A Geometric Model of Brightness Perception and Its Application to Color Images Correction

Batard, Thomas; Bertalmío, Marcelo

doi:10.1007/s10851-018-0792-2

Cited by 9 publications

(24 citation statements)

References 30 publications

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“…Retinex models of color vision aim to reproduce the perception of the colors of a scene inspired by psychophysical/physiological knowledge about color vision [5,31]. They can be interpreted as the averaging of perceptual distances between image pixels, as pointed out in [1].…”

Section: A Geometric Model Of Color Perceptionmentioning

confidence: 99%

“…for some nonlinear function ζ, and for any path γ y,x joining y to x, see [1]. The quantity ∇log(u k ) can be interpreted as the perceived gradient of the image according to Weber's law in vision.…”

Section: A Geometric Model Of Color Perceptionmentioning

confidence: 99%

“…On one hand, we establish a connection between the proposed operator and ANNs by showing that a linear activation of the neurons yields a convolutional layer corresponding to a polynomial of order 1 of a differential operator as in [22,23], whereas a nonlinear activation yields a residual unit [19]. On the other hand, we establish a connection with image processing by showing that, for some nonlinear activation function, the proposed operator is related to a variational model refining the color correction models in [4,1], and a linear activation yields a quadratic relaxation of the variational model.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, we show for some particular activation functions, that the proposed 2D simplification corresponds to the gradient descent equations of variational models for image processing refining the one in [4]. In Section 3, we improve the model developed in Section 2 by coupling the simplified Wilson-Cowan equations with a model of color perception introduced in [1] and inspired by the Retinex theory of color vision [24]. For particular activation functions, we show that the coupling model represents the gradient descent equations of variational models refining the one in [1].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, we improve the model developed in Section 2 by coupling the simplified Wilson-Cowan equations with a model of color perception introduced in [1] and inspired by the Retinex theory of color vision [24]. For particular activation functions, we show that the coupling model represents the gradient descent equations of variational models refining the one in [1].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Connection Between Image Processing and Artificial Neural Networks Layers Through a Geometric Model of Visual Perception

Batard¹,

Maldonado

Steidl

et al. 2019

Lecture Notes in Computer Science

Self Cite

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In this paper, we establish a connection between image processing, visual perception, and deep learning by introducing a mathematical model inspired by visual perception from which neural network layers and image processing models for color correction can be derived. Our model is inspired by the geometry of visual perception and couples a geometric model for the organization of some neurons in the visual cortex with a geometric model of color perception. More precisely, the model is a combination of a Wilson-Cowan equation describing the activity of neurons responding to edges and textures in the area V1 of the visual cortex and a Retinex model of color vision. For some particular activation functions, this yields a color correction model which processes simultaneously edges/textures, encoded into a Riemannian metric, and the color contrast, encoded into a nonlocal covariant derivative. Then, we show that the proposed model can be assimilated to a residual layer provided that the activation function is nonlinear and to a convolutional layer for a linear activation function. Finally, we show the accuracy of the model for deep learning by testing it on the MNIST dataset for digit classification.

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Section: A Geometric Model Of Color Perceptionmentioning

confidence: 99%

Section: A Geometric Model Of Color Perceptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Connection Between Image Processing and Artificial Neural Networks Layers Through a Geometric Model of Visual Perception

Batard¹,

Maldonado

Steidl

et al. 2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

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

Batard¹,

Hertrich²,

Steidl³

2020

J Math Imaging Vis

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Reproducing the perception of a real-world scene on a display device is a very challenging task which requires the understanding of the camera processing pipeline, the display process, and the way the human visual system processes the light it captures. Mathematical models based on psychophysical and physiological laws on color vision, named Retinex, provide efficient tools to handle degradations produced during the camera processing pipeline like the reduction of the contrast. In particular, Batard and Bertalmío [J Math. Imag. Vis. 60(6), 849-881 (2018)] described some psychophysical laws on brightness perception as covariant derivatives, included them into a variational model, and observed that the quality of the color image correction is correlated with the accuracy of the vision model it includes. Based on this observation, we postulate that this model can be improved by including more accurate data on vision with a special attention on visual neuroscience here. Then, inspired by the presence of neurons responding to different visual attributes in the area V1 of the visual cortex as orientation, color or movement, to name a few, and horizontal connections modeling the interactions between those neurons, we construct two variational models to process both local (edges,

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Recent advances in denoising of manifold-valued images

Bergmann

Laus

Persch

et al. 2019

Handbook of Numerical Analysis

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Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny inaccuracies, which result in noisy data. In this chapter, we review recent advances in denoising of manifoldvalued signals and images, where we restrict our attention to variational models and appropriate minimization algorithms. The algorithms are either classical as the subgradient algorithm or generalizations of the half-quadratic minimization method, the cyclic proximal point algorithm, and the Douglas-Rachford algorithm to manifolds. An important aspect when dealing with real-world data is the practical implementation. Here several groups provide software and toolboxes as the Manifold Optimization (Manopt) package and the manifold-valued image restoration toolbox (MVIRT).

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A Geometric Model of Brightness Perception and Its Application to Color Images Correction

Cited by 9 publications

References 30 publications

A Connection Between Image Processing and Artificial Neural Networks Layers Through a Geometric Model of Visual Perception

A Connection Between Image Processing and Artificial Neural Networks Layers Through a Geometric Model of Visual Perception

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

Recent advances in denoising of manifold-valued images

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