Non-convex non-local reactive flows for saliency detection and segmentation

Galiano, Gonzalo; Ramírez, Iván; Schiavi, Emanuele

doi:10.1016/j.cam.2020.112873

Cited by 5 publications

(5 citation statements)

References 32 publications

(40 reference statements)

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“…In recent years, the non-convex optimization has been widely used in image processing and there are many algorithms to solve non-convex optimization problems [17,[33][34][35][36]. In particular, the non-convex and non-smooth (NN) regularization has attracted much attention in image processing [3,[16][17][18][19][20][21][22][23]. Compared to the convex and smooth regularization, the NN one has remarkable advantages for edge-preserving restoration such as the anisotropic model [5]:…”

Section: Introductionmentioning

confidence: 99%

“…To integrate the NN regularization methods into the nonlocal methods, Galiano et al [21] proposed a nonlocal NN diffusion model, which is used for saliency detection and classification. The regularization term in this model was given as follows:…”

Section: Introductionmentioning

confidence: 99%

“…Although the good performance of the non-convex, non-smooth and nonlocal regularization has been verified numerically, there is no mathematical theory that can give the reasons. Besides, the model in [21] only considered a special class of the NN regularization: ϕ(t) = |t| p , 0 < p < 1. Moreover, the weighting function in [21] was given empirically and cannot be updated in iteration.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, the model in [21] only considered a special class of the NN regularization: ϕ(t) = |t| p , 0 < p < 1. Moreover, the weighting function in [21] was given empirically and cannot be updated in iteration.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization

Meng¹,

Wang²,

Cui³

et al. 2022

Inverse Problems

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In the inverse problem of image processing, we have witnessed that the non-convex and non-smooth regularizers can produce clearer image edges than convex ones such as total variation (TV). This fact can be explained by the uniform lower bound theory of the local gradient in non-convex and non-smooth regularization. In recent years, although it has been numerically shown that the nonlocal regularizers of various image patches based nonlocal methods can recover image textures well, we still desire a theoretical interpretation. To this end, we propose a non-convex non-smooth and block nonlocal (NNBN) regularization model based on image patches. By integrating the advantages of the non-convex and non-smooth potential function in the regularization term, the uniform lower bound theory of the image patches based nonlocal gradient is given. This approach partially explains why the proposed method can produce clearer image textures and edges. Compared to some classical regularization methods, such as total variation (TV), non-convex and non-smooth (NN) regularization, nonlocal total variation (NLTV) and block nonlocal total variation(BNLTV), our experimental results show that the proposed method improves restoration quality.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization

Meng¹,

Wang²,

Cui³

et al. 2022

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…For image processing tasks, specially for image denoising, filters involving expressions like (3) are known as bilateral filters [33,27,29,3,11,5,19] and are mostly applied in a single discrete time step, although other tasks like image segmentation and saliency detection may require more steps [14,16,18]. For other applications, these algorithms may result interesting when accuracy is secondary to execution time, e.g.…”

Section: Introductionmentioning

confidence: 99%

Error analysis of some nonlocal diffusion discretization schemes

Galiano¹

2021

Preprint

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We study two numerical approximations of solutions of nonlocal diffusion evolution problems which are inspired in algorithms for computing the bilateral denoising filtering of an image, and which are based on functional rearrangements and on the Fourier transform. Apart from the usual time-space discretization, these algorithms also use the discretization of the range of the solution (quantization). We show that the discrete approximations converge to the continuous solution in suitable functional spaces, and provide error estimates. Finally, we present some numerical experiments illustrating the performance of the algorithms, specially focusing in the execution time.

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A non-smooth non-local variational approach to saliency detection in real time

Alcaín

Muñoz

Schiavi

et al. 2020

J Real-Time Image Proc

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In this paper, we propose and solve numeri cally a general non-smooth, non-local variational model to tackle the saliency detection problem in natural im ages. In order to overcome the typical drawback of the non-local methods in image processing, which mainly is the inherent computationa.l complexity of non-local cal culus, as the non-local derivatives are computed w.r.t every point of the domain, we propose a different sce nario. We present a novel convex energy minimization problem in the feature space, which is efficiently solved by means of a non-local Primal-Dual method. Severa.! irnplementations and discussions are presented taking care ofthe computing platforms, CPU and GPU, achiev ing up to 33 fps a.nd 62 fps respectively for 300x400 image resolution, making the method eligible for real time a.pplications.

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Non-convex non-local reactive flows for saliency detection and segmentation

Cited by 5 publications

References 32 publications

The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization

The lower bound of nonlocal gradient for non-convex and non-smooth image patches based regularization

Error analysis of some nonlocal diffusion discretization schemes

A non-smooth non-local variational approach to saliency detection in real time

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