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A multifractal analysis (MFA) is performed on three-dimensional grayscale images associated with natural porous structures (soil samples). First, computed tomography (CT) scans are carried out on the samples to generate 3D grayscale images.…
In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…
We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…
V-variable fractals, where $V$ is a positive integer, are intuitively fractals with at most $V$ different "forms" or "shapes" at all levels of magnification. In this paper we describe how V-variable fractals can be used for the purpose of…
Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the…
Many real-world applications, such as interactive photo retouching, artistic content creation, and product design, require flexible and iterative image editing. However, existing image editing methods primarily focus on achieving the…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we…
Face morphing is a problem in computer graphics with numerous artistic and forensic applications. It is challenging due to variations in pose, lighting, gender, and ethnicity. This task consists of a warping for feature alignment and a…
We construct an image formation theory that covers the majority of optical microscopy techniques that use diverse coherent or incoherent light-matter interactions. The theories of individual microscopy methods could not previously be…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
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…
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
2D convolution is a staple of digital image processing. The advent of large format imagers makes it possible to literally ``pave'' with silicon the focal plane of an optical sensor, which results in very large images that can require a…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
Recently, text-guided image manipulation has received increasing attention in the research field of multimedia processing and computer vision due to its high flexibility and controllability. Its goal is to semantically manipulate parts of…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
During the acquisition of an image from its source, noise always becomes an integral part of it. Various algorithms have been used in past to denoise the images. Image denoising still has scope for improvement. Visual information…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…