2D and 3D Image Analysis by Gaussian-Hermite Moments

Yang, Bo; Suk, Tomáš; Dai, Mingjun; Flusser, Jan

doi:10.15579/gcsr.vol1.ch7

Cited by 7 publications

(6 citation statements)

References 30 publications

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“…Note that the concept of constructing rotational invariants using contractions of Cartesian tensors was initially introduced by Flusser et al, − where geometric and Gaussian–Hermite moments were used to address pattern recognition problems. Additionally, geometric moments were used to construct rotationally invariant bases for linear regression in PES construction. , …”

Section: Methodsmentioning

confidence: 99%

“…al. [25][26][27][28], where geometric and Gaussian-Hermite moments were used to address pattern recognition problems. Additionally, geometric moments were used to construct rotationally invariant bases for linear regression in PES construction [10,11].…”

Section: Molecular Descriptormentioning

confidence: 99%

“…In this work, we introduce a novel, physically inspired molecular descriptor, which can be used as input for any ML algorithm. We refer to it as Gaussian Moments (GM) since it was inspired by Gaussian-type atomic orbitals and derived from geometric moments previously used for pattern recognition. − We have chosen feed-forward NNs as an ML method for our applications. In addition to the structural description, we encode the information about the atomic species in the molecular representation.…”

Section: Introductionmentioning

confidence: 99%

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Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials

Zaverkin

Kästner

2020

J. Chem. Theory Comput.

150

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Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a machine learning method for constructing highdimensional potential energy surfaces based on feed-forward neural networks. As input to the neural network we propose an extendable invariant local molecular descriptor constructed from geometric moments. Their formulation via pairwise distance vectors and tensor contractions allows a very efficient implementation on graphical processing units (GPUs). The atomic species is encoded in the molecular descriptor, which allows the restriction to one neural network for the training of all atomic species in the data set. We demonstrate that the accuracy of the developed approach in representing both chemical and configurational spaces is comparable to the one of several established machine learning models. Due to its high accuracy and efficiency, the proposed machine-learned potentials can be used for any further tasks, for example the optimization of molecular geometries, the calculation of rate constants or molecular dynamics.

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Section: Methodsmentioning

confidence: 99%

Section: Molecular Descriptormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials

Zaverkin

Kästner

2020

J. Chem. Theory Comput.

150

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“…More details and facts are developed in [ 88 , 89 ] with applications related to signal processing, compression, and quality. See also [ 90 ].…”

Section: Two Wavelet/multiwavelet Processorsmentioning

confidence: 99%

Clifford Wavelet Entropy for Fetal ECG Extraction

Jallouli

Arfaoui

Mabrouk

et al. 2021

Entropy

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Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. In the present paper, a wavelet/multiwavelet method is proposed to perfectly extract the fetal ECG parameters from the abdominal mother ECG. In a first step, due to the wavelet/mutiwavelet processing, a denoising procedure is applied to separate the noised parts from the denoised ones. The denoised signal is assumed to be a mixture of both the MECG and the FECG. One of the well-known measures of accuracy in information processing is the concept of entropy. In the present work, a wavelet/multiwavelet Shannon-type entropy is constructed and applied to evaluate the order/disorder of the extracted FECG signal. The experimental results apply to a recent class of Clifford wavelets constructed in Arfaoui, et al. J. Math. Imaging Vis. 2020, 62, 73–97, and Arfaoui, et al.Acta Appl. Math.2020, 170, 1–35.. Additionally, classical Haar–Faber–Schauder wavelets are applied for the purpose of comparison. Two main well-known databases have been applied, the DAISY database and the CinC Challenge 2013 database. The achieved accuracy over the test databases resulted in Se=100%, PPV=100% for FECG extraction and peak detection.

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“…More details and facts are developed in [11,12] with applications related to signal processing, image compression, perceptual image quality. See also [49].…”

Section: Wavelet and Multi-wavelet Fecg Processingmentioning

confidence: 99%

Clifford wavelets for fetal ECG extraction

Jallouli,

Arfaoui,

Mabrouk

et al. 2021

Preprint

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2D and 3D Image Analysis by Gaussian-Hermite Moments

Cited by 7 publications

References 30 publications

Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials

Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials

Clifford Wavelet Entropy for Fetal ECG Extraction

Clifford wavelets for fetal ECG extraction

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