Related papers: Shape analysis using fractal dimension: a curvatur…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean…
3D model retrieval techniques can be classified as histogram-based, view-based and graph-based approaches. We propose a hybrid shape descriptor which combines the global and local radial distance features by utilizing the histogram-based…
Cracks on a painting is not a defect but an inimitable signature of an artwork which can be used for origin examination, aging monitoring, damage identification, and even forgery detection. This work presents the development of a new…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
High energy impacts at joint locations often generate highly fragmented, or comminuted, bone fractures. Current approaches for treatment require physicians to decide how to classify the fracture within a hierarchy fracture severity…
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical…
In the last few years, new insights have permitted unexpected progress in the study of fractal shapes in two dimensions. A new approach, called Schramm-Loewner evolution, or SLE, has arisen through analytic function theory and probability…
This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered…
Retrieving similar images from a large dataset based on the image content has been a very active research area and is a very challenging task. Studies have shown that retrieving similar images based on their shape is a very effective…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
Shape and geometric patterns are essential in defining stylistic identity. However, current 3D style transfer methods predominantly focus on transferring colors and textures, often overlooking geometric aspects. In this paper, we introduce…
This paper presents a novel multi scale gradient and a corner point based shape descriptors. The novel multi scale gradient based shape descriptor is combined with generic Fourier descriptors to extract contour and region based shape…
The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…
In this paper, we describe a novel shape classification method which is embedded in the Bayesian paradigm. We discuss the modelling and the resulting shape classification algorithm for two and three dimensional data shapes. We conclude by…
Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…
The paper surveys some recent results concerning vector analysis on fractals. We start with a local regular Dirichlet form and use the framework of 1-forms and derivations introduced by Cipriani and Sauvageot to set up some elements of a…
We present alphaPDE, a new multivariate analysis technique for parameter estimation. The method is based on a direct construction of joint probability densities of known variables and the parameters to be estimated. We show how posterior…