A Quaternion Deterministic Monogenic CNN Layer for Contrast Invariance

Moya-Sánchez, E. Ulises; Xambó-Descamps, Sebastià; Salazar-Colores, Sebastián; Pérez, Abraham Sánchez; Cortés, Ulises

doi:10.1007/978-3-030-74486-1_7

Cited by 5 publications

(3 citation statements)

References 34 publications

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“…In [36], the authors reported a cortical adaptation to brightness and darkness in the macaque primary visual cortex V1. In relation to this, it is worth mentioning that the experimental results of the present work confirm the expectation advanced in [30,29,25] that the local phase and local orientation should be invariant with respect to brightness and contrast changes due to its geometry representation.…”

Section: Bio-inspired Properties and Toolssupporting

confidence: 90%

“…A previous version of the M6 layer, still deterministic, was presented in [25], but already with quite robust responses for illumination or contrast variations. In another recent work [19], the authors propose a bio-inspired approach to leverage quaternion Gabor filters to improve the classification even with contrast degradations.…”

Section: Related Workmentioning

confidence: 99%

“…It should be noted that we use Keras-turner (Bayesian optimization) [47] to choose the kernel size and learning rate of the convolution layer. The initial parameters of M6 layer are s = 1, f = 1, σ = 0.33, ω = 1 based on the previous version of the layer [25]. All datasets were normalized to one by dividing each pixel value by 255.…”

Section: Architectures Training and Testmentioning

confidence: 99%

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

Moya-Sánchez¹,

Xambó-Descamps²,

Sánchez³

et al. 2021

Preprint

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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.

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Section: Bio-inspired Properties and Toolssupporting

confidence: 90%

Section: Related Workmentioning

confidence: 99%

Section: Architectures Training and Testmentioning

confidence: 99%

See 1 more Smart Citation

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

Moya-Sánchez¹,

Xambó-Descamps²,

Sánchez³

et al. 2021

Preprint

Self Cite

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Geometric Calculi and Automatic Learning An Outline

Xambó-Descamps¹,

Moya

2021

Systems, Patterns and Data Engineering With Geometric Calculi

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Machine Learning Clifford Invariants of ADE Coxeter Elements

Chen,

Dechant,

et al. 2024

Adv. Appl. Clifford Algebras

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There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for $$A_8$$ A 8 , $$D_8$$ D 8 and $$E_8$$ E 8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results.

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A Quaternion Deterministic Monogenic CNN Layer for Contrast Invariance

Cited by 5 publications

References 34 publications

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

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

Geometric Calculi and Automatic Learning An Outline

Machine Learning Clifford Invariants of ADE Coxeter Elements

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