Journal of Mathematical Imaging and Vision最新文献

{"title":"Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group","authors":"Michael Quellmalz, Léo Buecher, Gabriele Steidl","doi":"10.1007/s10851-024-01206-w","DOIUrl":"https://doi.org/10.1007/s10851-024-01206-w","url":null,"abstract":"<p>Sliced optimal transport, which is basically a Radon transform followed by one-dimensional optimal transport, became popular in various applications due to its efficient computation. In this paper, we deal with sliced optimal transport on the sphere <span>(mathbb {S}^{d-1})</span> and on the rotation group <span>(textrm{SO}(3))</span>. We propose a parallel slicing procedure of the sphere which requires again only optimal transforms on the line. We analyze the properties of the corresponding parallelly sliced optimal transport, which provides in particular a rotationally invariant metric on the spherical probability measures. For <span>(textrm{SO}(3))</span>, we introduce a new two-dimensional Radon transform and develop its singular value decomposition. Based on this, we propose a sliced optimal transport on <span>(textrm{SO}(3))</span>. As Wasserstein distances were extensively used in barycenter computations, we derive algorithms to compute the barycenters with respect to our new sliced Wasserstein distances and provide synthetic numerical examples on the 2-sphere that demonstrate their behavior for both the free- and fixed-support setting of discrete spherical measures. In terms of computational speed, they outperform the existing methods for semicircular slicing as well as the regularized Wasserstein barycenters.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"321 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777775","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}

{"title":"An Edge-Preserving Regularization Model for the Demosaicing of Noisy Color Images","authors":"Antonio Boccuto, Ivan Gerace, Valentina Giorgetti, Francesca Martinelli, Anna Tonazzini","doi":"10.1007/s10851-024-01204-y","DOIUrl":"https://doi.org/10.1007/s10851-024-01204-y","url":null,"abstract":"<p>This paper proposes an edge-preserving regularization technique to solve the color image demosaicing problem in the realistic case of noisy data. We enforce intra-channel local smoothness of the intensity (low-frequency components) and inter-channel local similarity of the depth of object borders and textures (high-frequency components). Discontinuities of both the low-frequency and high-frequency components are accounted for implicitly, i.e., through suitable functions of the proper derivatives. For the treatment of even the finest image details, derivatives of first, second, and third orders are considered. The solution to the demosaicing problem is defined as the minimizer of an energy function, accounting for all these constraints plus a data fidelity term. This non-convex energy is minimized via an iterative deterministic algorithm, applied to a family of approximating functions, each implicitly referring to geometrically consistent image edges. Our method is general because it does not refer to any specific color filter array. However, to allow quantitative comparisons with other published results, we tested it in the case of the Bayer CFA and on the Kodak 24-image dataset, the McMaster (IMAX) 18-image dataset, the Microsoft Demosaicing Canon 57-image dataset, and the Microsoft Demosaicing Panasonic 500-image dataset. The comparisons with some of the most recent demosaicing algorithms show the good performance of our method in both the noiseless and noisy cases.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"20 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777776","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}

{"title":"Re-initialization-Free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation","authors":"Fanghui Song, Jiebao Sun, Shengzhu Shi, Zhichang Guo, Dazhi Zhang","doi":"10.1007/s10851-024-01205-x","DOIUrl":"https://doi.org/10.1007/s10851-024-01205-x","url":null,"abstract":"<p>Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be unstable, which results in over flatted or over sharpened contours and segmentation failure. To improve the accuracy and stability of evolution, we propose a high-order level set variational segmentation method integrated with molecular beam epitaxy (MBE) equation regularization. This method uses the crystal growth in the MBE process to limit the evolution of the level set function. Thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve and keep the segmentation results independent of the initial curve selection. It also works for noisy images with intensity inhomogeneity, which is a challenge in image segmentation. To solve the variational model, we derive the gradient flow and design a scalar auxiliary variable scheme, which can significantly improve the computational efficiency compared with the traditional semi-implicit and semi-explicit scheme. Numerical experiments show that the proposed method can generate smooth segmentation curves, preserve segmentation details and obtain robust segmentation results of small objects. Compared to existing level set methods, this model is state-of-the-art in both accuracy and efficiency.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"30 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531054","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}

