Symmetry Feature Extraction Based on Quaternionic Local Phase

Moya-Sánchez, E. Ulises; Bayro–Corrochano, Eduardo

doi:10.1007/s00006-014-0457-1

Cited by 4 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is known that lines and edges are key features in biological visual systems. Moya-Sánchez and Bayro-Corrochano [179] utilized the atomic function-based Riez transform in a multi-scale approach to extract characteristics of object symmetric shapes from images and to build feature-signature vectors for object classification. Bernal-Marin and Bayro-Corrochano [48] used the 2D and 3D Hough transform in conformal geometric algebra to construct 3D geometric maps utilizing lines and planes.…”

Section: ) Feature Extraction Algorithmsmentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

View full text Add to dashboard Cite

Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020. After a brief introduction of GA, the applications of GA are reviewed across many fields. We discuss the characteristics of the applications of GA to various problems of computer science and engineering. In addition, the challenges and prospects of various applications proposed by many researchers are analyzed. We analyze the developments using GA in image processing, computer vision, neurocomputing, quantum computing, robot modeling, control, and tracking, as well as improvement of computer hardware performance. We believe that up to now GA has proven to be a powerful geometric language for a variety of applications. Furthermore, there is evidence that this is the appropriate geometric language to tackle a variety of existing problems and that consequently, step-by-step GA-based algorithms should continue to be further developed. We also believe that this extensive review will guide and encourage researchers to continue the advancement of geometric computing for intelligent machines.INDEX TERMS Geometric algebra, Clifford algebra, quaternion algebra, screw theory, signal processing, electrical engineering and power systems, geometric and quantum computing, image processing, computer vision, graphic engineering, artificial intelligence, machine learning, neural networks, control engineering, robotics, biomedical engineering, and biotechnology.

show abstract

Section: ) Feature Extraction Algorithmsmentioning

confidence: 99%

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

Bayro–Corrochano

2021

IEEE Access

View full text Add to dashboard Cite

show abstract

“…Moreover, beyond the global Fourier phase (not localized), the analytic signal encodes simultaneously both local space and frequency characteristics of a signal. The phase-based feature detection has been investigated extensively in the classic computer vision approach, as in [29,31,32,33]. For a 1D real signal (function) f (x), its analytical signal f A (x) is defined as follows [30]:…”

Section: Analytic Signalmentioning

confidence: 99%

A trainable monogenic ConvNet layer robust in front of large contrast changes in image classification

Moya-Sánchez¹,

Xambó-Descamps²,

Sánchez³

et al. 2021

Preprint

View full text Add to dashboard Cite

Convolutional Neural Networks (ConvNets) at present achieve remarkable performance in image classification tasks. However, current ConvNets cannot guarantee the capabilities of the mammalian visual systems such as invariance to contrast and illumination changes. Some ideas to overcome the illumination and contrast variations usually have to be tuned manually and tend to fail when tested with other types of data degradation. In this context, we present a new bio-inspired entry layer, M6, which detects low-level geometric features (lines, edges, and orientations) which are similar to patterns detected by the V1 visual cortex. This new trainable layer is capable of coping with image classification even with large contrast variations. The explanation for this behavior is the monogenic signal geometry, which represents each pixel value in a 3D space using quaternions, a fact that confers a degree of explainability to the networks. We compare M6 with a conventional convolutional layer (C) and a deterministic quaternion local phase layer (Q9). The experimental setup is designed to evaluate the robustness of our M6 enriched ConvNet model and includes three architectures, four datasets, three types of contrast degradation (including non-uniform haze degradations). The numerical results reveal that the models with M6 are the most robust in front of any kind of contrast variations. This amounts to a significant enhancement of the C models, which usually have reasonably good performance only when the same training and test degradation are used, except for the case of maximum degradation. Moreover, the Structural Similarity Index Measure (SSIM) is used to analyze and explain the robustness effect of the M6 feature maps under any kind of contrast degradations.

show abstract

A bio-inspired quaternion local phase CNN layer with contrast invariance and linear sensitivity to rotation angles

Moya-Sánchez

Xambó-Descamps

Pérez

et al. 2020

Pattern Recognition Letters

View full text Add to dashboard Cite

Symmetry Feature Extraction Based on Quaternionic Local Phase

Cited by 4 publications

References 9 publications

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020

A trainable monogenic ConvNet layer robust in front of large contrast changes in image classification

A bio-inspired quaternion local phase CNN layer with contrast invariance and linear sensitivity to rotation angles

Contact Info

Product

Resources

About