A Convex Approach to Superresolution and Regularization of Lines in Images

Polisano, Kévin; Condat, Laurent; Clausel, Marianne; Perrier, Valérie

doi:10.1137/18m118116x

Cited by 6 publications

(9 citation statements)

References 70 publications

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“…To compare the SSRT performances with ones of the most recent works [15] aiming at recovering linear structures in images through, among others, detecting their centerlines, we consider an image of size

201 \times 201

, consisting of three structures of centerline parameters

false(ρ_{1}, θ_{1} false) = false(- 141.077, 144 false)

false(ρ_{2}, θ_{2} false) = false(65.148, 11 false)

and

false(ρ_{3}, θ_{3} false) = false(45.629, 30 false)

. These structures are created by a Gaussian blurring process with

κ = 8

, as presented by the authors in [15]. We synthesis, from the obtained image, two different noisy images with

ζ = 100

and

ζ = 200

.…”

Section: Methodsmentioning

confidence: 99%

“…In this table, we consider Δ i = | i −̃i| and Δ i = | i −̃i| with i = 1, 2, 3 and root mean square error (RMSE) computed as and c) HT in the presence of blur and noise FIGURE 17 Line detection estimates for Ref. [15] and SSRT for blur and noise parameters ( , ) = (8,0), (8,100) and (8,200)…”

Section: Synthetic Linear Structure Imagesmentioning

confidence: 99%

“…However, it is not suitable for irregular or occluded linear shape structures. Recently, Polisano et al [15] present a new formulation for the problem of recovering lines in degraded images using the framework of atomic norm minimization. They have used a primal-dual splitting algorithm to solve the convex optimization problem.…”

Section: Introductionmentioning

confidence: 99%

“…Line parameters estimation errors and runtime for Ref [15]. and SSRT with blur and noise ( , ) equal to (8,0),(8,100) and(8,200) …”

mentioning

confidence: 99%

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Scale space Radon transform

Ziou

Nacereddine

Goumeidane

2021

IET Image Processing

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An extension of Radon transform by using a measure function capturing the user need is proposed. The new transform, called scale space Radon transform, is devoted to the case where the embedded shape in the image is not filiform. A case study is brought on a straight line and an ellipse where the SSRT behaviour in the scale space and in the presence of noise is deeply analyzed. In order to show the effectiveness of the proposed transform, the experiments have been carried out, first, on linear and elliptical structures generated synthetically subjected to strong altering conditions such blur and noise and then on structures images issued from real-world applications such as road traffic, satellite imagery and weld X-ray imaging. Comparisons in terms of detection accuracy and computational time with wellknown transforms and recent work dedicated to this purpose are conducted, where the proposed transform shows an outstanding performance in detecting the above-mentioned structures and targeting accurately their spatial locations even in low-quality images. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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201 \times 201

, consisting of three structures of centerline parameters

false(ρ_{1}, θ_{1} false) = false(- 141.077, 144 false)

false(ρ_{2}, θ_{2} false) = false(65.148, 11 false)

and

false(ρ_{3}, θ_{3} false) = false(45.629, 30 false)

. These structures are created by a Gaussian blurring process with

κ = 8

, as presented by the authors in [15]. We synthesis, from the obtained image, two different noisy images with

ζ = 100

and

ζ = 200

.…”

Section: Methodsmentioning

confidence: 99%

Section: Synthetic Linear Structure Imagesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Line parameters estimation errors and runtime for Ref [15]. and SSRT with blur and noise ( , ) equal to (8,0),(8,100) and(8,200) …”

mentioning

confidence: 99%

See 2 more Smart Citations

Scale space Radon transform

Ziou

Nacereddine

Goumeidane

2021

IET Image Processing

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show abstract

“…A fast proximal gradient descent algorithm for solving the optimization problem arising from the implementation of this formulation was proposed in [16] and further improved in [7]. The new dual discrete TV led to improvement in accuracy of TV computation and was used to solve TV-regularization based optimization problems with applications to image denoising, inpainting, motion estimation, and multi-label image segmentation [20,7,1,21,3].…”

Section: Introductionmentioning

confidence: 99%

On the TVD property of second order methods for 2D scalar conservation laws

Krivodonova,

Smirnov

2021

Preprint

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The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging to extend this approach to two-dimensional problems. Using the anisotropic definition for discrete total variation (TV), it was shown in [14] that TVD solutions of two-dimensional hyperbolic equations are at most first order accurate. We propose to use an alternative definition resulting from a full discretization of the semi-discrete Raviart-Thomas TV. We demonstrate numerically using the second order discontinuous Galerkin method that limited solutions of two-dimensional hyperbolic equations are TVD in means when total variation is computed using the new definition.

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Atomic norm minimization for decomposition into complex exponentials and optimal transport in Fourier domain

Condat

2020

Journal of Approximation Theory

Self Cite

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This paper is devoted to the decomposition of vectors into sampled complex exponentials; or, equivalently, to the information over discrete measures captured in a finite sequence of their Fourier coefficients. We study existence, uniqueness, and cardinality properties, as well as computational aspects of estimation using convex semidefinite programs. We then explore optimal transport between measures, of which only a finite sequence of Fourier coefficients is known.

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A Convex Approach to Superresolution and Regularization of Lines in Images

Cited by 6 publications

References 70 publications

Scale space Radon transform

Scale space Radon transform

On the TVD property of second order methods for 2D scalar conservation laws

Atomic norm minimization for decomposition into complex exponentials and optimal transport in Fourier domain

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