Variational Models for Color Image Correction Inspired by Visual Perception and Neuroscience

Batard, Thomas; Hertrich, Johannes; Steidl, Gabriele

doi:10.1007/s10851-020-00978-1

Cited by 4 publications

(3 citation statements)

References 36 publications

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“…Since p n+1 ∈ Σ f , there exists some u n+1 ∈ (H 1 (Ω)) 3 such that p n+1 = ∇u n+1 . Furthermore, u n+1 solves arg min…”

Section: 7mentioning

confidence: 99%

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Elastica Models for Color Image Regularization

Líu¹,

Tai²,

Kimmel³

et al. 2022

Preprint

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The choice of a proper regularization measure plays an important role in the field of image processing. One classical approach treats color images as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the chromatic coordinates as dominating over the spatial ones, the image spatial coordinates could be thought of as a paramterization of the image surface manifold in a three dimensional color space. Minimizing the area of the image manifold leads to the Beltrami flow or mean curvature flow of the image surface in the 3D color space, while minimizing the elastica of the image surface yields an additional interesting regularization. Recently, the authors proposed a color elastica model, which minimizes both the surface area and elastica of the image manifold. In this paper, we propose to modify the color elastica and introduce two new models for color image regularization. The revised measures are motivated by the relations between the color elastica model, Euler's elastica model and the total variation model for gray level images. Compared to our previous color elastica model, the new models are direct extensions of Euler's elastica model to color images. The proposed models are nonlinear and challenging to minimize. To overcome this difficulty, two operator-splitting methods are suggested. Specifically, nonlinearities are decoupled by introducing new vector-and matrix-valued variables. Then, the minimization problems are converted to solving initial value problems which are time-discretized by operator splitting. Each subproblem, after splitting either, has a closed-form solution or can be solved efficiently. The effectiveness and advantages of the proposed models are demonstrated by comprehensive experiments. The benefits of incorporating the elastica of the image surface as regularization terms compared to common alternatives are empirically validated.

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“…Since p n+1 ∈ Σ f , there exists some u n+1 ∈ (H 1 (Ω)) 3 such that p n+1 = ∇u n+1 . Furthermore, u n+1 solves arg min…”

Section: 7mentioning

confidence: 99%

“…Efficient algorithms for this family of regularizers are studied in [5,14]. Algorithms dedicated to color image enchancement are studied in [2,3,32,31,33,46]. Another geometry based regularizer for color images is the Beltrami framework, which was proposed in [24,42] and further investigated in [25,43,48,38,50].…”

Section: Introductionmentioning

confidence: 99%

Elastica Models for Color Image Regularization

Líu¹,

Tai²,

Kimmel³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…There is a growing interest in designing human vision-inspired mathematical models in image processing and computer vision (see e.g. [1], [3], [4], [6], [7], [9], [17], [25]). Dealing with restoration of natural images, this approach is justified by the fact that one aims to maintain the perception of the original scene rather than reproducing its light intensity.…”

Section: New Perspective On Image Restorationmentioning

confidence: 99%

DIP-VBTV: A Color Image Restoration Model Combining a Deep Image Prior and a Vector Bundle Total Variation

Batard¹,

Haro

Ballester

2021

SIAM J. Imaging Sci.

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In this paper, we introduce a new variational model for color image restoration, called DIP-VBTV, which combines two priors: a deep image prior (DIP), which assumes that the restored image can be generated through a neural network and a Vector Bundle Total Variation (VBTV) which generalizes the Vectorial Total Variation (VTV) on vector bundles. VBTV is determined by a geometric triplet: a Riemannian metric on the base manifold, a covariant derivative and a metric on the vector bundle. Whereas VTV prior encourages the restored images to be piece-wise constant, VBTV prior encourages them to be piece-wise parallel with respect to a covariant derivative. For well-chosen geometric triplets, we show that the minimization of VBTV encourages the solutions of the restoration model to share some visual content with the clean image. Then, we show on experiments that DIP-VBTV benefits from this property by outperforming DIP-VTV and stateof-the-art unsupervised methods, which demonstrates the relevance of combining DIP and VBTV priors.

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Perceptible differences in material properties of Ag and its alloys with Cu–As: A comment on Eshel et al. (2021)

Elsayed-Ali

2022

Journal of Archaeological Science

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Variational Models for Color Image Correction Inspired by Visual Perception and Neuroscience

Cited by 4 publications

References 36 publications

Elastica Models for Color Image Regularization

Elastica Models for Color Image Regularization

DIP-VBTV: A Color Image Restoration Model Combining a Deep Image Prior and a Vector Bundle Total Variation

Perceptible differences in material properties of Ag and its alloys with Cu–As: A comment on Eshel et al. (2021)

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