Related papers: Vertex characterization via second-order topologic…
In this paper, we propose a flexible notion of characteristic functions defined on graph vertices to describe the distribution of vertex features at multiple scales. We introduce FEATHER, a computationally efficient algorithm to calculate a…
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…
Let $G$ be a finite, simple, and undirected graph of order $n$ and average degree $d$. Up to terms of smaller order, we characterize the minimal intervals $I$ containing $d$ that are guaranteed to contain some vertex degree. In particular,…
Image restoration is a class of important tasks that emerges from a wide range of scientific disciplines. It has been noticed that most practical images can be modeled as a composition from a sparse singularity set (edges) where the image…
Text network analysis has received increasing attention as a consequence of its wide range of applications. In this work, we extend a previous work founded on the study of topological features of mesoscopic networks. Here, the geometrical…
Given a computer model of a physical object, it is often quite difficult to visualize and quantify any global effects on the shape representation caused by local uncertainty and local errors in the data. This problem is further amplified…
In this paper, we address the problem of image anomaly detection and segmentation. Anomaly detection involves making a binary decision as to whether an input image contains an anomaly, and anomaly segmentation aims to locate the anomaly on…
It has been broadly acknowledged that vortex detection algorithms, usually based on linear-algebraic properties of the velocity gradient tensor, can be plagued with severe shortcomings and may become, in practical terms, dependent on the…
The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…
Domain warping is a technique commonly used in creative coding to distort graphics and add visual interest to a work. The approach has the potential to be used in 3D art as mesh vertices can be efficiently warped using a vertex shader in a…
A gray-level image texture descriptors based on fractal dimension estimation is proposed in this work. The proposed method estimates the fractal dimension using probability (Voss) method. The descriptors are computed applying a multiscale…
Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…
We propose an algorithm for identifying vertices from three dimensional (3D) meshes that are most important for a geometric shape creation. Extracting such a set of vertices from a 3D mesh is important in applications such as digital…
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…
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…
Recognition of occluded objects in unseen indoor environments is a challenging problem for mobile robots. This work proposes a new slicing-based topological descriptor that captures the 3D shape of object point clouds to address this…
Effective representation of 2D images is fundamental in digital image processing, where traditional methods like raster and vector graphics struggle with sharpness and textural complexity respectively. Current neural fields offer…
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…
The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the…