Graz University of Technology
Abstract:We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed inexactly. To estimate the accuracy of the computed hypergradient, we derive an a-posteriori error bound, which provides guides for setting the tolerance for the lower-level problem, as well as the piggyback algorithm. To efficiently solve the upper-level optimization, we also propose an adaptive method for choosing a suitable step-size. To illustrate the proposed method, we consider a few learned regularizer problems, such as training an input-convex neural network.
Abstract:Medical image segmentation is a crucial task that relies on the ability to accurately identify and isolate regions of interest in medical images. Thereby, generative approaches allow to capture the statistical properties of segmentation masks that are dependent on the respective structures. In this work we propose FlowSDF, an image-guided conditional flow matching framework to represent the signed distance function (SDF) leading to an implicit distribution of segmentation masks. The advantage of leveraging the SDF is a more natural distortion when compared to that of binary masks. By learning a vector field that is directly related to the probability path of a conditional distribution of SDFs, we can accurately sample from the distribution of segmentation masks, allowing for the evaluation of statistical quantities. Thus, this probabilistic representation allows for the generation of uncertainty maps represented by the variance, which can aid in further analysis and 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 utility in medical image segmentation applications.
Abstract:Concerns for the privacy of individuals captured in public imagery have led to privacy-preserving action recognition. Existing approaches often suffer from issues arising through obfuscation being applied globally and a lack of interpretability. Global obfuscation hides privacy sensitive regions, but also contextual regions important for action recognition. Lack of interpretability erodes trust in these new technologies. We highlight the limitations of current paradigms and propose a solution: Human selected privacy templates that yield interpretability by design, an obfuscation scheme that selectively hides attributes and also induces temporal consistency, which is important in action recognition. Our approach is architecture agnostic and directly modifies input imagery, while existing approaches generally require architecture training. Our approach offers more flexibility, as no retraining is required, and outperforms alternatives on three widely used datasets.
Abstract:We present a novel diffusion-based approach to generate synthetic histopathological Whole Slide Images (WSIs) at an unprecedented gigapixel scale. Synthetic WSIs have many potential applications: They can augment training datasets to enhance the performance of many computational pathology applications. They allow the creation of synthesized copies of datasets that can be shared without violating privacy regulations. Or they can facilitate learning representations of WSIs without requiring data annotations. Despite this variety of applications, no existing deep-learning-based method generates WSIs at their typically high resolutions. Mainly due to the high computational complexity. Therefore, we propose a novel coarse-to-fine sampling scheme to tackle image generation of high-resolution WSIs. In this scheme, we increase the resolution of an initial low-resolution image to a high-resolution WSI. Particularly, a diffusion model sequentially adds fine details to images and increases their resolution. In our experiments, we train our method with WSIs from the TCGA-BRCA dataset. Additionally to quantitative evaluations, we also performed a user study with pathologists. The study results suggest that our generated WSIs resemble the structure of real WSIs.
Abstract:In this work we tackle the problem of estimating the density $ f_X $ of a random variable $ X $ by successive smoothing, such that the smoothed random variable $ Y $ fulfills the diffusion partial differential equation $ (\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0 $ with initial condition $ f_Y(\,\cdot\,, 0) = f_X $. We propose a product-of-experts-type model utilizing Gaussian mixture experts and study configurations that admit an analytic expression for $ f_Y (\,\cdot\,, t) $. In particular, with a focus on image processing, we derive conditions for models acting on filter-, wavelet-, and shearlet responses. Our construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show numerical results for image denoising where our models are competitive while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our models can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise.
Abstract:We examine the assumption that the hidden-state vectors of recurrent neural networks (RNNs) tend to form clusters of semantically similar vectors, which we dub the clustering hypothesis. While this hypothesis has been assumed in the analysis of RNNs in recent years, its validity has not been studied thoroughly on modern neural network architectures. We examine the clustering hypothesis in the context of RNNs that were trained to recognize regular languages. This enables us to draw on perfect ground-truth automata in our evaluation, against which we can compare the RNN's accuracy and the distribution of the hidden-state vectors. We start with examining the (piecewise linear) separability of an RNN's hidden-state vectors into semantically different classes. We continue the analysis by computing clusters over the hidden-state vector space with multiple state-of-the-art unsupervised clustering approaches. We formally analyze the accuracy of computed clustering functions and the validity of the clustering hypothesis by determining whether clusters group semantically similar vectors to the same state in the ground-truth model. Our evaluation supports the validity of the clustering hypothesis in the majority of examined cases. We observed that the hidden-state vectors of well-trained RNNs are separable, and that the unsupervised clustering techniques succeed in finding clusters of similar state vectors.
Abstract:We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte Carlo (MCMC) methods derived from discretizations of the overdamped Langevin diffusions, which are commonly known as Langevin Monte Carlo algorithms. Furthermore, we are also interested in two nonsmooth cases for which a large class of proximal MCMC methods have been developed: (i) a nonsmooth prior is considered with a Gaussian mixture likelihood; (ii) a Laplacian mixture distribution. Such nonsmooth and non-log-concave sampling tasks arise from a wide range of applications to Bayesian inference and imaging inverse problems such as image deconvolution. We perform numerical simulations to compare the performance of most commonly used Langevin Monte Carlo algorithms.
Abstract: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.
Abstract:In this paper, we propose a unified framework of denoising score-based models in the context of graduated non-convex energy minimization. We show that for sufficiently large noise variance, the associated negative log density -- the energy -- becomes convex. Consequently, denoising score-based models essentially follow a graduated non-convexity heuristic. We apply this framework to learning generalized Fields of Experts image priors that approximate the joint density of noisy images and their associated variances. These priors can be easily incorporated into existing optimization algorithms for solving inverse problems and naturally implement a fast and robust graduated non-convexity mechanism.
Abstract:In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) = f_X$. With a focus on image processing, we propose a product/fields of experts model with Gaussian mixture experts that admits an analytic expression for $f_Y (\,\cdot\,, t)$ under an orthogonality constraint on the filters. This construction naturally allows the model to be trained simultaneously over the entire diffusion horizon using empirical Bayes. We show preliminary results on image denoising where our model leads to competitive results while being tractable, interpretable, and having only a small number of learnable parameters. As a byproduct, our model can be used for reliable noise estimation, allowing blind denoising of images corrupted by heteroscedastic noise.