arXiv subjects

Carola-Bibiane Schönlieb

Publications and source records attributed to Carola-Bibiane Schönlieb.

At least 163 records · Page 9Linked to original sources

arXiv2023

Your diffusion model secretly knows the dimension of the data manifold

In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted version of the target distribution for varying levels of corruption. We prove that, if the data concentrates around a manifold embedded in the high-dimensional ambient space, then as the level of corruption decreases, the score function points towards the manifold, as this direction becomes the direction of maximal likelihood increase. Therefore, for small levels of corruption, the diffusion model provides us with access to an approximation of the normal bundle of the data manifold. This allows us to estimate the dimension of the tangent space, thus, the intrinsic dimension of the data manifold. To the best of our knowledge, our method is the first estimator of the data manifold dimension based on diffusion models and it outperforms well established statistical estimators in controlled experiments on both Euclidean and image data.

cs.LG↗

arXiv2023

Variational Diffusion Auto-encoder: Latent Space Extraction from Pre-trained Diffusion Models

As a widely recognized approach to deep generative modeling, Variational Auto-Encoders (VAEs) still face challenges with the quality of generated images, often presenting noticeable blurriness. This issue stems from the unrealistic assumption that approximates the conditional data distribution, $p(\textbf{x} | \textbf{z})$, as an isotropic Gaussian. In this paper, we propose a novel solution to address these issues. We illustrate how one can extract a latent space from a pre-existing diffusion model by optimizing an encoder to maximize the marginal data log-likelihood. Furthermore, we demonstrate that a decoder can be analytically derived post encoder-training, employing the Bayes rule for scores. This leads to a VAE-esque deep latent variable model, which discards the need for Gaussian assumptions on $p(\textbf{x} | \textbf{z})$ or the training of a separate decoder network. Our method, which capitalizes on the strengths of pre-trained diffusion models and equips them with latent spaces, results in a significant enhancement to the performance of VAEs.

cs.LG↗

arXiv2023

Tree species classification from hyperspectral data using graph-regularized neural networks

We propose a novel graph-regularized neural network (GRNN) algorithm for tree species classification. The proposed algorithm encompasses superpixel-based segmentation for graph construction, a pixel-wise neural network classifier, and the label propagation technique to generate an accurate and realistic (emulating tree crowns) classification map on a sparsely annotated data set. GRNN outperforms several state-of-the-art techniques not only for the standard Indian Pines HSI but also achieves a high classification accuracy (approx. 92%) on a new HSI data set collected over the heterogeneous forests of French Guiana (FG) when less than 1% of the pixels are labeled. We further show that GRNN is competitive with the state-of-the-art semi-supervised methods and exhibits a small deviation in accuracy for different numbers of training samples and over repeated trials with randomly sampled labeled pixels for training.

cs.CV↗

arXiv2023

Class-Guided Image-to-Image Diffusion: Cell Painting from Brightfield Images with Class Labels

Image-to-image reconstruction problems with free or inexpensive metadata in the form of class labels appear often in biological and medical image domains. Existing text-guided or style-transfer image-to-image approaches do not translate to datasets where additional information is provided as discrete classes. We introduce and implement a model which combines image-to-image and class-guided denoising diffusion probabilistic models. We train our model on a real-world dataset of microscopy images used for drug discovery, with and without incorporating metadata labels. By exploring the properties of image-to-image diffusion with relevant labels, we show that class-guided image-to-image diffusion can improve the meaningful content of the reconstructed images and outperform the unguided model in useful downstream tasks.

cs.CV↗

arXiv2023

SCOTCH and SODA: A Transformer Video Shadow Detection Framework

Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliu-cambridge.github.io/scotch_and_soda/

cs.CV↗

arXiv2023

CoNIC Challenge: Pushing the Frontiers of Nuclear Detection, Segmentation, Classification and Counting

