Related papers: Fractal Descriptors Based on Fourier Spectrum Appl…
The refractive index fluctuations in the connective tissue layer (stroma) of human cervical tissues having different grades of precancers (dysplasia) was quantified using a wavelet-based multifractal detrended fluctuation analysis model.…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
Cracks on a painting is not a defect but an inimitable signature of an artwork which can be used for origin examination, aging monitoring, damage identification, and even forgery detection. This work presents the development of a new…
AI-generated imagery has reached near-photorealistic fidelity, yet this technology poses significant threats to information security and societal trust. Existing deepfake detection methods often exhibit limited robustness in open-world…
Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…
Ultrasound (US) image segmentation is an active research area that requires real-time and highly accurate analysis in many scenarios. The detect-to-segment (DTS) frameworks have been recently proposed to balance accuracy and efficiency.…
Fractals are a basic tool to phenomenologically describe natural objects having a high degree of temporal or spatial variability. From a physical point of view the fractal properties of natural systems can also be interpreted by using the…
We explored the fractal and multifractal characteristics of breast mammogram micrographs to identify quantitative biomarkers associated with breast cancer progression. In addition to conventional fractal and multifractal analyses, we…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
One-dimensional detrended fluctuation analysis (1D DFA) and multifractal detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling analysis of fractal and multifractal time series because of being accurate and easy to…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
The similarity in fractal dimensions of paint ``blobs'' in samples of gestural expressionist art implies that these pigment structures are statistically indistinguishable from one another. This result suggests that such dimensions cannot be…
Convolutional neural networks have shown successful results in image classification achieving real-time results superior to the human level. However, texture images still pose some challenge to these models due, for example, to the limited…
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…
In this paper, we proposed a novel pipeline for image-level classification in the hyperspectral images. By doing this, we show that the discriminative spectral information at image-level features lead to significantly improved performance…
This work presents a differentiable rendering approach that allows latent fractal flame parameters to be learned from image supervision using gradient descent optimization. The approach extends the state-of-the-art in differentiable…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…