Journal of Mathematical Imaging and Vision最新文献

A solid object in (mathbb {R}^3) 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.

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.

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.

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.

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 a contrario 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 (AUROC), as well as the area under the per-region-overlap curve (AUPRO). 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 AUROC of 98.74%. Code and trained models are available at https://github.com/mtailanian/uflow.

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 least squares and the gradient weighted algebraic fits. 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.

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.

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.