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Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian approximations such as ensembles have shown promise, they still suffer from high training and inference costs. Existing approaches mainly address the costs of BNN inference post-training, with little focus on improving training efficiency and reducing parameter complexity. This study introduces a training procedure for a sparse (partial) Bayesian network. Our method selectively assigns a subset of parameters as Bayesian by assessing their deterministic saliency through gradient sensitivity analysis. The resulting network combines deterministic and Bayesian parameters, exploiting the advantages of both representations to achieve high task-specific performance and minimize predictive uncertainty. Demonstrated on multi-label ChestMNIST for classification and ISIC, LIDC-IDRI for segmentation, our approach achieves competitive performance and predictive uncertainty estimation by reducing Bayesian parameters by over 95\%, significantly reducing computational expenses compared to fully Bayesian and ensemble methods.

Ensuring reliable confidence scores from deep neural networks is of paramount significance in critical decision-making systems, particularly in real-world domains such as healthcare. Recent literature on calibrating deep segmentation networks has resulted in substantial progress. Nevertheless, these approaches are strongly inspired by the advancements in classification tasks, and thus their uncertainty is usually modeled by leveraging the information of individual pixels, disregarding the local structure of the object of interest. Indeed, only the recent Spatially Varying Label Smoothing (SVLS) approach considers pixel spatial relationships across classes, by softening the pixel label assignments with a discrete spatial Gaussian kernel. In this work, we first present a constrained optimization perspective of SVLS and demonstrate that it enforces an implicit constraint on soft class proportions of surrounding pixels. Furthermore, our analysis shows that SVLS lacks a mechanism to balance the contribution of the constraint with the primary objective, potentially hindering the optimization process. Based on these observations, we propose NACL (Neighbor Aware CaLibration), a principled and simple solution based on equality constraints on the logit values, which enables to control explicitly both the enforced constraint and the weight of the penalty, offering more flexibility. Comprehensive experiments on a wide variety of well-known segmentation benchmarks demonstrate the superior calibration performance of the proposed approach, without affecting its discriminative power. Furthermore, ablation studies empirically show the model agnostic nature of our approach, which can be used to train a wide span of deep segmentation networks., Comment: Under review. arXiv admin note: text overlap with arXiv:2303.06268

Semi-supervised learning relaxes the need of large pixel-wise labeled datasets for image segmentation by leveraging unlabeled data. A prominent way to exploit unlabeled data is to regularize model predictions. Since the predictions of unlabeled data can be unreliable, uncertainty-aware schemes are typically employed to gradually learn from meaningful and reliable predictions. Uncertainty estimation methods, however, rely on multiple inferences from the model predictions that must be computed for each training step, which is computationally expensive. Moreover, these uncertainty maps capture pixel-wise disparities and do not consider global information. This work proposes a novel method to estimate segmentation uncertainty by leveraging global information from the segmentation masks. More precisely, an anatomically-aware representation is first learnt to model the available segmentation masks. The learnt representation thereupon maps the prediction of a new segmentation into an anatomically-plausible segmentation. The deviation from the plausible segmentation aids in estimating the underlying pixel-level uncertainty in order to further guide the segmentation network. The proposed method consequently estimates the uncertainty using a single inference from our representation, thereby reducing the total computation. We evaluate our method on two publicly available segmentation datasets of left atria in cardiac MRIs and of multiple organs in abdominal CTs. Our anatomically-aware method improves the segmentation accuracy over the state-of-the-art semi-supervised methods in terms of two commonly used evaluation metrics., Comment: Accepted at Medical Image Analysis. Code is available at: $\href{https://github.com/adigasu/Anatomically-aware_Uncertainty_for_Semi-supervised_Segmentation}{Github}$

