Related papers: How to Transform and Filter Images using Iterated …
Approximation theory plays an important role in image processing, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past thirty years. The goal of this…
This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
Image segmentation is the process of partitioning an image into a set of meaningful regions according to some criteria. Hierarchical segmentation has emerged as a major trend in this regard as it favors the emergence of important regions at…
A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are…
Photorealism is a complex concept that cannot easily be formulated mathematically. Deep Photo Style Transfer is an attempt to transfer the style of a reference image to a content image while preserving its photorealism. This is achieved by…
The iterative development process is a framework used to design products and applications across a wide range of domains. It centers around building prototypes, testing them, and updating based on the test results. We discuss how we applied…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f.s. with those of more standard i.f.s. and with those of…
A new multifocus image fusion approach is presented in this paper. First the contourlet transform is used to decompose the source images into different components. Then, some salient features are extracted from components. In order to…
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…
Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…
The generalization performance of AI-generated image detection remains a critical challenge. Although most existing methods perform well in detecting images from generative models included in the training set, their accuracy drops…
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…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
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…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
We provide a new algorithm to generate images of the generalized fuzzy fractal attractors described in Oliveira-2017. We also provide some important results on the approximation of fractal operators to discrete subspaces with application to…