Directional global three-part image decomposition

Thai, Duy Hoang; Gottschlich, Carsten

doi:10.1186/s13640-016-0110-0

Cited by 6 publications

(28 citation statements)

References 54 publications

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“…In the area of computer vision and image processing, important applications include image enhancement, denoising, inpainting, feature extraction and compression. In one subdomain of image processing, these challenges are approached by decomposing images into two or three parts [27], e.g. a cartoon component, which contains piecewise constant or piecewise smooth parts, a texture component, which captures oscillating patterns, and a noise component, which contains small scale objects (corresponding to high frequency parts in the Fourier domain).…”

Section: Discussionmentioning

confidence: 99%

DOTmark – A Benchmark for Discrete Optimal Transport

2017

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The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly complex data, the computation of these distances via optimal transport is often the limiting factor. Inspired by this challenge, a variety of new approaches to optimal transport has been proposed in recent years and along with these new methods comes the need for a meaningful comparison.In this paper, we introduce a benchmark for discrete optimal transport, called DOTmark, which is designed to serve as a neutral collection of problems, where discrete optimal transport methods can be tested, compared to one another, and brought to their limits on large-scale instances. It consists of a variety of grayscale images, in various resolutions and classes, such as several types of randomly generated images, classical test images and real data from microscopy.Along with the DOTmark we present a survey and a performance test for a cross section of established methods ranging from more traditional algorithms, such as the transportation simplex, to recently developed approaches, such as the shielding neighborhood method, and including also a comparison with commercial solvers.

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Section: Discussionmentioning

confidence: 99%

DOTmark – A Benchmark for Discrete Optimal Transport

2017

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“…The G3PD method [ 64 ] follows a variational approach to decompose a fingerprint image into three parts and obtains the ROI based on the texture component. The further advanced and more general DG3PD method [ 66 ] has also been applied to latent fingerprint segmentation. The method by Bartůněk [ 65 ] relies on normalisation and local kurtosis estimation as a novel feature for segmentation.…”

Section: Discussionmentioning

confidence: 99%

Filter Design and Performance Evaluation for Fingerprint Image Segmentation

Thai¹,

Huckemann²,

Gottschlich³

2016

PLoS ONE

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Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing step of most fingerprint algorithms and it divides an image into foreground, the region of interest, and background. Two types of error can occur during this step which both have a negative impact on the recognition performance: ‘true’ foreground can be labeled as background and features like minutiae can be lost, or conversely ‘true’ background can be misclassified as foreground and spurious features can be introduced. The contribution of this paper is threefold: firstly, we propose a novel factorized directional bandpass (FDB) segmentation method for texture extraction based on the directional Hilbert transform of a Butterworth bandpass (DHBB) filter interwoven with soft-thresholding. Secondly, we provide a manually marked ground truth segmentation for 10560 images as an evaluation benchmark. Thirdly, we conduct a systematic performance comparison between the FDB method and four of the most often cited fingerprint segmentation algorithms showing that the FDB segmentation method clearly outperforms these four widely used methods. The benchmark and the implementation of the FDB method are made publicly available.

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“…We define a method for restoration of the original noisy/non-noisy image f with a set of known missing regions D . The proposed model is a generalized version of DG3PD [ 35 ] for the inpainting and denoising problem. This modification for our DG3PD inpainting is inspired by Elad et al [ 23 ].…”

Section: Inpainting By Dg3pdmentioning

confidence: 99%

“…Note that if there are no missing regions, i.e. χ c D [ k ] = 1, ∀ k ∈ Ω , the minimization problem ( 2.1 ) becomes the DG3PD model [ 35 ]. Next, we discuss how to solve the DG3PD-inpainting model ( 2.1 ).…”

Section: Inpainting By Dg3pdmentioning

confidence: 99%

“…Existing inpainting methods in the literature typically assume that the non-missing pixels in a given image contain only a small amount of noise or are noise free, and existing methods for denoising typically assume that all pixels of the noisy image are known. The proposed method for solving this challenging problem is inspired by the works of Efros & Leung [ 30 ], Bertalmio et al [ 31 ], Vese & Osher [ 33 ], Aujol & Chambolle [ 34 ], Buades et al [ 13 ] and Elad et al [ 23 ], and is based on the directional global three-part decomposition (DG3PD) [ 35 ]. The DG3PD method decomposes an image into three parts: a cartoon image, a texture image and a residual image.…”

Section: Introduction and Related Workmentioning

confidence: 99%

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Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing

Thai

Gottschlich

2018

R. Soc. open sci.

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We consider the very challenging task of restoring images (i) that have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise, and (iii) that ideally contain both cartoon and texture elements. The combination of these three properties makes this inverse problem a very difficult one. The solution proposed in this manuscript is based on directional global three-part decomposition (DG3PD) (Thai, Gottschlich. 2016 EURASIP. J. Image Video Process. 2016, 1–20 (doi:10.1186/s13640-015-0097-y10.1186/s13640-015-0097-y)) with a directional total variation norm, directional G-norm and ℓ∞-norm in the curvelet domain as key ingredients of the model. Image decomposition by DG3PD enables a decoupled inpainting and denoising of the cartoon and texture components. A comparison with existing approaches for inpainting and denoising shows the advantages of the proposed method. Moreover, we regard the image restoration problem from the viewpoint of a Bayesian framework and we discuss the connections between the proposed solution by function space and related image representation by harmonic analysis and pyramid decomposition.

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Directional global three-part image decomposition

Cited by 6 publications

References 54 publications

DOTmark – A Benchmark for Discrete Optimal Transport

DOTmark – A Benchmark for Discrete Optimal Transport

Filter Design and Performance Evaluation for Fingerprint Image Segmentation

Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing

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