Journal of Mathematical Imaging and Vision最新文献_第3页

Hypergraph p-Laplacians and Scale Spaces 超图 p-Laplacians 和尺度空间

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-04-23 DOI: 10.1007/s10851-024-01183-0

Ariane Fazeny, Daniel Tenbrinck, Kseniia Lukin, Martin Burger

{"title":"Hypergraph p-Laplacians and Scale Spaces","authors":"Ariane Fazeny, Daniel Tenbrinck, Kseniia Lukin, Martin Burger","doi":"10.1007/s10851-024-01183-0","DOIUrl":"https://doi.org/10.1007/s10851-024-01183-0","url":null,"abstract":"The aim of this paper is to revisit the definition of differential operators on hypergraphs, which are a natural extension of graphs in systems based on interactions beyond pairs. In particular, we focus on the definition of Laplacian and p-Laplace operators for oriented and unoriented hypergraphs, their basic properties, variational structure, and their scale spaces. We illustrate that diffusion equations on hypergraphs are possible models for different applications such as information flow on social networks or image processing. Moreover, the spectral analysis and scale spaces induced by these operators provide a potential method to further analyze complex data and their multiscale structure. The quest for spectral analysis and suitable scale spaces on hypergraphs motivates in particular a definition of differential operators with trivial first eigenfunction and thus more interpretable second eigenfunctions. This property is not automatically satisfied in existing definitions of hypergraph p-Laplacians, and we hence provide a novel axiomatic approach that extends previous definitions and can be specialized to satisfy such (or other) desired properties.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"31 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140799365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially Varying Generalised Gaussian Models 基于空间变化广义高斯模型的联合图像复原和特征提取变分法

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-04-12 DOI: 10.1007/s10851-024-01184-z

Émilie Chouzenoux, Marie-Caroline Corbineau, Jean-Christophe Pesquet, Gabriele Scrivanti

引用次数: 0

Finding Space-Time Boundaries with Deformable Hypersurfaces 用可变形超曲面寻找时空边界

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-04-09 DOI: 10.1007/s10851-024-01185-y

Patrick M. Jensen, J. Andreas Bærentzen, Anders B. Dahl, Vedrana A. Dahl

引用次数: 0

Regularised Diffusion–Shock Inpainting 正则化扩散冲击涂色

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-04-01 DOI: 10.1007/s10851-024-01175-0

Kristina Schaefer, Joachim Weickert

{"title":"Regularised Diffusion–Shock Inpainting","authors":"Kristina Schaefer, Joachim Weickert","doi":"10.1007/s10851-024-01175-0","DOIUrl":"https://doi.org/10.1007/s10851-024-01175-0","url":null,"abstract":"We introduce regularised diffusion–shock (RDS) inpainting as a modification of diffusion–shock inpainting from our SSVM 2023 conference paper. RDS inpainting combines two carefully chosen components: homogeneous diffusion and coherence-enhancing shock filtering. It benefits from the complementary synergy of its building blocks: The shock term propagates edge data with perfect sharpness and directional accuracy over large distances due to its high degree of anisotropy. Homogeneous diffusion fills large areas efficiently. The second order equation underlying RDS inpainting inherits a maximum–minimum principle from its components, which is also fulfilled in the discrete case, in contrast to competing anisotropic methods. The regularisation addresses the largest drawback of the original model: It allows a drastic reduction in model parameters without any loss in quality. Furthermore, we extend RDS inpainting to vector-valued data. Our experiments show a performance that is comparable to or better than many inpainting methods based on partial differential equations and related integrodifferential models, including anisotropic processes of second or fourth order.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"32 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Averaged Deep Denoisers for Image Regularization 用于图像正规化的平均深度去噪器

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-03-24 DOI: 10.1007/s10851-024-01181-2

{"title":"Averaged Deep Denoisers for Image Regularization","authors":"","doi":"10.1007/s10851-024-01181-2","DOIUrl":"https://doi.org/10.1007/s10851-024-01181-2","url":null,"abstract":"<h3>Abstract</h3> Plug-and-Play (PnP) and Regularization-by-Denoising (RED) are recent paradigms for image reconstruction that leverage the power of modern denoisers for image regularization. In particular, they have been shown to deliver state-of-the-art reconstructions with CNN denoisers. Since the regularization is performed in an ad-hoc manner, understanding the convergence of PnP and RED has been an active research area. It was shown in recent works that iterate convergence can be guaranteed if the denoiser is averaged or nonexpansive. However, integrating nonexpansivity with gradient-based learning is challenging, the core issue being that testing nonexpansivity is intractable. Using numerical examples, we show that existing CNN denoisers tend to violate the nonexpansive property, which can cause PnP or RED to diverge. In fact, algorithms for training nonexpansive denoisers either cannot guarantee nonexpansivity or are computationally intensive. In this work, we construct contractive and averaged image denoisers by unfolding splitting-based optimization algorithms applied to wavelet denoising and demonstrate that their regularization capacity for PnP and RED can be matched with CNN denoisers. To our knowledge, this is the first work to propose a simple framework for training contractive denoisers using network unfolding. ","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"7 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sparse Resultant-Based Minimal Solvers in Computer Vision and Their Connection with the Action Matrix 计算机视觉中基于稀疏结果的最小求解器及其与动作矩阵的联系

