Related papers: Learning Image Fractals Using Chaotic Differentiab…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
Plasma fractals is a technique to generate random and realistic clouds, textures and terrains~-- traditionally using recursive subdivision. We demonstrate a new approach, based on iterative expansion. It gives a family of algorithms that…
What is a diffusion model actually doing when it turns noise into a photograph? We show that the deterministic DDIM reverse chain operates as a Partitioned Iterated Function System (PIFS) and that this framework serves as a unified design…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…
The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…
In this paper a new fractal image compression algorithm is proposed in which the time of encoding process is considerably reduced. The algorithm exploits a domain pool reduction approach, along with using innovative predefined values for…
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…
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…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
In the realm of fractal geometry, intricate structures emerge from simple iterative processes that partition parameter spaces into regions of stability and instability. Likewise, training large language models involves iteratively applying…
One of the most important tasks in image processing problem and machine vision is object recognition, and the success of many proposed methods relies on a suitable choice of algorithm for the segmentation of an image. This paper focuses on…
We introduce inverse transport networks as a learning architecture for inverse rendering problems where, given input image measurements, we seek to infer physical scene parameters such as shape, material, and illumination. During training,…
This work proposes the development and study of a novel technique for the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal…
Despite the recent success of convolutional neural networks in texture recognition, model-based descriptors are still competitive, especially when we do not have access to large amounts of annotated data for training and the interpretation…
Inverse rendering seeks to reconstruct both geometry and spatially varying BRDFs (SVBRDFs) from captured images. To address the inherent ill-posedness of inverse rendering, basis BRDF representations are commonly used, modeling SVBRDFs as…
We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, non-ergodic extended (fractal) and localized phases in various systems:…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…