Image compression based on PDEs

Zhao, Cuifang; Du, Meng

doi:10.1109/iccsnt.2011.6182311

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…They date back to early approaches of Carlsson [32]. Contemporary semantic codecs are particularly popular for the compression of images with pronounced edges [33,34] such as cartoons [35][36][37][38], depth maps [29,39,40], or flow fields [41]. These methods extract and store image edges and use those as known data for inpainting.…”

Section: Related Workmentioning

confidence: 99%

A Systematic Evaluation of Coding Strategies for Sparse Binary Images

Mohideen¹,

Peter²,

Weickert³

2020

Preprint

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Inpainting-based compression represents images in terms of a sparse subset of its pixel data. Storing the carefully optimised positions of known data creates a lossless compression problem on sparse and often scattered binary images. This central issue is crucial for the performance of such codecs. Since it has only received little attention in the literature, we conduct the first systematic investigation of this problem so far. To this end, we first review and compare a wide range of existing methods from image compression and general purpose coding in terms of their coding efficiency and runtime. Afterwards, an ablation study enables us to identify and isolate the most useful components of existing methods. With context mixing, we combine those ingredients into new codecs that offer either better compression ratios or a more favourable trade-off between speed and performance.

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Section: Related Workmentioning

confidence: 99%

A Systematic Evaluation of Coding Strategies for Sparse Binary Images

Mohideen¹,

Peter²,

Weickert³

2020

Preprint

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show abstract

“…Also within coding, publications that exploit information from edges or segment boundaries and combine it with inpainting processes have a long tradition [1,7,18,21,27,36,55,57,65,80,84,87,90,137,143]. However, for general images these features are often suboptimal as inpainting data.…”

Section: Contour-based Featuresmentioning

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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Deep spatial and tonal data optimisation for homogeneous diffusion inpainting

Peter

Schrader

Alt

et al. 2023

Pattern Anal Applic

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Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression, where the original image is known. Selecting the known data constitutes a challenging optimisation problem, that has so far been only investigated with model-based approaches. So far, these methods require a choice between either high quality or high speed since qualitatively convincing algorithms rely on many time-consuming inpaintings. We propose the first neural network architecture that allows fast optimisation of pixel positions and pixel values for homogeneous diffusion inpainting. During training, we combine two optimisation networks with a neural network-based surrogate solver for diffusion inpainting. This novel concept allows us to perform backpropagation based on inpainting results that approximate the solution of the inpainting equation. Without the need for a single inpainting during test time, our deep optimisation accelerates data selection by more than four orders of magnitude compared to common model-based approaches. This provides real-time performance with high quality results.

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Image compression based on PDEs

Cited by 4 publications

References 7 publications

A Systematic Evaluation of Coding Strategies for Sparse Binary Images

A Systematic Evaluation of Coding Strategies for Sparse Binary Images

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

Deep spatial and tonal data optimisation for homogeneous diffusion inpainting

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