Journal of Mathematical Imaging and Vision最新文献

{"title":"U-Flow: A U-Shaped Normalizing Flow for Anomaly Detection with Unsupervised Threshold","authors":"Matías Tailanian, Álvaro Pardo, Pablo Musé","doi":"10.1007/s10851-024-01193-y","DOIUrl":"https://doi.org/10.1007/s10851-024-01193-y","url":null,"abstract":"<p>In this work, we propose a one-class self-supervised method for anomaly segmentation in images that benefits from both a modern machine learning approach and a more classic statistical detection theory. The method consists of four phases. First, features are extracted using a multi-scale image transformer architecture. Then, these features are fed into a U-shaped normalizing flow (NF) that lays the theoretical foundations for the subsequent phases. The third phase computes a pixel-level anomaly map from the NF embedding, and the last phase performs a segmentation based on the <i>a contrario</i> framework. This multiple hypothesis testing strategy permits the derivation of robust unsupervised detection thresholds, which are crucial in real-world applications where an operational point is needed. The segmentation results are evaluated using the mean intersection over union metric, and for assessing the generated anomaly maps we report the area under the receiver operating characteristic curve (<i>AUROC</i>), as well as the area under the per-region-overlap curve (<i>AUPRO</i>). Extensive experimentation in various datasets shows that the proposed approach produces state-of-the-art results for all metrics and all datasets, ranking first in most MVTec-AD categories, with a mean pixel-level <i>AUROC</i> of 98.74%. Code and trained models are available at https://github.com/mtailanian/uflow.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"55 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192097","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":"Concentric Ellipse Fitting with Bias Correction and Specialized Geometric-Based Clustering Approach","authors":"Ali Al-Sharadqah, Giuliano Piga","doi":"10.1007/s10851-024-01197-8","DOIUrl":"https://doi.org/10.1007/s10851-024-01197-8","url":null,"abstract":"<p>This paper addresses the problem of fitting concentric ellipses under general assumptions. We study two methods of obtaining an estimator of the concentric ellipse parameters under this model, namely the <i>least squares</i> and the <i>gradient weighted algebraic fits</i>. We address some practical issues in obtaining these estimators. In this paper, we study the statistical properties of those estimators and we developed a refinement with the highest accuracy for each estimator. We also address a practical issue in concentric ellipse fitting, namely, that each observation in the data set should be recognized as belonging to only one of the concentric ellipses. Most well-known clustering methods, such as spectral clustering, fail for this problem. We propose a clustering approach that can effectively be used for the implementation of our model. Our theory has been validated through intensive numerical experiments on synthetic and real data.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"30 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149263","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":"Subspace Discrimination for Multiway Data","authors":"Hayato Itoh, Atsushi Imiya","doi":"10.1007/s10851-024-01188-9","DOIUrl":"https://doi.org/10.1007/s10851-024-01188-9","url":null,"abstract":"<p>Sampled values of volumetric data are expressed as third-order tensors. Object-oriented data analysis requires us to process and analyse volumetric data without embedding into a higher-dimensional vector space. Multiway forms of volumetric data require quantitative methods for the discrimination of multiway forms. Tensor principal component analysis is an extension of image singular value decomposition for planar images to higher-dimensional images. It is an efficient discrimination analysis method when used with the multilinear subspace method. The multilinear subspace method enables us to analyse spatial textures of volumetric images and spatiotemporal variations of volumetric video sequences. We define a distance metric for subspaces of multiway data arrays using the transport between two probability measures on the Stiefel manifold. Numerical examples show that the Stiefel distance is superior to the Euclidean distance, Grassmann distance and projection-based similarity for the longitudinal analysis of volumetric sequences.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"31 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149261","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":"Uncertainty Quantification for Scale-Space Blob Detection","authors":"Fabian Parzer, Clemens Kirisits, Otmar Scherzer","doi":"10.1007/s10851-024-01194-x","DOIUrl":"https://doi.org/10.1007/s10851-024-01194-x","url":null,"abstract":"<p>We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube. The resulting non-smooth optimization problem is challenging to solve, and we compare various numerical approaches for its solution and relate them to the literature on constrained total variation denoising. Finally, the proposed methodology is illustrated on numerical experiments for deconvolution and models related to astrophysics, where it is demonstrated that it allows to represent the uncertainty in the detected blobs in a precise and physically interpretable way.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"3 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149262","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 $$varGamma $$ -Convergence Result and An Off-the-Grid Charge Algorithm for Curve Reconstruction in Inverse Problems","authors":"Bastien Laville, Laure Blanc-Féraud, Gilles Aubert","doi":"10.1007/s10851-024-01190-1","DOIUrl":"https://doi.org/10.1007/s10851-024-01190-1","url":null,"abstract":"<p>Several numerical algorithms have been developed in the literature and employed for curves reconstruction. However, these techniques are developed within the discrete setting, namely the super-resolved image is defined on a finer grid than the observed images. Conversely, off-the-grid (or gridless) optimisation does not rely on a fine grid and offer a tractable theoretical and numerical framework. In this work, we present a gridless method accounting for the reconstruction of both open and closed curves, based on the latest theoretical development in off-the-grid curve reconstruction. This paper also shows <span>(varGamma )</span>-convergence results of the discretised surrogate functional towards the continuous energy we coined CROC.