Ensuring reliable confidence scores from deep networks is of pivotal importance in critical decision-making systems, notably in the medical domain. While recent literature on calibrating deep segmentation networks has led to significant progress, their uncertainty is usually modeled by leveraging the information of individual pixels, which disregards the local structure of the object of interest. In particular, only the recent Spatially Varying Label Smoothing (SVLS) approach addresses this issue by softening the pixel label assignments with a discrete spatial Gaussian kernel. In this work, we first present a constrained optimization perspective of SVLS and demonstrate that it enforces an implicit constraint on soft class proportions of surrounding pixels. Furthermore, our analysis shows that SVLS lacks a mechanism to balance the contribution of the constraint with the primary objective, potentially hindering the optimization process. Based on these observations, we propose a principled and simple solution based on equality constraints on the logit values, which enables to control explicitly both the enforced constraint and the weight of the penalty, offering more flexibility. Comprehensive experiments on a variety of well-known segmentation benchmarks demonstrate the superior performance of the proposed approach., Comment: MICCAI 2023

The performance of learning-based algorithms improves with the amount of labelled data used for training. Yet, manually annotating data is particularly difficult for medical image segmentation tasks because of the limited expert availability and intensive manual effort required. To reduce manual labelling, active learning (AL) targets the most informative samples from the unlabelled set to annotate and add to the labelled training set. On the one hand, most active learning works have focused on the classification or limited segmentation of natural images, despite active learning being highly desirable in the difficult task of medical image segmentation. On the other hand, uncertainty-based AL approaches notoriously offer sub-optimal batch-query strategies, while diversity-based methods tend to be computationally expensive. Over and above methodological hurdles, random sampling has proven an extremely difficult baseline to outperform when varying learning and sampling conditions. This work aims to take advantage of the diversity and speed offered by random sampling to improve the selection of uncertainty-based AL methods for segmenting medical images. More specifically, we propose to compute uncertainty at the level of batches instead of samples through an original use of stochastic batches (SB) during sampling in AL. Stochastic batch querying is a simple and effective add-on that can be used on top of any uncertainty-based metric. Extensive experiments on two medical image segmentation datasets show that our strategy consistently improves conventional uncertainty-based sampling methods. Our method can hence act as a strong baseline for medical image segmentation. The code is available on: https://github.com/Minimel/StochasticBatchAL.git., Comment: Accepted to Medical Image Analysis, 17 pages

Deep learning methods typically depend on the availability of labeled data, which is expensive and time-consuming to obtain. Active learning addresses such effort by prioritizing which samples are best to annotate in order to maximize the performance of the task model. While frameworks for active learning have been widely explored in the context of classification of natural images, they have been only sparsely used in medical image segmentation. The challenge resides in obtaining an uncertainty measure that reveals the best candidate data for annotation. This paper proposes Test-time Augmentation for Active Learning (TAAL), a novel semi-supervised active learning approach for segmentation that exploits the uncertainty information offered by data transformations. Our method applies cross-augmentation consistency during training and inference to both improve model learning in a semi-supervised fashion and identify the most relevant unlabeled samples to annotate next. In addition, our consistency loss uses a modified version of the JSD to further improve model performance. By relying on data transformations rather than on external modules or simple heuristics typically used in uncertainty-based strategies, TAAL emerges as a simple, yet powerful task-agnostic semi-supervised active learning approach applicable to the medical domain. Our results on a publicly-available dataset of cardiac images show that TAAL outperforms existing baseline methods in both fully-supervised and semi-supervised settings. Our implementation is publicly available on https://github.com/melinphd/TAAL., Comment: Accepted to MICCAI-DALI 2022 (LNCS Proceedings, vol.13567), 11 pages

Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by computational cost. In this application scenario, which typically involves transportable simulators, the computing hardware severely constrains the size or the level of details of the simulated scene. To address this limitation, data-driven approaches have been suggested to simulate mechanical deformations by learning the mapping rules from FEM generated datasets. Herein, we propose a deep learning method for predicting displacement fields of soft tissues with viscoelastic properties. The main contribution of this work is the use of a physics-guided loss function for the optimization of the deep learning model parameters. The proposed deep learning model is based on convolutional (CNN) and recurrent layers (LSTM) to predict spatiotemporal variations. It is augmented with a mass conservation law in the lost function to prevent the generation of physically inconsistent results. The deep learning model is trained on a set of FEM datasets that are generated from a commercially available state-of-the-art numerical neurosurgery simulator. The use of the physics-guided loss function in a deep learning model has led to a better generalization in the prediction of deformations in unseen simulation cases. Moreover, the proposed method achieves a better accuracy over the conventional CNN models, where improvements were observed in unseen tissue from 8% to 30% depending on the magnitude of external forces. It is hoped that the present investigation will help in filling the gap in applying deep learning in virtual reality simulators, hence improving their computational performance (compared to FEM simulations) and ultimately their usefulness.

Learning similarity is a key aspect in medical image analysis, particularly in recommendation systems or in uncovering the interpretation of anatomical data in images. Most existing methods learn such similarities in the embedding space over image sets using a single metric learner. Images, however, have a variety of object attributes such as color, shape, or artifacts. Encoding such attributes using a single metric learner is inadequate and may fail to generalize. Instead, multiple learners could focus on separate aspects of these attributes in subspaces of an overarching embedding. This, however, implies the number of learners to be found empirically for each new dataset. This work, Dynamic Subspace Learners, proposes to dynamically exploit multiple learners by removing the need of knowing apriori the number of learners and aggregating new subspace learners during training. Furthermore, the visual interpretability of such subspace learning is enforced by integrating an attention module into our method. This integrated attention mechanism provides a visual insight of discriminative image features that contribute to the clustering of image sets and a visual explanation of the embedding features. The benefits of our attention-based dynamic subspace learners are evaluated in the application of image clustering, image retrieval, and weakly supervised segmentation. Our method achieves competitive results with the performances of multiple learners baselines and significantly outperforms the classification network in terms of clustering and retrieval scores on three different public benchmark datasets. Moreover, our attention maps offer a proxy-labels, which improves the segmentation accuracy up to 15% in Dice scores when compared to state-of-the-art interpretation techniques.

Supervised learning is well-known to fail at generalization under distribution shifts. In typical clinical settings, the source data is inaccessible and the target distribution is represented with a handful of samples: adaptation can only happen at test time on a few or even a single subject(s). We investigate test-time single-subject adaptation for segmentation, and propose a Shape-guided Entropy Minimization objective for tackling this task. During inference for a single testing subject, our loss is minimized with respect to the batch normalization's scale and bias parameters. We show the potential of integrating various shape priors to guide adaptation to plausible solutions, and validate our method in two challenging scenarios: MRI-to-CT adaptation of cardiac segmentation and cross-site adaptation of prostate segmentation. Our approach exhibits substantially better performances than the existing test-time adaptation methods. Even more surprisingly, it fares better than state-of-the-art domain adaptation methods, although it forgoes training on additional target data during adaptation. Our results question the usefulness of training on target data in segmentation adaptation, and points to the substantial effect of shape priors on test-time inference. Our framework can be readily used for integrating various priors and for adapting any segmentation network, and our code is available., Comment: Early Accept at International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) 2022

Semi-supervised segmentation tackles the scarcity of annotations by leveraging unlabeled data with a small amount of labeled data. A prominent way to utilize the unlabeled data is by consistency training which commonly uses a teacher-student network, where a teacher guides a student segmentation. The predictions of unlabeled data are not reliable, therefore, uncertainty-aware methods have been proposed to gradually learn from meaningful and reliable predictions. Uncertainty estimation, however, relies on multiple inferences from model predictions that need to be computed for each training step, which is computationally expensive. This work proposes a novel method to estimate the pixel-level uncertainty by leveraging the labeling representation of segmentation masks. On the one hand, a labeling representation is learnt to represent the available segmentation masks. The learnt labeling representation is used to map the prediction of the segmentation into a set of plausible masks. Such a reconstructed segmentation mask aids in estimating the pixel-level uncertainty guiding the segmentation network. The proposed method estimates the uncertainty with a single inference from the labeling representation, thereby reducing the total computation. We evaluate our method on the 3D segmentation of left atrium in MRI, and we show that our uncertainty estimates from our labeling representation improve the segmentation accuracy over state-of-the-art methods.

