Related papers: Fractal Dimensions in Perceptual Color Space: A Co…
The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
While many image colorization algorithms have recently shown the capability of producing plausible color versions from gray-scale photographs, they still suffer from limited semantic understanding. To address this shortcoming, we propose to…
Color constancy and color illusion perception are two phenomena occurring in the human visual system, which can help us reveal unknown mechanisms of human perception. For decades computer vision scientists have developed numerous color…
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 propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
Texture plays an important role in computer vision. It is one of the most important visual attributes used in image analysis, once it provides information about pixel organization at different regions of the image. This paper presents a…
In digital painting software, layers organize paintings. However, layers are not explicitly represented, transmitted, or published with the final digital painting. We propose a technique to decompose a digital painting into layers. In our…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
Optical scattering strength of fractal optical disordered media with varying fractal dimension is reported. The diffusion limited aggregation (DLA) technique is used to generate fractal samples in 2D and 3D, and fractal dimensions are…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…
Developing a robust generalization measure for the performance of machine learning models is an important and challenging task. A lot of recent research in the area focuses on the model decision boundary when predicting generalization. In…
Fractal image compression is attractive except for its high encoding time requirements. The image is encoded as a set of contractive affine transformations. The image is partitioned into non-overlapping range blocks, and a best matching…
Moving around in a 3D world, requires the visual system of a living individual to rely on three channels of image recognition, which is done through three types of retinal cones. Newton, Grasmann, Helmholz and Schr$\ddot{o}$dinger laid down…
Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to…
Self-supervised models create representation spaces that lack clear semantic meaning. This interpretability problem of representations makes traditional explainability methods ineffective in this context. In this paper, we introduce a novel…
We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…
We study the fractal dimension of the contour of the liquid-gas interface in a spray. Our images include both, the linking region and the break-up region and are obtained with a high-resolution shadowgraph technique; this means that the…
Bacteria light harvesters are interpreted as Vicsek fractal, based upon their morphology, even though such fractals contain only one, or perhaps two, generations. After using fractal dimensions to describe the geometry, we progress to use…