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In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…

General Mathematics · Mathematics 2023-10-26 Alireza Khalili Golmankhaneh , Donatella Bongiorno

A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables.…

Artificial Intelligence · Computer Science 2026-04-30 Mauricio Gonzalez-Soto , Ivan R. Feliciano-Avelino , L. Enrique Sucar , Hugo J. Escalante Balderas

Similarity analysis using neural networks has emerged as a powerful technique for understanding and categorizing complex patterns in various domains. By leveraging the latent representations learned by neural networks, data objects such as…

Computer Vision and Pattern Recognition · Computer Science 2023-07-26 Cyril Juliani

It is well-known that modern computer vision systems often exhibit behaviors misaligned with those of humans: from adversarial attacks to image corruptions, deep learning vision models suffer in a variety of settings that humans capably…

Computer Vision and Pattern Recognition · Computer Science 2024-10-18 Leonard Tang , Dan Ley

This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a…

General Mathematics · Mathematics 2024-04-15 Alireza Khalili Golmankhaneh , Palle E. T. Jørgensen , Dimiter Prodanov

Most state-of-the-art methods of object detection suffer from poor generalization ability when the training and test data are from different domains, e.g., with different styles. To address this problem, previous methods mainly use holistic…

Computer Vision and Pattern Recognition · Computer Science 2021-02-16 Aming Wu , Yahong Han , Linchao Zhu , Yi Yang

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…

Optimization and Control · Mathematics 2024-06-05 Ashwani Aggarwal

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…

adap-org · Physics 2015-06-30 C. M. Arizmendi

Humans excel at building generalizations of new concepts from just one single example. Contrary to this, current computer vision models typically require large amount of training samples to achieve a comparable accuracy. In this work we…

Artificial Intelligence · Computer Science 2024-09-16 Octavio Arriaga , Jichen Guo , Rebecca Adam , Sebastian Houben , Frank Kirchner

Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence…

Artificial Intelligence · Computer Science 2013-02-08 Luis M. de Campos , Juan F. Huete

Distortion is widely existed in the images captured by popular wide-angle cameras and fisheye cameras. Despite the long history of distortion rectification, accurately estimating the distortion parameters from a single distorted image is…

Computer Vision and Pattern Recognition · Computer Science 2024-04-30 Kang Liao , Chunyu Lin , Yao Zhao

Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation…

Computer Vision and Pattern Recognition · Computer Science 2017-03-20 Hongteng Xu , Junchi Yan , Nils Persson , Weiyao Lin , Hongyuan Zha

Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…

Metric Geometry · Mathematics 2015-06-22 Evgeny Spodarev , Peter Straka , Steffen Winter

Current automatic vision systems face two major challenges: scalability and extreme variability of appearance. First, the computational time required to process an image typically scales linearly with the number of pixels in the image,…

Computer Vision and Pattern Recognition · Computer Science 2014-05-22 Marc'Aurelio Ranzato

We propose a novel technique for producing high-quality 3D models that match a given target object image or scan. Our method is based on retrieving an existing shape from a database of 3D models and then deforming its parts to match the…

Computer Vision and Pattern Recognition · Computer Science 2021-04-14 Mikaela Angelina Uy , Vladimir G. Kim , Minhyuk Sung , Noam Aigerman , Siddhartha Chaudhuri , Leonidas Guibas

We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…

Graphics · Computer Science 2023-03-21 James F. O'Brien , Jessica K. Hodgins

Deformable shape representations, parameterized by deformations relative to a given template, have proven effective for improved image analysis tasks. However, their broader applicability is hindered by two major challenges. First, existing…

Computer Vision and Pattern Recognition · Computer Science 2025-03-25 Tonmoy Hossain , Miaomiao Zhang

Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their…

Chaotic Dynamics · Physics 2025-01-30 David Valle , Alexandre Wagemakers , Alvar Daza , Miguel A. F. Sanjuán

Large intra-class variation is the result of changes in multiple object characteristics. Images, however, only show the superposition of different variable factors such as appearance or shape. Therefore, learning to disentangle and…

Computer Vision and Pattern Recognition · Computer Science 2019-06-18 Dominik Lorenz , Leonard Bereska , Timo Milbich , Björn Ommer