相关论文: The multi-fractal structure of contrast changes in…

Naive scale invariance is not a true property of natural images. Natural monochrome images posses a much richer geometrical structure, that is particularly well described in terms of multiscaling relations. This means that the pixels of a…

Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this work we show that those properties uniquely define an {\em intrinsic wavelet} and present a suitable…

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…

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…

It has been recently proven that natural images exhibit scaling properties analogue to those of turbulent flows. These properties allow regarding each image as a multifractal object, for which its most singular manifold conveys the most of…

Self-similarity is the essence of fractal images and, as such, characterizes natural stochastic textures. This paper is concerned with the property of self-similarity in the statistical sense in the case of fully-textured images that…

The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at…

Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…

We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…

A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…

We report results on the scaling properties of changes in contrast of natural images in different visual environments. This study confirms the existence, in a vast class of images, of a multiplicative process relating the variations in…

A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…

In this work, we present a multiscale kinetic framework for consensus-based image segmentation. By interpreting an image as a system of interacting particles, each pixel is characterised by its spatial position and an internal feature…

The texture is defined as spatial structure of the intensities of the pixels in an image that is repeated periodically in the whole image or regions, and makes the concept of the image. Texture, color and shape are three main components…

Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished…

Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…

In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…

In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…

A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…

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,…