Spatial color image processing using Clifford algebras: application to color active contour

Carré, Philippe; Denis, Patrice; Fernández-Maloigne, Christine

doi:10.1007/s11760-012-0366-5

Cited by 16 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that orthogonal polynomials are widely applied in wavelet theory and signal processing. See, for example, [ 66 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 ].…”

Section: Two Wavelet/multiwavelet Processorsmentioning

confidence: 99%

See 1 more Smart Citation

Clifford Wavelet Entropy for Fetal ECG Extraction

Jallouli

Arfaoui

Mabrouk

et al. 2021

Entropy

View full text Add to dashboard Cite

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.

show abstract

Section: Two Wavelet/multiwavelet Processorsmentioning

confidence: 99%

“…Recall that orthogonal polynomials are widely applied in wavelet theory and signal processing. See, for example, [66,[71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87].…”

Section: Clifford Wavelets and Multiwaveletsmentioning

confidence: 99%

Clifford Wavelet Entropy for Fetal ECG Extraction

Jallouli

Arfaoui

Mabrouk

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…12a to 12c [10]). Unfortunately, this hypothesis is never or rarely satisfied in ⊥ spaces [14][15][16][17] Color invariant [18,19] Hue vs Lightness [20][21][22] Clifford algebra [22][23][24] Marginal [11,25,26] ⊥ hypothesis [9,10,27] Color median [28,29] Morphology [21,[30][31][32] Full-vector gradient [33] Direct processing [32,34,35] CAM [36,37] the case of color and spectral imaging sensors. Cumani [9] presented an extension to multi-spectral data of Di Zenzo approach.…”

Section: I F Gmentioning

confidence: 99%

“…Working in the Fourier domain is very attractive for intensity images. Following this idea, Clifford algebra [22][23][24] offer the use of quaternions to estimate a gradient. These color spaces are generally rotated from the initial RGB color spaces.…”

Section: I F Gmentioning

confidence: 99%

Gradient in spectral and color images: from the Di Zenzo initial construction to a generic proposition

et al. 2019

Self Cite

View full text Add to dashboard Cite

In this paper, we define a generic gradient for color and spectral images, in regards to a proposed taxonomy of the state of the art. The full-vector gradient, taking into account the sensor's characteristics, respects the metrological properties of genericity, robustness and reproducibility. We construct a protocol to compare gradients from different sensors. The comparison is developed simulating sensors using their spectral characteristics. We develop three experiments using this protocol. The first one shows the results consistency for similar sensors. The second one demonstrates the genericity of the approach, adapted to any kind of imaging sensors. The last one focuses on the channel inter-correlation considering sensors as in the color vision deficiency case.

show abstract

“…The creation of a high-quality image based on human visual perception requires the alignment of correlated pixels within and among adjacent local and global neighborhoods [ 22 ]. Such alignment is based on the global and local adaptation of the reference image axis during image enhancement [ 23 ]. Therefore, a suitable computation results in better edge preservation, low errors, high signal-to-noise ratios, and a high conformance with the original image.…”

Section: Introductionmentioning

confidence: 99%

Geometric Regularized Hopfield Neural Network for Medical Image Enhancement

Alenezi

Santosh

2021

International Journal of Biomedical Imaging

View full text Add to dashboard Cite

One of the major shortcomings of Hopfield neural network (HNN) is that the network may not always converge to a fixed point. HNN, predominantly, is limited to local optimization during training to achieve network stability. In this paper, the convergence problem is addressed using two approaches: (a) by sequencing the activation of a continuous modified HNN (MHNN) based on the geometric correlation of features within various image hyperplanes via pixel gradient vectors and (b) by regulating geometric pixel gradient vectors. These are achieved by regularizing proposed MHNNs under cohomology, which enables them to act as an unconventional filter for pixel spectral sequences. It shifts the focus to both local and global optimizations in order to strengthen feature correlations within each image subspace. As a result, it enhances edges, information content, contrast, and resolution. The proposed algorithm was tested on fifteen different medical images, where evaluations were made based on entropy, visual information fidelity (VIF), weighted peak signal-to-noise ratio (WPSNR), contrast, and homogeneity. Our results confirmed superiority as compared to four existing benchmark enhancement methods.

show abstract

Spatial color image processing using Clifford algebras: application to color active contour

Cited by 16 publications

References 19 publications

Clifford Wavelet Entropy for Fetal ECG Extraction

Clifford Wavelet Entropy for Fetal ECG Extraction

Gradient in spectral and color images: from the Di Zenzo initial construction to a generic proposition

Geometric Regularized Hopfield Neural Network for Medical Image Enhancement

Contact Info

Product

Resources

About