{"title":"Computing the Minimal Perimeter Polygon for Sets of Rectangular Tiles based on Visibility Cones","authors":"Petra Wiederhold","doi":"10.1007/s10851-024-01203-z","DOIUrl":"https://doi.org/10.1007/s10851-024-01203-z","url":null,"abstract":"<p>To study convexity properties of digital planar objects, the minimum perimeter polygon (MPP) was defined in the 1970 s in articles by Sklansky, Chazin, Hansen, Kibler, and Kim, where pixels were identified with polygonal tiles in mosaics, and two algorithms (1972, 1976) were proposed to determine the MPP vertices. These algorithms are based on constructing and iteratively restricting visibility cones, the MPP vertices result as special vertices of the tiles. The present paper proposes a novel MPP algorithm for objects given as regular complexes in rectangular mosaics, which are edge-adjacency-connected sets of tiles that have neither end tiles nor holes and whose boundaries not necessarily are simple. The new algorithm takes as input the canonical boundary path, we also propose a boundary tracing algorithm to obtain this path. We review the two classic MPP algorithms for rectangular tiles and a simplified adaptation for square tiles that is recommended in widely used modern textbooks on digital image analysis (2018, 2020) to produce approximations of simple digital 4-contours. We show that all these algorithms fail and that their mathematical basis is flawed, we correct the errors to develop the new MPP algorithm. Our MPP algorithm is illustrated using examples and its correctness is proved. Under our assumptions, the MPP coincides with the relative convex hull of a set <i>A</i> with respect to a polygon <span>(Bsupset A)</span>, where <i>A</i> is not necessarily a polygon, not even connected.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509057","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}

{"title":"Discrete Approximations of Gaussian Smoothing and Gaussian Derivatives","authors":"Tony Lindeberg","doi":"10.1007/s10851-024-01196-9","DOIUrl":"https://doi.org/10.1007/s10851-024-01196-9","url":null,"abstract":"<p>This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and the Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways of discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region, to aim at suppressing some of the severe artefacts of sampled Gaussian kernels and sampled Gaussian derivatives at very fine scales, or (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data.</p><p>We study the properties of these three main discretization methods both theoretically and experimentally and characterize their performance by quantitative measures, including the results they give rise to with respect to the task of scale selection, investigated for four different use cases, and with emphasis on the behaviour at fine scales. The results show that the sampled Gaussian kernels and the sampled Gaussian derivatives as well as the integrated Gaussian kernels and the integrated Gaussian derivatives perform very poorly at very fine scales. At very fine scales, the discrete analogue of the Gaussian kernel with its corresponding discrete derivative approximations performs substantially better. The sampled Gaussian kernel and the sampled Gaussian derivatives do, on the other hand, lead to numerically very good approximations of the corresponding continuous results, when the scale parameter is sufficiently large, in most of the experiments presented in the paper, when the scale parameter is greater than a value of about 1, in units of the grid spacing. Below a standard deviation of about 0.75, the derivative estimates obtained from convolutions with the sampled Gaussian derivative kernels are, however, not numerically accurate or consistent, while the results obtained from the discrete analogue of the Gaussian kernel, with its associated central difference operators applied to the spatially smoothed image data, are then a much better choice.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"45 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500559","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}

{"title":"Generalised Diffusion Probabilistic Scale-Spaces","authors":"Pascal Peter","doi":"10.1007/s10851-024-01202-0","DOIUrl":"https://doi.org/10.1007/s10851-024-01202-0","url":null,"abstract":"<p>Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results in a tractable probability distribution. A corresponding learned reverse process generates images and can be conditioned on side information, which leads to a wide variety of practical applications. Most of the research focus currently lies on practice-oriented extensions. In contrast, the theoretical background remains largely unexplored, in particular the relations to drift-diffusion. In order to shed light on these connections to classical image filtering, we propose a generalised scale-space theory for diffusion probabilistic models. Moreover, we show conceptual and empirical connections to diffusion and osmosis filters.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"15 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509058","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}

