Related papers: Fractal Descriptors Based on Fourier Spectrum Appl…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
To address the issue of feature descriptors being ineffective in representing grayscale feature information when images undergo high affine transformations, leading to a rapid decline in feature matching accuracy, this paper proposes a…
Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
The current digital era, driven by growing threats to data security, requires a robust image encryption technique. Classical encryption algorithms suffer from a trade-off among security, image fidelity, and computational efficiency. This…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
Texture analysis and classification remain as one of the biggest challenges for the field of computer vision and pattern recognition. On this matter, Gabor wavelets has proven to be a useful technique to characterize distinctive texture…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
While vision transformers achieve significant breakthroughs in various image restoration (IR) tasks, it is still challenging to efficiently scale them across multiple types of degradations and resolutions. In this paper, we propose…
Recent progress in image deblurring techniques focuses mainly on operating in both frequency and spatial domains using the Fourier transform (FT) properties. However, their performance is limited due to the dependency of FT on stationary…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time series and spatial data. The graph of a smooth, differentiable surface indexed in $\mathbb{R}^d$ has topological and fractal dimension $d$. If the surface…
Understanding fracture in cementitious materials caused by the deposition and growth of corrosion products requires scale-bridging approaches due to the large length-scale difference between the micro-pores, where deposition occurs, and the…
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…
Texture recognition is one of the most important tasks in computer vision and, despite the recent success of learning-based approaches, there is still need for model-based solutions. This is especially the case when the amount of data…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
Several devices for substrate texture detection based on diffractive optics, for paper, textiles and non-wovens have been proposed in the past for direct inspection during the production processes. In spite of the presence of devices…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…