Nuclear detection, segmentation and morphometric profiling are essential in helping us further understand the relationship between histology and patient outcome. To drive innovation in this area, we setup a community-wide challenge using the largest available dataset of its kind to assess nuclear segmentation and cellular composition. Our challenge, named CoNIC, stimulated the development of reproducible algorithms for cellular recognition with real-time result inspection on public leaderboards. We conducted an extensive post-challenge analysis based on the top-performing models using 1,658 whole-slide images of colon tissue. With around 700 million detected nuclei per model, associated features were used for dysplasia grading and survival analysis, where we demonstrated that the challenge's improvement over the previous state-of-the-art led to significant boosts in downstream performance. Our findings also suggest that eosinophils and neutrophils play an important role in the tumour microevironment. We release challenge models and WSI-level results to foster the development of further methods for biomarker discovery.

cs.CV↗

arXiv2023

Hidden Knowledge: Mathematical Methods for the Extraction of the Fingerprint of Medieval Paper from Digital Images

Medieval paper, a handmade product, is made with a mould which leaves an indelible imprint on the sheet of paper. This imprint includes chain lines, laid lines and watermarks which are often visible on the sheet. Extracting these features allows the identification of paper stock and gives information about chronology, localisation and movement of books and people. Most computational work for feature extraction of paper analysis has so far focused on radiography or transmitted light images. While these imaging methods provide clear visualisation for the features of interest, they are expensive and time consuming in their acquisition and not feasible for smaller institutions. However, reflected light images of medieval paper manuscripts are abundant and possibly cheaper in their acquisition. In this paper, we propose algorithms to detect and extract the laid and chain lines from reflected light images. We tackle the main drawback of reflected light images, that is, the low contrast attenuation of lines and intensity jumps due to noise and degradation, by employing the spectral total variation decomposition and develop methods for subsequent line extraction. Our results clearly demonstrate the feasibility of using reflected light images in paper analysis. This work enables the feature extraction for paper manuscripts that have otherwise not been analysed due to a lack of appropriate images. We also open the door for paper stock identification at scale.

cs.CV↗

arXiv2023

Data-Driven Mirror Descent with Input-Convex Neural Networks

Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in terms of convergence speed, especially for convex problems. Many existing data-driven optimization methods are based on parameterizing the update step and learning the optimal parameters (typically scalars) from the available data. We propose a novel functional parameterization approach for learned convex optimization solvers based on the classical mirror descent (MD) algorithm. Specifically, we seek to learn the optimal Bregman distance in MD by modeling the underlying convex function using an input-convex neural network (ICNN). The parameters of the ICNN are learned by minimizing the target objective function evaluated at the MD iterate after a predetermined number of iterations. The inverse of the mirror map is modeled approximately using another neural network, as the exact inverse is intractable to compute. We derive convergence rate bounds for the proposed learned mirror descent (LMD) approach with an approximate inverse mirror map and perform extensive numerical evaluation on various convex problems such as image inpainting, denoising, learning a two-class support vector machine (SVM) classifier and a multi-class linear classifier on fixed features.

math.OC↗

arXiv2023

Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI

4D flow MRI is a non-invasive imaging method that can measure blood flow velocities over time. However, the velocity fields detected by this technique have limitations due to low resolution and measurement noise. Coordinate-based neural networks have been researched to improve accuracy, with SIRENs being suitable for super-resolution tasks. Our study investigates SIRENs for time-varying 3-directional velocity fields measured in the aorta by 4D flow MRI, achieving denoising and super-resolution. We trained our method on voxel coordinates and benchmarked our approach using synthetic measurements and a real 4D flow MRI scan. Our optimized SIREN architecture outperformed state-of-the-art techniques, producing denoised and super-resolved velocity fields from clinical data. Our approach is quick to execute and straightforward to implement for novel cases, achieving 4D super-resolution.

eess.IV↗

arXiv2023

Why Deep Surgical Models Fail?: Revisiting Surgical Action Triplet Recognition through the Lens of Robustness

