Journal of Mathematical Imaging and Vision最新文献

{"title":"About the Incorporation of Topological Prescriptions in CNNs for Medical Image Semantic Segmentation","authors":"Zoé Lambert, Carole Le Guyader","doi":"10.1007/s10851-024-01172-3","DOIUrl":"https://doi.org/10.1007/s10851-024-01172-3","url":null,"abstract":"<p>Incorporating prior knowledge into a segmentation task, whether it be under the form of geometrical constraints (area/volume penalisation, convexity enforcement, etc.) or of topological constraints (to preserve the contextual relations between objects, to monitor the number of connected components), proves to increase accuracy in medical image segmentation. In particular, it allows to compensate for the issue of weak boundary definition, of imbalanced classes, and to be more in line with anatomical consistency even though the data do not explicitly exhibit those features. This observation underpins the introduced contribution that aims, in a hybrid setting, to leverage the best of both worlds that variational methods and supervised deep learning approaches embody: (a) versatility and adaptability in the mathematical formulation of the problem to encode geometrical/topological constraints, (b) interpretability of the results for the former formalism, while (c) more efficient and effective processing models, (d) ability to become more proficient at learning intricate features and executing more computationally intensive tasks, for the latter one. To be more precise, a unified variational framework involving topological prescriptions in the training of convolutional neural networks through the design of a suitable penalty in the loss function is provided. These topological constraints are implicitly enforced by viewing the segmentation procedure as a registration task between the processed image and its associated ground truth under incompressibility conditions, thus making them homeomorphic. A very preliminary version (Lambert et al., in Calatroni, Donatelli, Morigi, Prato, Santacesaria (eds) Scale space and variational methods in computer vision, Springer, Berlin, 2023, pp. 363–375) of this work has been published in the proceedings of the Ninth International Conference on Scale Space and Variational Methods in Computer Vision, 2023. It contained neither all the theoretical results, nor the detailed related proofs, nor did it include the numerical analysis of the designed algorithm. Besides these more involved developments in the present version, a more complete, systematic and thorough analysis of the numerical experiments is also conducted, addressing several issues: (i) limited amount of labelled data in the training phase, (ii) low contrast or imbalanced classes exhibited by the data, and (iii) explainability of the results.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"1 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923724","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":"Geodesic Tracking via New Data-Driven Connections of Cartan Type for Vascular Tree Tracking","authors":"Nicky J. van den Berg, Bart M. N. Smets, Gautam Pai, Jean-Marie Mirebeau, Remco Duits","doi":"10.1007/s10851-023-01170-x","DOIUrl":"https://doi.org/10.1007/s10851-023-01170-x","url":null,"abstract":"<p>We introduce a data-driven version of the plus Cartan connection on the homogeneous space <span>({mathbb {M}}_2)</span> of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and parallel momentum, respectively) with respect to this new data-driven connection and corresponding Riemannian manifold. Then we use these shortest curves for geodesic tracking of complex vasculature in multi-orientation image representations defined on <span>({mathbb {M}}_{2})</span>. The data-driven Cartan connection characterizes the Hamiltonian flow of all geodesics. It also allows for improved adaptation to curvature and misalignment of the (lifted) vessel structure that we track via globally optimal geodesics. We compute these geodesics numerically via steepest descent on distance maps on <span>({mathbb {M}}_2)</span> that we compute by a new modified anisotropic fast-marching method.Our experiments range from tracking single blood vessels with fixed endpoints to tracking complete vascular trees in retinal images. Single vessel tracking is performed in a single run in the multi-orientation image representation, where we project the resulting geodesics back onto the underlying image. The complete vascular tree tracking requires only two runs and avoids prior segmentation, placement of extra anchor points, and dynamic switching between geodesic models. Altogether we provide a geodesic tracking method using a single, flexible, transparent, data-driven geodesic model providing globally optimal curves which correctly follow highly complex vascular structures in retinal images. All experiments in this article can be reproduced via documented <i>Mathematica</i> notebooks available at van den Berg (Data-driven left-invariant tracking in <i>Mathematica</i>, 2022).</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"21 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139461111","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":"Dyadic Partition-Based Training Schemes for TV/TGV Denoising.","authors":"Elisa Davoli, Rita Ferreira, Irene Fonseca, José A Iglesias","doi":"10.1007/s10851-024-01213-x","DOIUrl":"10.1007/s10851-024-01213-x","url":null,"abstract":"<p><p>Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these automatically through multilevel approaches, for example by optimizing performance on noisy/clean image pairs. In this work, we consider such methods with space-dependent parameters which are piecewise constant on dyadic grids, with the grid itself being part of the minimization. We prove existence of minimizers for fixed discontinuous parameters under mild assumptions on the data, which lead to existence of finite optimal partitions. We further establish that these assumptions are equivalent to the commonly used box constraints on the parameters. On the numerical side, we consider a simple subdivision scheme for optimal partitions built on top of any other bilevel optimization method for scalar parameters, and demonstrate its improved performance on some representative test images when compared with constant optimized parameters.