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"33 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939303","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":"Comparison of Different Parallel Transport Methods for the Study of Deformations in 3D Cardiac Data","authors":"Paolo Piras, Nicolas Guigui, Valerio Varano","doi":"10.1007/s10851-024-01186-x","DOIUrl":"https://doi.org/10.1007/s10851-024-01186-x","url":null,"abstract":"<p>Comparing the deformations of different beating hearts is a challenging operation. As in clinics the impaired condition is often recognized upon (local and global) deformation parameters, the particular nature of heart deformation during one beat can be compared among different individuals in the same ordination space more effectively if initial inter-individual form (shape + size) differences are filtered out. This is even more true if the shape of cardiac trajectory itself is under consideration. This need is satisfied by applying a geometric machinery named “parallel transport” in the field of differential geometry. In recent years several parallel transport methods have been applied to cardiological data acquired via echocardiography, CT scan or magnetic resonance. Concomitantly, some efforts were made for comparing different parallel transport algorithms applied to a variety of toy examples and real deformational data. Here we face the problem of comparing the heavily used LDDMM parallel transport with the recently proposed Riemannian “TPS space” in the context of the deformation of the right ventricle. Using local tensors diagnostics and global energy-based and shape distance-based parameters, we explored the maintenance of original deformations in transported data in four systo-diastolic deformations belonging to one healthy subject and three individuals affected by tetralogy of Fallot, atrial septal defect and pulmonary hypertension. We also do the same in a larger dataset relative to the left ventricle of 82 heathly subjects and 21 patients affected by hypertrophic cardiomyopathy. We also do the same in a larger dataset relative to the left ventricle of 82 heathly subjects and 21 patients affected by hypertrophic cardiomyopathy. In particular, we contrasted the TPS space with classic LDDMM and a modified LDDMM able to manage spherical differences. Our results point toward a neat superiority of TPS space over classic LDDMM. The modified LDDMM performs similarly as it maintains better the chosen diagnostics.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"145 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835658","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":"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":"<p>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 <i>p</i>-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 <i>p</i>-Laplacians, and we hence provide a novel axiomatic approach that extends previous definitions and can be specialized to satisfy such (or other) desired properties.</p>","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}

{"title":"A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially Varying Generalised Gaussian Models","authors":"Émilie Chouzenoux, Marie-Caroline Corbineau, Jean-Christophe Pesquet, Gabriele Scrivanti","doi":"10.1007/s10851-024-01184-z","DOIUrl":"https://doi.org/10.1007/s10851-024-01184-z","url":null,"abstract":"<p>The joint problem of reconstruction/feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly propose a novel non-smooth and non-convex variational formulation of the problem. For this purpose, we introduce a versatile generalised Gaussian prior whose parameters, including its exponent, are space-variant. Secondly, we design an alternating proximal-based optimisation algorithm that efficiently exploits the structure of the proposed non-convex objective function. We also analyse the convergence of this algorithm. As shown in numerical experiments conducted on joint deblurring/segmentation tasks, the proposed method provides high-quality results.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"19 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594632","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":"Finding Space-Time Boundaries with Deformable Hypersurfaces","authors":"Patrick M. Jensen, J. Andreas Bærentzen, Anders B. Dahl, Vedrana A. Dahl","doi":"10.1007/s10851-024-01185-y","DOIUrl":"https://doi.org/10.1007/s10851-024-01185-y","url":null,"abstract":"<p>Dynamic 3D imaging is increasingly used to study evolving objects. We address the problem of detecting and tracking simple objects that merge or split in time. Common solutions involve detecting topological changes. Instead, we solve the problem in 4D by exploiting the observation that if objects only merge or only split, they appear as a single component in 4D. This allows us to initiate a topologically simple 3D hypersurface and deform it to fit the surface of all objects at all times. This gives an extremely compact representation of the objects’ evolution. We test our method on artificial 4D images and compare it to other segmentation methods. We also apply our method to a 4D X-ray data set to quantify evolving topology. Our method performs comparably to existing methods with better resource use and improved robustness.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"32 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140594590","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":"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":"<p>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.</p>","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}