Surgical action triplet recognition provides a better understanding of the surgical scene. This task is of high relevance as it provides the surgeon with context-aware support and safety. The current go-to strategy for improving performance is the development of new network mechanisms. However, the performance of current state-of-the-art techniques is substantially lower than other surgical tasks. Why is this happening? This is the question that we address in this work. We present the first study to understand the failure of existing deep learning models through the lens of robustness and explainability. Firstly, we study current existing models under weak and strong $δ-$perturbations via an adversarial optimisation scheme. We then analyse the failure modes via feature based explanations. Our study reveals that the key to improving performance and increasing reliability is in the core and spurious attributes. Our work opens the door to more trustworthy and reliable deep learning models in surgical data science.

cs.CV↗

arXiv2023

Can Physics-Informed Neural Networks beat the Finite Element Method?

Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for instance, is a usual standard methodology to do so. The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a large range of partial differential equations. So far, physics-informed neural networks and the finite element method have mainly been studied in isolation of each other. In this work, we compare the methodologies in a systematic computational study. Indeed, we employ both methods to numerically solve various linear and nonlinear partial differential equations: Poisson in 1D, 2D, and 3D, Allen-Cahn in 1D, semilinear Schrödinger in 1D and 2D. We then compare computational costs and approximation accuracies. In terms of solution time and accuracy, physics-informed neural networks have not been able to outperform the finite element method in our study. In some experiments, they were faster at evaluating the solved PDE.

math.NA↗

arXiv2023

Continuous U-Net: Faster, Greater and Noiseless

Image segmentation is a fundamental task in image analysis and clinical practice. The current state-of-the-art techniques are based on U-shape type encoder-decoder networks with skip connections, called U-Net. Despite the powerful performance reported by existing U-Net type networks, they suffer from several major limitations. Issues include the hard coding of the receptive field size, compromising the performance and computational cost, as well as the fact that they do not account for inherent noise in the data. They have problems associated with discrete layers, and do not offer any theoretical underpinning. In this work we introduce continuous U-Net, a novel family of networks for image segmentation. Firstly, continuous U-Net is a continuous deep neural network that introduces new dynamic blocks modelled by second order ordinary differential equations. Secondly, we provide theoretical guarantees for our network demonstrating faster convergence, higher robustness and less sensitivity to noise. Thirdly, we derive qualitative measures to tailor-made segmentation tasks. We demonstrate, through extensive numerical and visual results, that our model outperforms existing U-Net blocks for several medical image segmentation benchmarking datasets.

cs.CV↗

arXiv2023

Regularising orientation estimation in Cryo-EM 3D map refinement through measure-based lifting over Riemannian manifolds

Motivated by the trade-off between noise-robustness and data-consistency for joint 3D map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularising and approximating the global minimiser of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimiser we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimiser. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimisation problems have to be solved and where regularisation is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularising effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimisation would.

math.OC↗

arXiv2023

Joint reconstruction-segmentation on graphs

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation, using each to guide the other. However, this work has so far employed relatively simple segmentation methods, such as the Chan--Vese algorithm. In this paper, we present a method for joint reconstruction-segmentation using graph-based segmentation methods, which have been seeing increasing recent interest. Complications arise due to the large size of the matrices involved, and we show how these complications can be managed. We then analyse the convergence properties of our scheme. Finally, we apply this scheme to distorted versions of ``two cows'' images familiar from previous graph-based segmentation literature, first to a highly noised version and second to a blurred version, achieving highly accurate segmentations in both cases. We compare these results to those obtained by sequential reconstruction-segmentation approaches, finding that our method competes with, or even outperforms, those approaches in terms of reconstruction and segmentation accuracy.

