Related papers: Shape analysis using fractal dimension: a curvatur…
Feature extraction is a critical technology to realize the automatic transmission of feature information throughout product life cycles. As CAD models primarily capture the 3D geometry of products, feature extraction heavily relies on…
The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
Shape descriptors, i.e., per-vertex features of 3D meshes or point clouds, are fundamental to shape analysis. Historically, various handcrafted geometry-aware descriptors and feature refinement techniques have been proposed. Recently,…
The paper aims at proposing the first shape identification and classification algorithm in echolocation. The approach is based on first extracting geometric features from the reflected waves and then matching them with precomputed ones…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
In constraint languages for RDF graphs, such as ShEx and SHACL, constraints on nodes and their properties in RDF graphs are known as "shapes". Schemas in these languages list the various shapes that certain targeted nodes must satisfy for…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
This paper is a sharp and focussed exploration of the Fibonacci substitution and the mathematical entity it gives rise to, the Fibonacci word. Our investigations are both of an algebraic and a geometric nature. Indeed, it is the combination…
This paper presents a fractal analysis of radiographic patterns obtained from specimens with three types of inserted welding defects: lack of fusion, lack of penetration, and porosity. The study focused on patterns of carbon steel beads…
The fractal dimension of a liquid column is a crucial parameter in several models describing the main features of the primary break-up occurring at the interface of a liquid phase surrounded by the gas-flow. In this work, the deformation of…
The influence of phase transformation-induced plastic deformation in Pd|H system on the electrode surface was investigated. Since the Pd surface is subject of severe plastic deformation during this process, the structure and roughness of…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
In the field of brittle fracture animation, generating realistic destruction animations using physics-based simulation methods is computationally expensive. While techniques based on Voronoi diagrams or pre-fractured patterns are effective…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…