Fractional-Order Colour Image Processing

Henriques, Manuel; Valério, Duarte; Gordo, Paulo; Melício, Rui

doi:10.3390/math9050457

Cited by 16 publications

(7 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Algorithms for edge detection methods often involve first or second order derivatives, which can be generalised using a fractional order derivative instead [5]. The goal of this paper is to apply fractional edge detection to satellite images, verifying how appropriate these algorithms are for the job.…”

Section: Objective and Contributionmentioning

confidence: 99%

“…Since then, a few already extant image treatment methods have been adapted to include fractional derivatives (instead of usual, integer order derivatives), such as the fractional Roberts operator [11], the fractional Sobel method [12,13], the fractional Canny method [6], or the fractional Laplacian of Gaussian method [14]. These methods will be addressed below in Section 2 and details can be found in [5].…”

Section: Previous Work On Fractional Image Processingmentioning

confidence: 99%

See 1 more Smart Citation

Fractional Order Processing of Satellite Images

2021

Self Cite

View full text Add to dashboard Cite

Nowadays, satellite images are used in many applications, and their automatic processing is vital. Conventional integer grey-scale edge detection algorithms are often used for this. This study shows that the use of color-based, fractional order edge detection may enhance the results obtained using conventional techniques in satellite images. It also shows that it is possible to find a fixed set of parameters, allowing automatic detection while maintaining high performance.

show abstract

Section: Objective and Contributionmentioning

confidence: 99%

Section: Previous Work On Fractional Image Processingmentioning

confidence: 99%

Fractional Order Processing of Satellite Images

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Certainly, the application of fractional derivatives is not recent, and it can be verified in previous works on different areas, including linear viscoelastivity [12], partial differential equations [13], signal processing [14], and image processing [15], among others.…”

Section: Introductionmentioning

confidence: 96%

Fractional Gradient Optimizers for PyTorch: Enhancing GAN and BERT

Herrera-Alcántara,

Castelán-Aguilar

2023

Fractal Fract

View full text Add to dashboard Cite

Machine learning is a branch of artificial intelligence that dates back more than 50 years. It is currently experiencing a boom in research and technological development. With the rise of machine learning, the need to propose improved optimizers has become more acute, leading to the search for new gradient-based optimizers. In this paper, the ancient concept of fractional derivatives has been applied to some optimizers available in PyTorch. A comparative study is presented to show how the fractional versions of gradient optimizers could improve their performance on generative adversarial networks (GAN) and natural language applications with Bidirectional Encoder Representations from Transformers (BERT). The results are encouraging for both state-of-the art algorithms, GAN and BERT, and open up the possibility of exploring further applications of fractional calculus in machine learning.

show abstract

“…This provides greater flexibility and adaptability, which improves its application in real problems. Therefore, fractional order systems based on fractional order calculus have been proven to have excellent performance in various industries, for example, in the fields of speech recognition [35], image processing [36,37], and automatic control [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

A Bearing Fault Diagnosis Method under Small Sample Conditions Based on the Fractional Order Siamese Deep Residual Shrinkage Network

Li,

Wu,

Luo

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

A bearing fault is one of the major causes of rotating machinery faults. However, in real industrial scenarios, the harsh and complex environment makes it very difficult to collect sufficient fault data. Due to this limitation, most of the current methods cannot accurately identify the fault type in cases with limited data, so timely maintenance cannot be conducted. In order to solve this problem, a bearing fault diagnosis method based on the fractional order Siamese deep residual shrinkage network (FO-SDRSN) is proposed in this paper. After data collection, all kinds of vibration data are first converted into two-dimensional time series feature maps, and these feature maps are divided into the same or different types of fault sample pairs. Then, a Siamese network based on the deep residual shrinkage network (DRSN) is used to extract the features of the fault sample pairs, and the fault type is determined according to the features. After that, the contrastive loss function and diagnostic loss function of the sample pairs are combined, and the network parameters are continuously optimized using the fractional order momentum gradient descent method to reduce the loss function. This improves the accuracy of fault diagnosis with a small sample training dataset. Finally, four small sample datasets are used to verify the effectiveness of the proposed method. The results show that the FO-SDRSN method is superior to other advanced methods in terms of training accuracy and stability under small sample conditions.

show abstract

Fractional-Order Colour Image Processing

Cited by 16 publications

References 12 publications

Fractional Order Processing of Satellite Images

Fractional Order Processing of Satellite Images

Fractional Gradient Optimizers for PyTorch: Enhancing GAN and BERT

A Bearing Fault Diagnosis Method under Small Sample Conditions Based on the Fractional Order Siamese Deep Residual Shrinkage Network

Contact Info

Product

Resources

About