cs.CV↗

arXiv2022

Spectral decomposition of atomic structures in heterogeneous cryo-EM

We consider the problem of recovering the three-dimensional atomic structure of a flexible macromolecule from a heterogeneous cryo-EM dataset. The dataset contains noisy tomographic projections of the electrostatic potential of the macromolecule, taken from different viewing directions, and in the heterogeneous case, each image corresponds to a different conformation of the macromolecule. Under the assumption that the macromolecule can be modelled as a chain, or discrete curve (as it is for instance the case for a protein backbone with a single chain of amino-acids), we introduce a method to estimate the deformation of the atomic model with respect to a given conformation, which is assumed to be known a priori. Our method consists on estimating the torsion and bond angles of the atomic model in each conformation as a linear combination of the eigenfunctions of the Laplace operator in the manifold of conformations. These eigenfunctions can be approximated by means of a well-known technique in manifold learning, based on the construction of a graph Laplacian using the cryo-EM dataset. Finally, we test our approach with synthetic datasets, for which we recover the atomic model of two-dimensional and three-dimensional flexible structures from noisy tomographic projections.

eess.IV↗

arXiv2022

Maximum Entropy on the Mean and the Cramér Rate Function in Statistical Estimation and Inverse Problems: Properties, Models, and Algorithms

We explore a method of statistical estimation called Maximum Entropy on the Mean (MEM) which is based on an information-driven criterion that quantifies the compliance of a given point with a reference prior probability measure. At the core of this approach lies the MEM function which is a partial minimization of the Kullback-Leibler divergence over a linear constraint. In many cases, it is known that this function admits a simpler representation (known as the Cramér rate function). Via the connection to exponential families of probability distributions, we study general conditions under which this representation holds. We then address how the associated MEM estimator gives rise to a wide class of MEM-based regularized linear models for solving inverse problems. Finally, we propose an algorithmic framework to solve these problems efficiently based on the Bregman proximal gradient method, alongside proximal operators for commonly used reference distributions. The article is complemented by a software package for experimentation and exploration of the MEM approach in applications.

math.ST↗

arXiv2022

Self-Supervised Learning of Phenotypic Representations from Cell Images with Weak Labels

We propose WS-DINO as a novel framework to use weak label information in learning phenotypic representations from high-content fluorescent images of cells. Our model is based on a knowledge distillation approach with a vision transformer backbone (DINO), and we use this as a benchmark model for our study. Using WS-DINO, we fine-tuned with weak label information available in high-content microscopy screens (treatment and compound) and achieve state-of-the-art performance in not-same-compound mechanism of action prediction on the BBBC021 dataset (98%), and not-same-compound-and-batch performance (96%) using the compound as the weak label. Our method bypasses single cell cropping as a pre-processing step, and using self-attention maps we show that the model learns structurally meaningful phenotypic profiles.

cs.CV↗

arXiv2022

Calibrating the Dice loss to handle neural network overconfidence for biomedical image segmentation

The Dice similarity coefficient (DSC) is both a widely used metric and loss function for biomedical image segmentation due to its robustness to class imbalance. However, it is well known that the DSC loss is poorly calibrated, resulting in overconfident predictions that cannot be usefully interpreted in biomedical and clinical practice. Performance is often the only metric used to evaluate segmentations produced by deep neural networks, and calibration is often neglected. However, calibration is important for translation into biomedical and clinical practice, providing crucial contextual information to model predictions for interpretation by scientists and clinicians. In this study, we provide a simple yet effective extension of the DSC loss, named the DSC++ loss, that selectively modulates the penalty associated with overconfident, incorrect predictions. As a standalone loss function, the DSC++ loss achieves significantly improved calibration over the conventional DSC loss across six well-validated open-source biomedical imaging datasets, including both 2D binary and 3D multi-class segmentation tasks. Similarly, we observe significantly improved calibration when integrating the DSC++ loss into four DSC-based loss functions. Finally, we use softmax thresholding to illustrate that well calibrated outputs enable tailoring of recall-precision bias, which is an important post-processing technique to adapt the model predictions to suit the biomedical or clinical task. The DSC++ loss overcomes the major limitation of the DSC loss, providing a suitable loss function for training deep learning segmentation models for use in biomedical and clinical practice. Source code is available at: https://github.com/mlyg/DicePlusPlus.

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