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"66 6","pages":"1070-1108"},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11554743/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142621969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Properties of Pyramid-Transform-Based Resolution Conversion and Its Applications","authors":"Kento Hosoya, Kouki Nozawa, Hayato Itoh, Atsushi Imiya","doi":"10.1007/s10851-023-01166-7","DOIUrl":"https://doi.org/10.1007/s10851-023-01166-7","url":null,"abstract":"<p>In this paper, we aim to clarify the statistical and geometric properties of linear resolution conversion for registration between different resolutions observed using the same modality. The pyramid transform is achieved by smoothing and downsampling. The dual operation of the pyramid transform is achieved by linear smoothing after upsampling. The rational-order pyramid transform is decomposed into upsampling for smoothing and the conventional integer-order pyramid transform. By controlling the ratio between upsampling for smoothing and downsampling in the pyramid transform, the rational-order pyramid transform is computed. The tensor expression of the multiway pyramid transform implies that the transform yields orthogonal base systems for any ratio of the rational pyramid transform. The numerical evaluation of the transform shows that the rational-order pyramid transform preserves the normalised distribution of greyscale in images.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"204 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139035005","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 Two Linearization-Based Methods for 3-D EIT Reconstructions on a Simulated Chest","authors":"Kwancheol Shin, Sanwar Ahmad, Talles Batista Rattis Santos, Nilton Barbosa da Rosa Junior, Jennifer L. Mueller","doi":"10.1007/s10851-023-01169-4","DOIUrl":"https://doi.org/10.1007/s10851-023-01169-4","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"6 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138947475","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":"Non-monotone Boosted DC and Caputo Fractional Tailored Finite Point Algorithm for Rician Denoising and Deblurring","authors":"Kexin Sun, Youcai Xu, Minfu Feng","doi":"10.1007/s10851-023-01168-5","DOIUrl":"https://doi.org/10.1007/s10851-023-01168-5","url":null,"abstract":"<p>Since MRI is often corrupted by Rician noise, in medical image processing, Rician denoising and deblurring is an important research. In this work, considering the validity of the non-convex log term in the Rician denoising and deblurring model estimated by the maximum a posteriori (MAP) and total variation, we apply nmBDCA to deal with the model. A non-monotonic line search applied in nmBDCA can achieve possible growth of objective function values controlled by parameters. After that, the obtained convex problem is solved separately by alternating direction method of multipliers (ADMM). For <span>(u-)</span>subproblem in ADMM scheme, Caputo fractional derivative and tailored finite point method are applied to denoising, which retain more texture details and suppress the staircase effect. We also demonstrate the convergence of the model and perform the stability analysis on the numerical scheme. Numerical results show that our method can well improve the quality of image restoration.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"194 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138680504","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":"Geometry Parameter Estimation for Sparse X-Ray Log Imaging","authors":"Angelina Senchukova, Jarkko Suuronen, Jere Heikkinen, Lassi Roininen","doi":"10.1007/s10851-023-01167-6","DOIUrl":"https://doi.org/10.1007/s10851-023-01167-6","url":null,"abstract":"<p>We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow identification of the location of the source–detector pair, which creates the issue of unknown geometry. This work considers an approach for geometry estimation based on the calibration object. We parametrise the geometry using a set of 5 parameters. To estimate the geometry parameters, we calculate the maximum cross-correlation between a known-sized calibration object image and its filtered backprojection reconstruction and use differential evolution as an optimiser. The approach allows estimating geometry parameters from full-angle measurements as well as from sparse measurements. We show numerically that different sets of parameters can be used for artefact-free reconstruction. We deploy Bayesian inversion with first-order isotropic Cauchy difference priors for reconstruction of synthetic and real sawmill data with a very low number of measurements.\u0000</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"54 9","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505222","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":"Regularising Inverse Problems with Generative Machine Learning Models","authors":"Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt","doi":"10.1007/s10851-023-01162-x","DOIUrl":"https://doi.org/10.1007/s10851-023-01162-x","url":null,"abstract":"Abstract Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this survey paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family generative regularisers . The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess generative models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that restricting solutions of the inverse problem to lie exactly in the range of a generative model can give good results but that allowing small deviations from the range of the generator produces more consistent results. Finally, we discuss future directions and open problems in the field.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135043901","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":"QFPJFMs: Quaternion Fractional-Order Pseudo-Jacobi–Fourier Moments","authors":"Xiangyang Wang, Maoying Deng, Panpan Niu, Hongying Yang","doi":"10.1007/s10851-023-01165-8","DOIUrl":"https://doi.org/10.1007/s10851-023-01165-8","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134975699","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":"On Strong Basins of Attractions for Non-convex Sparse Spike Estimation: Upper and Lower Bounds","authors":"Yann Traonmilin, Jean-François Aujol, Pierre-Jean Bénard, Arthur Leclaire","doi":"10.1007/s10851-023-01163-w","DOIUrl":"https://doi.org/10.1007/s10851-023-01163-w","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135386446","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}