MULDE: Multiscale Log-Density Estimation via Denoising Score Matching for Video Anomaly Detection

We propose a novel approach to video anomaly detection: we treat feature vectors extracted from videos as realizations of a random variable with a fixed distribution and model this distribution with a neural network. This lets us estimate the likelihood of test videos and detect video anomalies by thresholding the likelihood estimates. We train our video anomaly detector using a modification of denoising score matching, a method that injects training data with noise to facilitate modeling its distribution. To eliminate hyperparameter selection, we model the distribution of noisy video features across a range of noise levels and introduce a regularizer that tends to align the models for different levels of noise. At test time, we combine anomaly indications at multiple noise scales with a Gaussian mixture model. Running our video anomaly detector induces minimal delays as inference requires merely extracting the features and forward-propagating them through a shallow neural network and a Gaussian mixture model. Our experiments on five popular video anomaly detection benchmarks demonstrate state-of-the-art performance, both in the object-centric and in the frame-centric setup.

Majorization-Minimization for sparse SVMs

Several decades ago, Support Vector Machines (SVMs) were introduced for performing binary classification tasks, under a supervised framework. Nowadays, they often outperform other supervised methods and remain one of the most popular approaches in the machine learning arena. In this work, we investigate the training of SVMs through a smooth sparse-promoting-regularized squared hinge loss minimization. This choice paves the way to the application of quick training methods built on majorization-minimization approaches, benefiting from the Lipschitz differentiabililty of the loss function. Moreover, the proposed approach allows us to handle sparsity-preserving regularizers promoting the selection of the most significant features, so enhancing the performance. Numerical tests and comparisons conducted on three different datasets demonstrate the good performance of the proposed methodology in terms of qualitative metrics (accuracy, precision, recall, and F 1 score) as well as computational cost.

Score-Based Generative Models for Medical Image Segmentation using Signed Distance Functions

Medical image segmentation is a crucial task that relies on the ability to accurately identify and isolate regions of interest in images. Thereby, generative approaches allow to capture the statistical properties of segmentation masks that are dependent on the respective medical images. In this work we propose a conditional score-based generative modeling framework that leverages the signed distance function to represent an implicit and smoother distribution of segmentation masks. The score function of the conditional distribution of segmentation masks is learned in a conditional denoising process, which can be effectively used to generate accurate segmentation masks. Moreover, uncertainty maps can be generated, which can aid in further analysis and thus enhance the predictive robustness. We qualitatively and quantitatively illustrate competitive performance of the proposed method on a public nuclei and gland segmentation data set, highlighting its potential utility in medical image segmentation applications.

Posterior-Variance-Based Error Quantification for Inverse Problems in Imaging

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, also a novel primal-dual Langevin algorithm for sampling from non-smooth distributions is introduced in this work.

Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.