In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral coordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to isometric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.

The physical and clinical constraints surrounding diffusion-weighted imaging (DWI) often limit the spatial resolution of the produced images to voxels up to 8 times larger than those of T1w images. Thus, the detailed information contained in T1w imagescould help in the synthesis of diffusion images in higher resolution. However, the non-Euclidean nature of diffusion imaging hinders current deep generative models from synthesizing physically plausible images. In this work, we propose the first Riemannian network architecture for the direct generation of diffusion tensors (DT) and diffusion orientation distribution functions (dODFs) from high-resolution T1w images. Our integration of the Log-Euclidean Metric into a learning objective guarantees, unlike standard Euclidean networks, the mathematically-valid synthesis of diffusion. Furthermore, our approach improves the fractional anisotropy mean squared error (FA MSE) between the synthesized diffusion and the ground-truth by more than 23% and the cosine similarity between principal directions by almost 5% when compared to our baselines. We validate our generated diffusion by comparing the resulting tractograms to our expected real data. We observe similar fiber bundles with streamlines having less than 3% difference in length, less than 1% difference in volume, and a visually close shape. While our method is able to generate high-resolution diffusion images from structural inputs in less than 15 seconds, we acknowledge and discuss the limits of diffusion inference solely relying on T1w images. Our results nonetheless suggest a relationship between the high-level geometry of the brain and the overall white matter architecture., Comment: Preprint submitted for review

Domain adaptation (DA) has drawn high interest for its capacity to adapt a model trained on labeled source data to perform well on unlabeled or weakly labeled target data from a different domain. Most common DA techniques require concurrent access to the input images of both the source and target domains. However, in practice, privacy concerns often impede the availability of source images in the adaptation phase. This is a very frequent DA scenario in medical imaging, where, for instance, the source and target images could come from different clinical sites. We introduce a source-free domain adaptation for image segmentation. Our formulation is based on minimizing a label-free entropy loss defined over target-domain data, which we further guide with a domain-invariant prior on the segmentation regions. Many priors can be derived from anatomical information. Here, a class ratio prior is estimated from anatomical knowledge and integrated in the form of a Kullback Leibler (KL) divergence in our overall loss function. Furthermore, we motivate our overall loss with an interesting link to maximizing the mutual information between the target images and their label predictions. We show the effectiveness of our prior aware entropy minimization in a variety of domain-adaptation scenarios, with different modalities and applications, including spine, prostate, and cardiac segmentation. Our method yields comparable results to several state of the art adaptation techniques, despite having access to much less information, as the source images are entirely absent in our adaptation phase. Our straightforward adaptation strategy uses only one network, contrary to popular adversarial techniques, which are not applicable to a source-free DA setting. Our framework can be readily used in a breadth of segmentation problems, and our code is publicly available: https://github.com/mathilde-b/SFDA, Comment: 18 pages, 8 figures, submitted to Elsevier Medical Image Analysis

Assessing the degree of disease severity in biomedical images is a task similar to standard classification but constrained by an underlying structure in the label space. Such a structure reflects the monotonic relationship between different disease grades. In this paper, we propose a straightforward approach to enforce this constraint for the task of predicting Diabetic Retinopathy (DR) severity from eye fundus images based on the well-known notion of Cost-Sensitive classification. We expand standard classification losses with an extra term that acts as a regularizer, imposing greater penalties on predicted grades when they are farther away from the true grade associated to a particular image. Furthermore, we show how to adapt our method to the modelling of label noise in each of the sub-problems associated to DR grading, an approach we refer to as Atomic Sub-Task modeling. This yields models that can implicitly take into account the inherent noise present in DR grade annotations. Our experimental analysis on several public datasets reveals that, when a standard Convolutional Neural Network is trained using this simple strategy, improvements of 3-5\% of quadratic-weighted kappa scores can be achieved at a negligible computational cost. Code to reproduce our results is released at https://github.com/agaldran/cost_sensitive_loss_classification., Comment: This paper has been accepted for publication at MICCAI 2020

