Related papers: Fractal Descriptors of Texture Images Based on the…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Convolutional neural networks have shown successful results in image classification achieving real-time results superior to the human level. However, texture images still pose some challenge to these models due, for example, to the limited…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
This paper presents an efficient method for texture retrieval using multiscale feature extraction and embedding based on the local extrema keypoints. The idea is to first represent each texture image by its local maximum and local minimum…
Noise is one of the major problems that hinder an effective texture analysis of disease in medical images, which may cause variability in the reported diagnosis. In this paper seven texture measurement methods (two wavelet, two model and…
The problem of recognizing various types of tissues present in multi-gigapixel histology images is an important fundamental pre-requisite for downstream analysis of the tumor microenvironment in a bottom-up analysis paradigm for…
Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…
Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement,…
Feature extraction is a key step in image processing for pattern recognition and machine learning processes. Its purpose lies in reducing the dimensionality of the input data through the computing of features which accurately describe the…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal…
This work presents a first evaluation of using spatio-temporal receptive fields from a recently proposed time-causal spatio-temporal scale-space framework as primitives for video analysis. We propose a new family of video descriptors based…
As a general means of expression, audio analysis and recognition has attracted much attentions for its wide applications in real-life world. Audio emotion recognition (AER) attempts to understand emotional states of human with the given…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
Plasma fractals is a technique to generate random and realistic clouds, textures and terrains~-- traditionally using recursive subdivision. We demonstrate a new approach, based on iterative expansion. It gives a family of algorithms that…
In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…
Given that visual foundation models (VFMs) are trained on extensive datasets but often limited to 2D images, a natural question arises: how well do they understand the 3D world? With the differences in architecture and training protocols…
Next-generation ground-based solar observations require good image quality metrics for post-facto processing techniques. Based on the assumption that texture features in solar images are multi-fractal which can be extracted by a trained…
The similarity in fractal dimensions of paint ``blobs'' in samples of gestural expressionist art implies that these pigment structures are statistically indistinguishable from one another. This result suggests that such dimensions cannot be…