodologies extract the geometric information using only a depth channel provided by an RGB-D sensor. These kinds of methodologies introduce possible errors due to…
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
We present a method that detects boundaries of parts in 3D shapes represented as point clouds. Our method is based on a graph convolutional network architecture that outputs a probability for a point to lie in an area that separates two or…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Unsupervised anomaly detection in time series is essential in industrial applications, as it significantly reduces the need for manual intervention. Multivariate time series pose a complex challenge due to their feature and temporal…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
We describe an algorithm which, given two essential curves on a surface $S$, computes their distance in the curve graph of $S$, up to multiplicative and additive errors. As an application, we present an algorithm to decide the…
In this paper, we reconsider the early computer vision bottom-up program, according to which higher level features (geometric structures) in an image could be built up recursively from elementary features by simple grouping principles…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
Topology identification comprises reconstructing the interaction Hamiltonian of a quantum network by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology…
Taking into account the regional characteristics of intrinsic and extrinsic properties of space is an essential issue in architectural design and urban renewal, which is often achieved step by step using image and graph-based GANs. However,…