arXiv subjects
Publications and source records attributed to Cheng Ouyang.
We study a stochastic dyadic model with both forward and backward energy cascade mechanisms for the inviscid and non-resistive magnetohydrodynamics. For a particular class of stochastic forcing, we show weak uniqueness for the stochastic system. However the solution dissipates the energy which is formally an invariant quantity for the system.
Deep learning models usually suffer from domain shift issues, where models trained on one source domain do not generalize well to other unseen domains. In this work, we investigate the single-source domain generalization problem: training a deep network that is robust to unseen domains, under the condition that training data is only available from one source domain, which is common in medical imaging applications. We tackle this problem in the context of cross-domain medical image segmentation. Under this scenario, domain shifts are mainly caused by different acquisition processes. We propose a simple causality-inspired data augmentation approach to expose a segmentation model to synthesized domain-shifted training examples. Specifically, 1) to make the deep model robust to discrepancies in image intensities and textures, we employ a family of randomly-weighted shallow networks. They augment training images using diverse appearance transformations. 2) Further we show that spurious correlations among objects in an image are detrimental to domain robustness. These correlations might be taken by the network as domain-specific clues for making predictions, and they may break on unseen domains. We remove these spurious correlations via causal intervention. This is achieved by resampling the appearances of potentially correlated objects independently. The proposed approach is validated on three cross-domain segmentation tasks: cross-modality (CT-MRI) abdominal image segmentation, cross-sequence (bSSFP-LGE) cardiac MRI segmentation, and cross-center prostate MRI segmentation. The proposed approach yields consistent performance gains compared with competitive methods when tested on unseen domains.
Background samples provide key contextual information for segmenting regions of interest (ROIs). However, they always cover a diverse set of structures, causing difficulties for the segmentation model to learn good decision boundaries with high sensitivity and precision. The issue concerns the highly heterogeneous nature of the background class, resulting in multi-modal distributions. Empirically, we find that neural networks trained with heterogeneous background struggle to map the corresponding contextual samples to compact clusters in feature space. As a result, the distribution over background logit activations may shift across the decision boundary, leading to systematic over-segmentation across different datasets and tasks. In this study, we propose context label learning (CoLab) to improve the context representations by decomposing the background class into several subclasses. Specifically, we train an auxiliary network as a task generator, along with the primary segmentation model, to automatically generate context labels that positively affect the ROI segmentation accuracy. Extensive experiments are conducted on several challenging segmentation tasks and datasets. The results demonstrate that CoLab can guide the segmentation model to map the logits of background samples away from the decision boundary, resulting in significantly improved segmentation accuracy. Code is available.
The quality of cardiac magnetic resonance (CMR) imaging is susceptible to respiratory motion artifacts. The model robustness of automated segmentation techniques in face of real-world respiratory motion artifacts is unclear. This manuscript describes the design of extreme cardiac MRI analysis challenge under respiratory motion (CMRxMotion Challenge). The challenge aims to establish a public benchmark dataset to assess the effects of respiratory motion on image quality and examine the robustness of segmentation models. The challenge recruited 40 healthy volunteers to perform different breath-hold behaviors during one imaging visit, obtaining paired cine imaging with artifacts. Radiologists assessed the image quality and annotated the level of respiratory motion artifacts. For those images with diagnostic quality, radiologists further segmented the left ventricle, left ventricle myocardium and right ventricle. The images of training set (20 volunteers) along with the annotations are released to the challenge participants, to develop an automated image quality assessment model (Task 1) and an automated segmentation model (Task 2). The images of validation set (5 volunteers) are released to the challenge participants but the annotations are withheld for online evaluation of submitted predictions. Both the images and annotations of the test set (15 volunteers) were withheld and only used for offline evaluation of submitted containerized dockers. The image quality assessment task is quantitatively evaluated by the Cohen's kappa statistics and the segmentation task is evaluated by the Dice scores and Hausdorff distances.
Probability calibration for deep models is highly desirable in safety-critical applications such as medical imaging. It makes output probabilities of deep networks interpretable, by aligning prediction probability with the actual accuracy in test data. In image segmentation, well-calibrated probabilities allow radiologists to identify regions where model-predicted segmentations are unreliable. These unreliable predictions often occur to out-of-domain (OOD) images that are caused by imaging artifacts or unseen imaging protocols. Unfortunately, most previous calibration methods for image segmentation perform sub-optimally on OOD images. To reduce the calibration error when confronted with OOD images, we propose a novel post-hoc calibration model. Our model leverages the pixel susceptibility against perturbations at the local level, and the shape prior information at the global level. The model is tested on cardiac MRI segmentation datasets that contain unseen imaging artifacts and images from an unseen imaging protocol. We demonstrate reduced calibration errors compared with the state-of-the-art calibration algorithm.
