Samuel Kadoury

Malo de Boisredon, Eugene Vorontsov, William Trung Le et al.

Deep neural networks are commonly used for automated medical image segmentation, but models will frequently struggle to generalize well across different imaging modalities. This issue is particularly problematic due to the limited availability of annotated data, making it difficult to deploy these models on a larger scale. To overcome these challenges, we propose a new semi-supervised training strategy called MoDATTS. Our approach is designed for accurate cross-modality 3D tumor segmentation on unpaired bi-modal datasets. An image-to-image translation strategy between imaging modalities is used to produce annotated pseudo-target volumes and improve generalization to the unannotated target modality. We also use powerful vision transformer architectures and introduce an iterative self-training procedure to further close the domain gap between modalities. MoDATTS additionally allows the possibility to extend the training to unannotated target data by exploiting image-level labels with an unsupervised objective that encourages the model to perform 3D diseased-to-healthy translation by disentangling tumors from the background. The proposed model achieves superior performance compared to other methods from participating teams in the CrossMoDA 2022 challenge, as evidenced by its reported top Dice score of 0.87+/-0.04 for the VS segmentation. MoDATTS also yields consistent improvements in Dice scores over baselines on a cross-modality brain tumor segmentation task composed of four different contrasts from the BraTS 2020 challenge dataset, where 95% of a target supervised model performance is reached. We report that 99% and 100% of this maximum performance can be attained if 20% and 50% of the target data is additionally annotated, which further demonstrates that MoDATTS can be leveraged to reduce the annotation burden.

William Trung Le, Chulmin Bang, Philippine Cordelle et al.

Adaptive radiotherapy is a growing field of study in cancer treatment due to it's objective in sparing healthy tissue. The standard of care in several institutions includes longitudinal cone-beam computed tomography (CBCT) acquisitions to monitor changes, but have yet to be used to improve tumor control while managing side-effects. The aim of this study is to demonstrate the clinical value of pre-treatment CBCT acquired daily during radiation therapy treatment for head and neck cancers for the downstream task of predicting severe toxicity occurrence: reactive feeding tube (NG), hospitalization and radionecrosis. For this, we propose a deformable 3D classification pipeline that includes a component analyzing the Jacobian matrix of the deformation between planning CT and longitudinal CBCT, as well as clinical data. The model is based on a multi-branch 3D residual convolutional neural network, while the CT to CBCT registration is based on a pair of VoxelMorph architectures. Accuracies of 85.8% and 75.3% was found for radionecrosis and hospitalization, respectively, with similar performance as early as after the first week of treatment. For NG tube risk, performance improves with increasing the timing of the CBCT fraction, reaching 83.1% after the $5_{th}$ week of treatment.

Malo Alefsen de Boisredon d'Assier, Eugene Vorontsov, Samuel Kadoury

Automated medical image segmentation using deep neural networks typically requires substantial supervised training. However, these models fail to generalize well across different imaging modalities. This shortcoming, amplified by the limited availability of expert annotated data, has been hampering the deployment of such methods at a larger scale across modalities. To address these issues, we propose M-GenSeg, a new semi-supervised generative training strategy for cross-modality tumor segmentation on unpaired bi-modal datasets. With the addition of known healthy images, an unsupervised objective encourages the model to disentangling tumors from the background, which parallels the segmentation task. Then, by teaching the model to convert images across modalities, we leverage available pixel-level annotations from the source modality to enable segmentation in the unannotated target modality. We evaluated the performance on a brain tumor segmentation dataset composed of four different contrast sequences from the public BraTS 2020 challenge data. We report consistent improvement in Dice scores over state-of-the-art domain-adaptive baselines on the unannotated target modality. Unlike the prior art, M-GenSeg also introduces the ability to train with a partially annotated source modality.

Matej Gazda, Peter Drotar, Liset Vazquez Romaguera et al.

Intensity modulated radiotherapy (IMRT) is one of the most common modalities for treating cancer patients. One of the biggest challenges is precise treatment delivery that accounts for varying motion patterns originating from free-breathing. Currently, image-guided solutions for IMRT is limited to 2D guidance due to the complexity of 3D tracking solutions. We propose a novel end-to-end attention graph neural network model that generates in real-time a triangular shape of the liver based on a reference segmentation obtained at the preoperative phase and a 2D MRI coronal slice taken during the treatment. Graph neural networks work directly with graph data and can capture hidden patterns in non-Euclidean domains. Furthermore, contrary to existing methods, it produces the shape entirely in a mesh structure and correctly infers mesh shape and position based on a surrogate image. We define two on-the-fly approaches to make the correspondence of liver mesh vertices with 2D images obtained during treatment. Furthermore, we introduce a novel task-specific identity loss to constrain the deformation of the liver in the graph neural network to limit phenomenons such as flying vertices or mesh holes. The proposed method achieves results with an average error of 3.06 +- 0.7 mm and Chamfer distance with L2 norm of 63.14 +- 27.28.