Image normalization is a building block in medical image analysis. Conventional approaches are customarily utilized on a per-dataset basis. This strategy, however, prevents the current normalization algorithms from fully exploiting the complex joint information available across multiple datasets. Consequently, ignoring such joint information has a direct impact on the performance of segmentation algorithms. This paper proposes to revisit the conventional image normalization approach by instead learning a common normalizing function across multiple datasets. Jointly normalizing multiple datasets is shown to yield consistent normalized images as well as an improved image segmentation. To do so, a fully automated adversarial and task-driven normalization approach is employed as it facilitates the training of realistic and interpretable images while keeping performance on-par with the state-of-the-art. The adversarial training of our network aims at finding the optimal transfer function to improve both the segmentation accuracy and the generation of realistic images. We evaluated the performance of our normalizer on both infant and adult brains images from the iSEG, MRBrainS and ABIDE datasets. Results reveal the potential of our normalization approach for segmentation, with Dice improvements of up to 57.5% over our baseline. Our method can also enhance data availability by increasing the number of samples available when learning from multiple imaging domains.

The segmentation of the retinal vasculature from eye fundus images represents one of the most fundamental tasks in retinal image analysis. Over recent years, increasingly complex approaches based on sophisticated Convolutional Neural Network architectures have been slowly pushing performance on well-established benchmark datasets. In this paper, we take a step back and analyze the real need of such complexity. Specifically, we demonstrate that a minimalistic version of a standard U-Net with several orders of magnitude less parameters, carefully trained and rigorously evaluated, closely approximates the performance of current best techniques. In addition, we propose a simple extension, dubbed W-Net, which reaches outstanding performance on several popular datasets, still using orders of magnitude less learnable weights than any previously published approach. Furthermore, we provide the most comprehensive cross-dataset performance analysis to date, involving up to 10 different databases. Our analysis demonstrates that the retinal vessel segmentation problem is far from solved when considering test images that differ substantially from the training data, and that this task represents an ideal scenario for the exploration of domain adaptation techniques. In this context, we experiment with a simple self-labeling strategy that allows us to moderately enhance cross-dataset performance, indicating that there is still much room for improvement in this area. Finally, we also test our approach on the Artery/Vein segmentation problem, where we again achieve results well-aligned with the state-of-the-art, at a fraction of the model complexity in recent literature. All the code to reproduce the results in this paper is released.

This compendium gathers all the accepted extended abstracts from the Third International Conference on Medical Imaging with Deep Learning (MIDL 2020), held in Montreal, Canada, 6-9 July 2020. Note that only accepted extended abstracts are listed here, the Proceedings of the MIDL 2020 Full Paper Track are published in the Proceedings of Machine Learning Research (PMLR)., Comment: Accepted extended abstracts can also be found at https://openreview.net/group?id=MIDL.io/2020/Conference#abstract-accept-papers

Domain adaptation (DA) has drawn high interests for its capacity to adapt a model trained on labeled source data to perform well on unlabeled or weakly labeled target data from a different domain. Most common DA techniques require the concurrent access to the input images of both the source and target domains. However, in practice, it is common that the source images are not available in the adaptation phase. This is a very frequent DA scenario in medical imaging, for instance, when the source and target images come from different clinical sites. We propose a novel formulation for adapting segmentation networks, which relaxes such a constraint. Our formulation is based on minimizing a label-free entropy loss defined over target-domain data, which we further guide with a domain invariant prior on the segmentation regions. Many priors can be used, derived from anatomical information. Here, a class-ratio prior is learned via an auxiliary network and integrated in the form of a Kullback-Leibler (KL) divergence in our overall loss function. We show the effectiveness of our prior-aware entropy minimization in adapting spine segmentation across different MRI modalities. Our method yields comparable results to several state-of-the-art adaptation techniques, even though is has access to less information, the source images being absent in the adaptation phase. Our straight-forward adaptation strategy only uses one network, contrary to popular adversarial techniques, which cannot perform without the presence of the source images. Our framework can be readily used with various priors and segmentation problems.

