SIAM J. Imaging Sci.最新文献_第7页

Elastica Models for Color Image Regularization 彩色图像正则化的弹性模型

SIAM J. Imaging Sci. Pub Date : 2022-03-18 DOI: 10.48550/arXiv.2203.09995

Hao Liu, X. Tai, R. Kimmel, R. Glowinski

{"title":"Elastica Models for Color Image Regularization","authors":"Hao Liu, X. Tai, R. Kimmel, R. Glowinski","doi":"10.48550/arXiv.2203.09995","DOIUrl":"https://doi.org/10.48550/arXiv.2203.09995","url":null,"abstract":"One classical approach to regularize color is to tream them as two dimensional surfaces embedded in a five dimensional spatial-chromatic space. In this case, a natural regularization term arises as the image surface area. Choosing the chromatic coordinates as dominating over the spatial ones, the image spatial coordinates could be thought of as a paramterization of the image surface manifold in a three dimensional color space. Minimizing the area of the image manifold leads to the Beltrami flow or mean curvature flow of the image surface in the 3D color space, while minimizing the elastica of the image surface yields an additional interesting regularization. Recently, the authors proposed a color elastica model, which minimizes both the surface area and elastica of the image manifold. In this paper, we propose to modify the color elastica and introduce two new models for color image regularization. The revised measures are motivated by the relations between the color elastica model, Euler's elastica model and the total variation model for gray level images. Compared to our previous color elastica model, the new models are direct extensions of Euler's elastica model to color images. The proposed models are nonlinear and challenging to minimize. To overcome this difficulty, two operator-splitting methods are suggested. Specifically, nonlinearities are decoupled by introducing new vector- and matrix-valued variables. Then, the minimization problems are converted to solving initial value problems which are time-discretized by operator splitting. Each subproblem, after splitting either, has a closed-form solution or can be solved efficiently. The effectiveness and advantages of the proposed models are demonstrated by comprehensive experiments. The benefits of incorporating the elastica of the image surface as regularization terms compared to common alternatives are empirically validated.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122256634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Recovery of Piecewise Smooth Density and Lamé Parameters from High Frequency Exterior Cauchy Data 从高频外部柯西数据中恢复分段光滑密度和lam<s:1>参数

SIAM J. Imaging Sci. Pub Date : 2022-03-16 DOI: 10.1137/22m1480951

Sombuddha Bhattacharyya, M. Hoop, Vitaly Katsnelson, G. Uhlmann

引用次数: 0

Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms PDE框架中的加速优化:微分同态流形的表达式

SIAM J. Imaging Sci. Pub Date : 2022-03-01 DOI: 10.1137/20m1381927

G. Sundaramoorthi, A. Yezzi, M. Benyamin

引用次数: 0

Parallel Transport Convolution: Deformable Convolutional Networks on Manifold-Structured Data 并行传输卷积:流形结构数据上的可变形卷积网络

SIAM J. Imaging Sci. Pub Date : 2022-03-01 DOI: 10.1137/21m1407616

Stefan C. Schonsheck, Bin Dong, Rongjie Lai

引用次数: 4

Matrix Balancing Based Interior Point Methods for Point Set Matching Problems 基于矩阵平衡的点集匹配问题的内点法

SIAM J. Imaging Sci. Pub Date : 2022-02-20 DOI: 10.1137/22m1479476

J. Wijesinghe, Peng Chen

{"title":"Matrix Balancing Based Interior Point Methods for Point Set Matching Problems","authors":"J. Wijesinghe, Peng Chen","doi":"10.1137/22m1479476","DOIUrl":"https://doi.org/10.1137/22m1479476","url":null,"abstract":"Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form of linear programming with dense constraints. Linear programming can be handled by interior point methods, provided that the involved ill-conditioned Hessians can be computed accurately. During the decade, matrix balancing has been employed to compute optimal transport under entropy regularization approaches. The solution quality in the interior point method relies on two ingredients: the accuracy of matrix balancing and the boundedness of the dual vector. To achieve high accurate matrix balancing, we employ Newton methods to implement matrix balancing of a sequence of matrices along one central path. In this work, we apply sparse support constraints to matrix-balancing based interior point methods, in which the sparse set fulfilling total support is iteratively updated to truncate the domain of the transport plan. Total support condition is one crucial condition, which guarantees the existence of matrix balancing as well as the boundedness of the dual vector.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130174713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Enhanced Digital Halftoning via Weighted Sigma-Delta Modulation 通过加权Sigma-Delta调制增强数字半调

SIAM J. Imaging Sci. Pub Date : 2022-02-10 DOI: 10.1137/22m151786x

F. Krahmer, Anna Veselovska

{"title":"Enhanced Digital Halftoning via Weighted Sigma-Delta Modulation","authors":"F. Krahmer, Anna Veselovska","doi":"10.1137/22m151786x","DOIUrl":"https://doi.org/10.1137/22m151786x","url":null,"abstract":"In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit Sigma-Delta quantization. We introduce a method to generate Sigma-Delta schemes for two-dimensional signals as a weighted combination of its one-dimensional counterparts and show that various error diffusion schemes proposed in the literature can be represented in this framework via Sigma-Delta schemes of first order. Under the model of two-dimensional bandlimited signals, which is motivated by a mathematical model of human visual perception, we derive quantitative error bounds for such weighted Sigma-Delta schemes. We see these bounds as a step towards a mathematical understanding of the good empirical performance of error diffusion, even though they are formulated in the supremum norm, which is known to not fully capture the visual similarity of images. Motivated by the correspondence between existing error diffusion algorithms and first-order Sigma-Delta schemes, we study the performance of the analogous weighted combinations of second-order Sigma-Delta schemes and show that they exhibit a superior performance in terms of guaranteed error decay for two-dimensional bandlimited signals. In extensive numerical simulations for real world images, we demonstrate that with some modifications to enhance stability this superior performance also translates to the problem of digital halftoning. More concretely, we find that certain second-order weighted Sigma-Delta schemes exhibit competitive performance for digital halftoning of real world images in terms of the Feature Similarity Index (FSIM), a state-of-the-art measure for image quality assessment.","PeriodicalId":185319,"journal":{"name":"SIAM J. Imaging Sci.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128154516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss 基于鲁棒纯四元数矩阵补全的彩色图像补全:误差界和加权损失

SIAM J. Imaging Sci. Pub Date : 2022-02-04 DOI: 10.1137/22M1476897

Junren Chen, Michael K. Ng

引用次数: 14

Total Variation-Based Reconstruction and Phase Retrieval for Diffraction Tomography 基于全变分的衍射层析成像重建与相位恢复

SIAM J. Imaging Sci. Pub Date : 2022-01-27 DOI: 10.1137/22M1474382

Robert Beinert, Michael Quellmalz

引用次数: 2

WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution WPPNets和WPPFlows: Wasserstein Patch prior的超分辨率能力

SIAM J. Imaging Sci. Pub Date : 2022-01-20 DOI: 10.1137/22m1496542

Fabian Altekrüger, J. Hertrich