{"title":"A Multi-spectral Geometric Approach for Shape Analysis","authors":"David Bensaïd, Ron Kimmel","doi":"10.1007/s10851-024-01192-z","DOIUrl":"https://doi.org/10.1007/s10851-024-01192-z","url":null,"abstract":"<p>A solid object in <span>(mathbb {R}^3)</span> can be represented by its smooth boundary surface which can be equipped with an intrinsic metric to form a 2-Riemannian manifold. In this paper, we analyze such surfaces using multiple metrics that give birth to multi-spectra by which a given surface can be characterized. Their relative sensitivity to different types of local structures allows each metric to provide a distinct perspective of the shape. Extensive experiments show that the proposed multi-metric approach significantly improves important tasks in geometry processing such as shape retrieval and find similarity and corresponding parts of non-rigid objects.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"9 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509059","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}

{"title":"Convergent Plug-and-Play with Proximal Denoiser and Unconstrained Regularization Parameter","authors":"Samuel Hurault, Antonin Chambolle, Arthur Leclaire, Nicolas Papadakis","doi":"10.1007/s10851-024-01195-w","DOIUrl":"https://doi.org/10.1007/s10851-024-01195-w","url":null,"abstract":"<p>In this work, we present new proofs of convergence for plug-and-play (PnP) algorithms. PnP methods are efficient iterative algorithms for solving image inverse problems where regularization is performed by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD) or Douglas–Rachford splitting (DRS). Recent research has explored convergence by incorporating a denoiser that writes exactly as a proximal operator. However, in these works, the corresponding PnP algorithm has the drawback to be necessarily run with stepsize equal to 1. The stepsize condition for nonconvex convergence of the proximal algorithm in use then translates to restrictive conditions on the regularization parameter of the inverse problem. This can severely degrade the restoration capacity of the algorithm. In this paper, we present two remedies for this limitation. First, we provide a novel convergence proof for PnP-DRS that does not impose any restriction on the regularization parameter. Second, we examine a relaxed version of the PGD algorithm that converges across a broader range of regularization parameters. Our experimental study, conducted on deblurring and super-resolution experiments, demonstrate that these two solutions both enhance the accuracy of image restoration.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"52 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509060","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}

{"title":"Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems","authors":"Nathan Buskulic, Jalal Fadili, Yvain Quéau","doi":"10.1007/s10851-024-01191-0","DOIUrl":"https://doi.org/10.1007/s10851-024-01191-0","url":null,"abstract":"<p>Neural networks have become a prominent approach to solve inverse problems in recent years. While a plethora of such methods was developed to solve inverse problems empirically, we are still lacking clear theoretical guarantees for these methods. On the other hand, many works proved convergence to optimal solutions of neural networks in a more general setting using overparametrization as a way to control the Neural Tangent Kernel. In this work we investigate how to bridge these two worlds and we provide deterministic convergence and recovery guarantees for the class of unsupervised feedforward multilayer neural networks trained to solve inverse problems. We also derive overparametrization bounds under which a two-layer Deep Inverse Prior network with smooth activation function will benefit from our guarantees.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"27 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253532","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}

{"title":"A Stochastic-Geometrical Framework for Object Pose Estimation Based on Mixture Models Avoiding the Correspondence Problem","authors":"Wolfgang Hoegele","doi":"10.1007/s10851-024-01200-2","DOIUrl":"https://doi.org/10.1007/s10851-024-01200-2","url":null,"abstract":"<p>Pose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic-geometrical modeling framework for object pose estimation based on observing multiple feature points. This framework utilizes mixture models for feature point densities in object space and for interpreting real measurements. Advantages are the avoidance to resolve individual feature correspondences and to incorporate correct stochastic dependencies in multi-view applications. First, the general modeling framework is presented, second, a general algorithm for pose estimation is derived, and third, two example models (camera and lateration setup) are presented. Numerical experiments show the effectiveness of this modeling and general algorithm by presenting four simulation scenarios for three observation systems, including the dependence on measurement resolution, object deformations and measurement noise. Probabilistic modeling utilizing mixture models shows the potential for accurate and robust pose estimations while avoiding the correspondence problem.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"2013 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253386","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}