Segmentation using deep learning has shown promising directions in medical imaging as it aids in the analysis and diagnosis of diseases. Nevertheless, a main drawback of deep models is that they require a large amount of pixel-level labels, which are laborious and expensive to obtain. To mitigate this problem, weakly supervised learning has emerged as an efficient alternative, which employs image-level labels, scribbles, points, or bounding boxes as supervision. Among these, image-level labels are easier to obtain. However, since this type of annotation only contains object category information, the segmentation task under this learning paradigm is a challenging problem. To address this issue, visual salient regions derived from trained classification networks are typically used. Despite their success to identify important regions on classification tasks, these saliency regions only focus on the most discriminant areas of an image, limiting their use in semantic segmentation. In this work, we propose a manifold driven attention-based network to enhance visual salient regions, thereby improving segmentation accuracy in a weakly supervised setting. Our method generates superior attention maps directly during inference without the need of extra computations. We evaluate the benefits of our approach in the task of segmentation using a public benchmark on skin lesion images. Results demonstrate that our method outperforms the state-of-the-art GradCAM by a margin of ~22% in terms of Dice score., Comment: Paper is submitted to MICCAI2020

The varying cortical geometry of the brain creates numerous challenges for its analysis. Recent developments have enabled learning surface data directly across multiple brain surfaces via graph convolutions on cortical data. However, current graph learning algorithms do fail when brain surface data are misaligned across subjects, thereby affecting their ability to deal with data from multiple domains. Adversarial training is widely used for domain adaptation to improve the segmentation performance across domains. In this paper, adversarial training is exploited to learn surface data across inconsistent graph alignments. This novel approach comprises a segmentator that uses a set of graph convolution layers to enable parcellation directly across brain surfaces in a source domain, and a discriminator that predicts a graph domain from segmentations. More precisely, the proposed adversarial network learns to generalize a parcellation across both, source and target domains. We demonstrate an 8% mean improvement in performance over a non-adversarial training strategy applied on multiple target domains extracted from MindBoggle, the largest publicly available manually-labeled brain surface dataset.

Unpaired image-to-image translation has been applied successfully to natural images but has received very little attention for manifold-valued data such as in diffusion tensor imaging (DTI). The non-Euclidean nature of DTI prevents current generative adversarial networks (GANs) from generating plausible images and has mainly limited their application to diffusion MRI scalar maps, such as fractional anisotropy (FA) or mean diffusivity (MD). Even if these scalar maps are clinically useful, they mostly ignore fiber orientations and therefore have limited applications for analyzing brain fibers. Here, we propose a manifold-aware CycleGAN that learns the generation of high-resolution DTI from unpaired T1w images. We formulate the objective as a Wasserstein distance minimization problem of data distributions on a Riemannian manifold of symmetric positive definite 3x3 matrices SPD(3), using adversarial and cycle-consistency losses. To ensure that the generated diffusion tensors lie on the SPD(3) manifold, we exploit the theoretical properties of the exponential and logarithm maps of the Log-Euclidean metric. We demonstrate that, unlike standard GANs, our method is able to generate realistic high-resolution DTI that can be used to compute diffusion-based metrics and potentially run fiber tractography algorithms. To evaluate our model's performance, we compute the cosine similarity between the generated tensors principal orientation and their ground-truth orientation, the mean squared error (MSE) of their derived FA values and the Log-Euclidean distance between the tensors. We demonstrate that our method produces 2.5 times better FA MSE than a standard CycleGAN and up to 30% better cosine similarity than a manifold-aware Wasserstein GAN while synthesizing sharp high-resolution DTI., Comment: Accepted at MICCAI 2020 International Workshop on Computational Diffusion MRI

