Anisotropic mesh adaptation for image representation

Li, Xianping

doi:10.1186/s13640-016-0132-7

Cited by 12 publications

(11 citation statements)

References 27 publications

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“…PDE-based codecs that select the inpainting mask with triangular or rectangular subdivisions have structural similarities to piecewise polynomial image approximations based on adaptive triangulations or quadtrees. Extensive research has been performed on these approximations; see [13,30,35,40,44,75,77,82,83,122,124,125] and the references therein. Often such approaches use linear polynomials within each triangle or rectangle.…”

Section: Relations To Other Methodsmentioning

confidence: 99%

2. Optimizing spatial and tonal data for PDE-based inpainting

Hoeltgen¹,

Mainberger²,

Hoffmann³

et al. 2016

Variational Methods

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Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. Apart from these specific contributions, we also give an extensive literature survey on PDE-based image compression methods. Summary and ConclusionsThe contributions of our work are twofold: On the one hand we gave a comprehensive survey on the state-of-the-art in PDE-based image compression.

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Section: Relations To Other Methodsmentioning

confidence: 99%

2. Optimizing spatial and tonal data for PDE-based inpainting

Hoeltgen¹,

Mainberger²,

Hoffmann³

et al. 2016

Variational Methods

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“…In practice, the measurement-adaptive image sampling/recovery scheme includes various applications from intelligent compressive imaging-based acquisition devices [20] to computer vision and graphics, and image processing technology, e.g. inpainting, remote sensing missing recovery, denoising of impulsive noise, and mesh-based image representation [21]. For reproduction purposes, simulation codes are available online 1 .…”

Section: B Motivations and Contributionsmentioning

confidence: 99%

Adaptive Sparse Image Sampling and Recovery

Taimori

Marvasti

2018

IEEE Trans. Comput. Imaging

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This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient information content of image patches. By leveraging texture in space, sparsity locations in DCT domain, and directional decomposition of gradients, the sampler structure consists of a combination of uniform, random, and nonuniform sampling strategies. For reconstruction, we model the recovery problem as a two-state cellular automaton to iteratively restore image with scalable windows from generation to generation. We demonstrate the recovery algorithm quickly converges after a few generations for an image with arbitrary degree of texture. For a given number of measurements, extensive experiments on standard image-sets, infra-red, and mega-pixel range imaging devices show that the proposed measurement matrix considerably increases the overall recovery performance, or equivalently decreases the number of sampled pixels for a specific recovery quality compared to random sampling matrix and Gaussian linear combinations employed by the state-of-the-art compressive sensing methods. In practice, the proposed measurement-adaptive sampling/recovery framework includes various applications from intelligent compressive imaging-based acquisition devices to computer vision and graphics, and image processing technology. Simulation codes are available online for reproduction purposes.

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“…There are many algorithms for solving the approximation problem using the multivariable function [26], find edges [27 -31], spline interpolation [32], including the use of adaptive triangular mesh [33,34], and wavelets [35]. These algorithms are useful, for example, for compressing images or for recognizing their elements.…”

Section: Introductionmentioning

confidence: 99%

Determination of the beam waist position for the spin-orbit interaction effect observation

et al. 2021

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The spin angular momentum and the extrinsic orbital angular momentum of light are associated with the polarization of light and the light propagation trajectory, respectively. Those momenta are interdependent not only in an inhomogeneous or anisotropic medium but even in free space. This interaction is called the spin-orbit interaction of light. The effects of the spin-orbit interaction of light manifest themselves in a small transverse shift of the beam field longitudinal component from the beam propagation axis in the waist region under the circular polarization sign change. They can be observed both for Gaussian beams and for structured beams. The effects of the spin-orbit interaction of light should be taken into account when nanophotonics devices are created, but the detailed investigation of the effect had not been performed yet due to the low intensity noise image of the beam waist. Precise measurements of the focal waist centerline are needed to determine the transverse shift of the beam field longitudinal component of the asymmetric converging beam's waist under the circular polarization sign change. We propose methods for determining the transverse and longitudinal positions of the beam waist. Computer image processing methods made it possible to obtain the value of the beam waist's transverse position with an accuracy of 0.1 mkm. These methods will allow further testing of the shifts' theoretical predictions, the values of which are the order of 1 mkm. The results obtained can also be used for laser processing of materials by polarized light and precise positioning of the beam's focal spot at a surface.

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Anisotropic mesh adaptation for image representation

Cited by 12 publications

References 27 publications

2. Optimizing spatial and tonal data for PDE-based inpainting

2. Optimizing spatial and tonal data for PDE-based inpainting

Adaptive Sparse Image Sampling and Recovery

Determination of the beam waist position for the spin-orbit interaction effect observation

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