In this note we focus our attention on a stochastic heat equation defined on the Heisenberg group $\mathbf{H}^{n}$ of order $n$. This equation is written as $\partial_t u=\frac{1}{2}Δu+u\dot{W}_α$, where $Δ$ is the hypoelliptic Laplacian on $\mathbf{H}^{n}$ and $\{\dot{W}_α; α>0\}$ is a family of Gaussian space-time noises which are white in time and have a covariance structure generated by $(-Δ)^{-α}$ in space. Our aim is threefold: (i) Give a proper description of the noise $W_α$; (ii) Prove that one can solve the stochastic heat equation in the Itô sense as soon as $α>\frac{n}{2}$; (iii) Give some basic moment estimates for the solution $u(t,x)$.
The success of neural networks on medical image segmentation tasks typically relies on large labeled datasets for model training. However, acquiring and manually labeling a large medical image set is resource-intensive, expensive, and sometimes impractical due to data sharing and privacy issues. To address this challenge, we propose AdvChain, a generic adversarial data augmentation framework, aiming at improving both the diversity and effectiveness of training data for medical image segmentation tasks. AdvChain augments data with dynamic data augmentation, generating randomly chained photo-metric and geometric transformations to resemble realistic yet challenging imaging variations to expand training data. By jointly optimizing the data augmentation model and a segmentation network during training, challenging examples are generated to enhance network generalizability for the downstream task. The proposed adversarial data augmentation does not rely on generative networks and can be used as a plug-in module in general segmentation networks. It is computationally efficient and applicable for both low-shot supervised and semi-supervised learning. We analyze and evaluate the method on two MR image segmentation tasks: cardiac segmentation and prostate segmentation with limited labeled data. Results show that the proposed approach can alleviate the need for labeled data while improving model generalization ability, indicating its practical value in medical imaging applications.
Convolutional neural networks (CNNs) have achieved remarkable segmentation accuracy on benchmark datasets where training and test sets are from the same domain, yet their performance can degrade significantly on unseen domains, which hinders the deployment of CNNs in many clinical scenarios. Most existing works improve model out-of-domain (OOD) robustness by collecting multi-domain datasets for training, which is expensive and may not always be feasible due to privacy and logistical issues. In this work, we focus on improving model robustness using a single-domain dataset only. We propose a novel data augmentation framework called MaxStyle, which maximizes the effectiveness of style augmentation for model OOD performance. It attaches an auxiliary style-augmented image decoder to a segmentation network for robust feature learning and data augmentation. Importantly, MaxStyle augments data with improved image style diversity and hardness, by expanding the style space with noise and searching for the worst-case style composition of latent features via adversarial training. With extensive experiments on multiple public cardiac and prostate MR datasets, we demonstrate that MaxStyle leads to significantly improved out-of-distribution robustness against unseen corruptions as well as common distribution shifts across multiple, different, unseen sites and unknown image sequences under both low- and high-training data settings. The code can be found at https://github.com/cherise215/MaxStyle.
Accurate computing, analysis and modeling of the ventricles and myocardium from medical images are important, especially in the diagnosis and treatment management for patients suffering from myocardial infarction (MI). Late gadolinium enhancement (LGE) cardiac magnetic resonance (CMR) provides an important protocol to visualize MI. However, automated segmentation of LGE CMR is still challenging, due to the indistinguishable boundaries, heterogeneous intensity distribution and complex enhancement patterns of pathological myocardium from LGE CMR. Furthermore, compared with the other sequences LGE CMR images with gold standard labels are particularly limited, which represents another obstacle for developing novel algorithms for automatic segmentation of LGE CMR. This paper presents the selective results from the Multi-Sequence Cardiac MR (MS-CMR) Segmentation challenge, in conjunction with MICCAI 2019. The challenge offered a data set of paired MS-CMR images, including auxiliary CMR sequences as well as LGE CMR, from 45 patients who underwent cardiomyopathy. It was aimed to develop new algorithms, as well as benchmark existing ones for LGE CMR segmentation and compare them objectively. In addition, the paired MS-CMR images could enable algorithms to combine the complementary information from the other sequences for the segmentation of LGE CMR. Nine representative works were selected for evaluation and comparisons, among which three methods are unsupervised methods and the other six are supervised. The results showed that the average performance of the nine methods was comparable to the inter-observer variations. The success of these methods was mainly attributed to the inclusion of the auxiliary sequences from the MS-CMR images, which provide important label information for the training of deep neural networks.