Image normalization is a critical step in medical imaging. This step is often done on a per-dataset basis, preventing current segmentation algorithms from the full potential of exploiting jointly normalized information across multiple datasets. To solve this problem, we propose an adversarial normalization approach for image segmentation which learns common normalizing functions across multiple datasets while retaining image realism. The adversarial training provides an optimal normalizer that improves both the segmentation accuracy and the discrimination of unrealistic normalizing functions. Our contribution therefore leverages common imaging information from multiple domains. The optimality of our common normalizer is evaluated by combining brain images from both infants and adults. Results on the challenging iSEG and MRBrainS datasets reveal the potential of our adversarial normalization approach for segmentation, with Dice improvements of up to 59.6% over the baseline., Comment: Submitted to ISBI 2020

Brain surface analysis is essential to neuroscience, however, the complex geometry of the brain cortex hinders computational methods for this task. The difficulty arises from a discrepancy between 3D imaging data, which is represented in Euclidean space, and the non-Euclidean geometry of the highly-convoluted brain surface. Recent advances in machine learning have enabled the use of neural networks for non-Euclidean spaces. These facilitate the learning of surface data, yet pooling strategies often remain constrained to a single fixed-graph. This paper proposes a new learnable graph pooling method for processing multiple surface-valued data to output subject-based information. The proposed method innovates by learning an intrinsic aggregation of graph nodes based on graph spectral embedding. We illustrate the advantages of our approach with in-depth experiments on two large-scale benchmark datasets. The flexibility of the pooling strategy is evaluated on four different prediction tasks, namely, subject-sex classification, regression of cortical region sizes, classification of Alzheimer's disease stages, and brain age regression. Our experiments demonstrate the superiority of our learnable pooling approach compared to other pooling techniques for graph convolution networks, with results improving the state-of-the-art in brain surface analysis.

The analysis of the brain surface modeled as a graph mesh is a challenging task. Conventional deep learning approaches often rely on data lying in the Euclidean space. As an extension to irregular graphs, convolution operations are defined in the Fourier or spectral domain. This spectral domain is obtained by decomposing the graph Laplacian, which captures relevant shape information. However, the spectral decomposition across different brain graphs causes inconsistencies between the eigenvectors of individual spectral domains, causing the graph learning algorithm to fail. Current spectral graph convolution methods handle this variance by separately aligning the eigenvectors to a reference brain in a slow iterative step. This paper presents a novel approach for learning the transformation matrix required for aligning brain meshes using a direct data-driven approach. Our alignment and graph processing method provides a fast analysis of brain surfaces. The novel Spectral Graph Transformer (SGT) network proposed in this paper uses very few randomly sub-sampled nodes in the spectral domain to learn the alignment matrix for multiple brain surfaces. We validate the use of this SGT network along with a graph convolution network to perform cortical parcellation. Our method on 101 manually-labeled brain surfaces shows improved parcellation performance over a no-alignment strategy, gaining a significant speed (1400 fold) over traditional iterative alignment approaches., Comment: Equal contribution of R. He and K. Gopinath

We propose to adapt segmentation networks with a constrained formulation, which embeds domain-invariant prior knowledge about the segmentation regions. Such knowledge may take the form of simple anatomical information, e.g., structure size or shape, estimated from source samples or known a priori. Our method imposes domain-invariant inequality constraints on the network outputs of unlabeled target samples. It implicitly matches prediction statistics between target and source domains with permitted uncertainty of prior knowledge. We address our constrained problem with a differentiable penalty, fully suited for standard stochastic gradient descent approaches, removing the need for computationally expensive Lagrangian optimization with dual projections. Unlike current two-step adversarial training, our formulation is based on a single loss in a single network, which simplifies adaptation by avoiding extra adversarial steps, while improving convergence and quality of training. The comparison of our approach with state-of-the-art adversarial methods reveals substantially better performance on the challenging task of adapting spine segmentation across different MRI modalities. Our results also show a robustness to imprecision of size priors, approaching the accuracy of a fully supervised model trained directly in a target domain.Our method can be readily used for various constraints and segmentation problems., Comment: Published in IEEE Transactions on Medical Imaging. First version in MICCAI 2019