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-03-23 DOI: 10.1007/s10851-024-01182-1

Snehal Bhayani, Janne Heikkilä, Zuzana Kukelova

{"title":"Sparse Resultant-Based Minimal Solvers in Computer Vision and Their Connection with the Action Matrix","authors":"Snehal Bhayani, Janne Heikkilä, Zuzana Kukelova","doi":"10.1007/s10851-024-01182-1","DOIUrl":"https://doi.org/10.1007/s10851-024-01182-1","url":null,"abstract":"Many computer vision applications require robust and efficient estimation of camera geometry from a minimal number of input data measurements. Minimal problems are usually formulated as complex systems of sparse polynomial equations. The systems usually are overdetermined and consist of polynomials with algebraically constrained coefficients. Most state-of-the-art efficient polynomial solvers are based on the action matrix method that has been automated and highly optimized in recent years. On the other hand, the alternative theory of sparse resultants based on the Newton polytopes has not been used so often for generating efficient solvers, primarily because the polytopes do not respect the constraints amongst the coefficients. In an attempt to tackle this challenge, here we propose a simple iterative scheme to test various subsets of the Newton polytopes and search for the most efficient solver. Moreover, we propose to use an extra polynomial with a special form to further improve the solver efficiency via Schur complement computation. We show that for some camera geometry problems our resultant-based method leads to smaller and more stable solvers than the state-of-the-art Gröbner basis-based solvers, while being significantly smaller than the state-of-the-art resultant-based methods. The proposed method can be fully automated and incorporated into existing tools for the automatic generation of efficient polynomial solvers. It provides a competitive alternative to popular Gröbner basis-based methods for minimal problems in computer vision. Additionally, we study the conditions under which the minimal solvers generated by the state-of-the-art action matrix-based methods and the proposed extra polynomial resultant-based method, are equivalent. Specifically, we consider a step-by-step comparison between the approaches based on the action matrix and the sparse resultant, followed by a set of substitutions, which would lead to equivalent minimal solvers.\u0000","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"86 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized Inversion of Nonlinear Operators 非线性算子的广义反演

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-03-19 DOI: 10.1007/s10851-024-01179-w

Eyal Gofer, Guy Gilboa

{"title":"Generalized Inversion of Nonlinear Operators","authors":"Eyal Gofer, Guy Gilboa","doi":"10.1007/s10851-024-01179-w","DOIUrl":"https://doi.org/10.1007/s10851-024-01179-w","url":null,"abstract":"Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most notable is the Moore–Penrose inverse, widely used in physics, statistics, and various fields of engineering. This work investigates generalized inversion of nonlinear operators. We first address broadly the desired properties of generalized inverses, guided by the Moore–Penrose axioms. We define the notion for general sets and then a refinement, termed pseudo-inverse, for normed spaces. We present conditions for existence and uniqueness of a pseudo-inverse and establish theoretical results investigating its properties, such as continuity, its value for operator compositions and projection operators, and others. Analytic expressions are given for the pseudo-inverse of some well-known, non-invertible, nonlinear operators, such as hard- or soft-thresholding and ReLU. We analyze a neural layer and discuss relations to wavelet thresholding. Next, the Drazin inverse, and a relaxation, are investigated for operators with equal domain and range. We present scenarios where inversion is expressible as a linear combination of forward applications of the operator. Such scenarios arise for classes of nonlinear operators with vanishing polynomials, similar to the minimal or characteristic polynomials for matrices. Inversion using forward applications may facilitate the development of new efficient algorithms for approximating generalized inversion of complex nonlinear operators.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"57 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Assessing Hierarchies by Their Consistent Segmentations 通过一致的细分来评估层次结构

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-03-18 DOI: 10.1007/s10851-024-01176-z

Zeev Gutman, Ritvik Vij, Laurent Najman, Michael Lindenbaum

引用次数: 0

Stochastic Primal–Dual Hybrid Gradient Algorithm with Adaptive Step Sizes 自适应步长的随机原始-双重混合梯度算法

IF 2 4区数学

Journal of Mathematical Imaging and Vision Pub Date : 2024-03-16 DOI: 10.1007/s10851-024-01174-1

引用次数: 0

Product of Gaussian Mixture Diffusion Models 高斯混合扩散模型的乘积

IF 2 4区数学