Deep learning-based segmentation methods are vulnerable to unforeseen data distribution shifts during deployment, e.g. change of image appearances or contrasts caused by different scanners, unexpected imaging artifacts etc. In this paper, we present a cooperative framework for training image segmentation models and a latent space augmentation method for generating hard examples. Both contributions improve model generalization and robustness with limited data. The cooperative training framework consists of a fast-thinking network (FTN) and a slow-thinking network (STN). The FTN learns decoupled image features and shape features for image reconstruction and segmentation tasks. The STN learns shape priors for segmentation correction and refinement. The two networks are trained in a cooperative manner. The latent space augmentation generates challenging examples for training by masking the decoupled latent space in both channel-wise and spatial-wise manners. We performed extensive experiments on public cardiac imaging datasets. Using only 10 subjects from a single site for training, we demonstrated improved cross-site segmentation performance and increased robustness against various unforeseen imaging artifacts compared to strong baseline methods. Particularly, cooperative training with latent space data augmentation yields 15% improvement in terms of average Dice score when compared to a standard training method.
Few-shot semantic segmentation (FSS) has great potential for medical imaging applications. Most of the existing FSS techniques require abundant annotated semantic classes for training. However, these methods may not be applicable for medical images due to the lack of annotations. To address this problem we make several contributions: (1) A novel self-supervised FSS framework for medical images in order to eliminate the requirement for annotations during training. Additionally, superpixel-based pseudo-labels are generated to provide supervision; (2) An adaptive local prototype pooling module plugged into prototypical networks, to solve the common challenging foreground-background imbalance problem in medical image segmentation; (3) We demonstrate the general applicability of the proposed approach for medical images using three different tasks: abdominal organ segmentation for CT and MRI, as well as cardiac segmentation for MRI. Our results show that, for medical image segmentation, the proposed method outperforms conventional FSS methods which require manual annotations for training.
The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: $\partial_{t} u_{t}(x) = \frac12 Δu_{t}(x) + u_{t}(x) \, \dot W_{t}(x)$, for $t\in\mathbb{R}_{+}$ and $x\in \mathbb{R}^{d}$, where $\dot W_{t}(x)$ is a Gaussian noise whose space time covariance function is singular. In this rough context, we shall give some information about the moments of $u_{t}(x)$ when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.
We construct a $K$-rough path above either a space-time or a spatial fractional Brownian motion, in any space dimension $d$. This allows us to provide an interpretation and a unique solution for the corresponding parabolic Anderson model, understood in the renormalized sense. We also consider the case of a spatial fractional noise.
This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution. Our methodology relies heavily on the rough paths structure of the equation.
This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform ellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution.
Neural network-based approaches can achieve high accuracy in various medical image segmentation tasks. However, they generally require large labelled datasets for supervised learning. Acquiring and manually labelling a large medical dataset is expensive and sometimes impractical due to data sharing and privacy issues. In this work, we propose an adversarial data augmentation method for training neural networks for medical image segmentation. Instead of generating pixel-wise adversarial attacks, our model generates plausible and realistic signal corruptions, which models the intensity inhomogeneities caused by a common type of artefacts in MR imaging: bias field. The proposed method does not rely on generative networks, and can be used as a plug-in module for general segmentation networks in both supervised and semi-supervised learning. Using cardiac MR imaging we show that such an approach can improve the generalization ability and robustness of models as well as provide significant improvements in low-data scenarios.
We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution for any fixed time $t>0$. In addition, we provide Varadhan estimates for the asymptotic behavior of the density for small noise. The emphasis is on working with general Gaussian processes with covariance function satisfying suitable abstract, checkable conditions.
We prove a geometric extension of Lévy's occupation time arcsine law near a hypersurface on a Riemannian manifold. The deviation from the classic arcsine law is of the order of the square-root of the time horizon and is expressed explicitly in terms of the mean curvature of the hypersurface and the local time of the underlying standard Brownian motion.