Early diagnosis of Alzheimer's disease plays a key role in understanding the degree of the patient's mental decline and determining preventive therapies. In this study, we introduce WaveletBrain, a novel representation of the white and gray matter surfaces of the cortex. The proposed framework innovates by deriving localized shape information from a global harmonic representation, that can be used in large-scale population studies of surface data. Results show that WaveletBrain leads to statistically significant improvements in comparison to the ShapeDNA representation in a variety of experiments including (i) classification of Alzheimer's disease, normal aging, and mild cognitive impairment, (ii) sex classification and (iii) age prediction of subjects. We performed our analysis on 719 patients and 2,876 surfaces. While this work focuses primarily on Alzheimer's disease diagnosis, our proposed framework can be used to address general surface analysis problems in neuroscience.

Recently, dense connections have attracted substantial attention in computer vision because they facilitate gradient flow and implicit deep supervision during training. Particularly, DenseNet, which connects each layer to every other layer in a feed-forward fashion, has shown impressive performances in natural image classification tasks. We propose HyperDenseNet, a 3D fully convolutional neural network that extends the definition of dense connectivity to multi-modal segmentation problems. Each imaging modality has a path, and dense connections occur not only between the pairs of layers within the same path, but also between those across different paths. This contrasts with the existing multi-modal CNN approaches, in which modeling several modalities relies entirely on a single joint layer (or level of abstraction) for fusion, typically either at the input or at the output of the network. Therefore, the proposed network has total freedom to learn more complex combinations between the modalities, within and in-between all the levels of abstraction, which increases significantly the learning representation. We report extensive evaluations over two different and highly competitive multi-modal brain tissue segmentation challenges, iSEG 2017 and MRBrainS 2013, with the former focusing on 6-month infant data and the latter on adult images. HyperDenseNet yielded significant improvements over many state-of-the-art segmentation networks, ranking at the top on both benchmarks. We further provide a comprehensive experimental analysis of features re-use, which confirms the importance of hyper-dense connections in multi-modal representation learning. Our code is publicly available at https://www.github.com/josedolz/HyperDenseNet., Comment: Paper accepted at IEEE TMI in October 2018. Last version of this paper updates the reference to the IEEE TMI paper which compares the submissions to the iSEG 2017 MICCAI Challenge

Neuronal cell bodies mostly reside in the cerebral cortex. The study of this thin and highly convoluted surface is essential for understanding how the brain works. The analysis of surface data is, however, challenging due to the high variability of the cortical geometry. This paper presents a novel approach for learning and exploiting surface data directly across surface domains. Current approaches rely on geometrical simplifications, such as spherical inflations, a popular but costly process. For instance, the widely used FreeSurfer takes about 3 hours to parcellate brain surfaces on a standard machine. Direct learning of surface data via graph convolutions would provide a new family of fast algorithms for processing brain surfaces. However, the current limitation of existing state-of-the-art approaches is their inability to compare surface data across different surface domains. Surface bases are indeed incompatible between brain geometries. This paper leverages recent advances in spectral graph matching to transfer surface data across aligned spectral domains. This novel approach enables a direct learning of surface data across compatible surface bases. It exploits spectral filters over intrinsic representations of surface neighborhoods. We illustrate the benefits of this approach with an application to brain parcellation. We validate the algorithm over 101 manually labeled brain surfaces. The results show a significant improvement in labeling accuracy over recent Euclidean approaches, while gaining a drastic speed improvement over conventional methods., Comment: 8 pages, Under review in MICCAI 2018