Mohamed El Amine Elforaici, Emmanuel Montagnon, Francisco Perdigon Romero et al.

Colorectal liver metastases (CLM) significantly impact colon cancer patients, influencing survival based on systemic chemotherapy response. Traditional methods like tumor grading scores (e.g., tumor regression grade - TRG) for prognosis suffer from subjectivity, time constraints, and expertise demands. Current machine learning approaches often focus on radiological data, yet the relevance of histological images for survival predictions, capturing intricate tumor microenvironment characteristics, is gaining recognition. To address these limitations, we propose an end-to-end approach for automated prognosis prediction using histology slides stained with H&E and HPS. We first employ a Generative Adversarial Network (GAN) for slide normalization to reduce staining variations and improve the overall quality of the images that are used as input to our prediction pipeline. We propose a semi-supervised model to perform tissue classification from sparse annotations, producing feature maps. We use an attention-based approach that weighs the importance of different slide regions in producing the final classification results. We exploit the extracted features for the metastatic nodules and surrounding tissue to train a prognosis model. In parallel, we train a vision Transformer (ViT) in a knowledge distillation framework to replicate and enhance the performance of the prognosis prediction. In our evaluation on a clinical dataset of 258 patients, our approach demonstrates superior performance with c-indexes of 0.804 (0.014) for OS and 0.733 (0.014) for TTR. Achieving 86.9% to 90.3% accuracy in predicting TRG dichotomization and 78.5% to 82.1% accuracy for the 3-class TRG classification task, our approach outperforms comparative methods. Our proposed pipeline can provide automated prognosis for pathologists and oncologists, and can greatly promote precision medicine progress in managing CLM patients.

Gautier Hénique, William Le, Gabriel Dayan et al.

Extranodal extension (ENE) is an emerging prognostic factor in human papillomavirus (HPV)-associated oropharyngeal cancer (OPC), although it is currently omitted as a clinical staging criteria. Recent works have advocated for the inclusion of iENE as a prognostic marker in HPV-positive OPC staging. However, several practical limitations continue to hinder its clinical integration, including inconsistencies in segmentation, low contrast in the periphery of metastatic lymph nodes on CT imaging, and laborious manual annotations. To address these limitations, we propose a fully automated end-to-end pipeline that uses computed tomography (CT) images with clinical data to assess the status of nodal ENE and predict treatment outcomes. Our approach includes a hierarchical 3D semi-supervised segmentation model designed to detect and delineate relevant iENE from radiotherapy planning CT scans. From these segmentations, a set of radiomics and deep features are extracted to train an imaging-detected ENE grading classifier. The predicted ENE status is then evaluated for its prognostic value and compared with existing staging criteria. Furthermore, we integrate these nodal features with primary tumor characteristics in a multimodal, attention-based outcome prediction model, providing a dynamic framework for outcome prediction. Our method is validated in an internal cohort of 397 HPV-positive OPC patients treated with radiation therapy or chemoradiotherapy between 2009 and 2020. For outcome prediction at the 2-year mark, our pipeline surpassed baseline models with 88.2% (4.8) in AUC for metastatic recurrence, 79.2% (7.4) for overall survival, and 78.1% (8.6) for disease-free survival. We also obtain a concordance index of 83.3% (6.5) for metastatic recurrence, 71.3% (8.9) for overall survival, and 70.0% (8.1) for disease-free survival, making it feasible for clinical decision making.

Zeinab Abboud, Herve Lombaert, Samuel Kadoury

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.

Eugene Vorontsov, Samuel Kadoury

Imperfect labels limit the quality of predictions learned by deep neural networks. This is particularly relevant in medical image segmentation, where reference annotations are difficult to collect and vary significantly even across expert annotators. Prior work on mitigating label noise focused on simple models of mostly uniform noise. In this work, we explore biased and unbiased errors artificially introduced to brain tumour annotations on MRI data. We found that supervised and semi-supervised segmentation methods are robust or fairly robust to unbiased errors but sensitive to biased errors. It is therefore important to identify the sorts of errors expected in medical image labels and especially mitigate the biased errors.

Hongliang Li, Tal Mezheritsky, Liset Vazquez Romaguera et al.

Ultrasound (US) speckles are granular patterns which can impede image post-processing tasks, such as image segmentation and registration. Conventional filtering approaches are commonly used to remove US speckles, while their main drawback is long run-time in a 3D scenario. Although a few studies were conducted to remove 2D US speckles using deep learning, to our knowledge, there is no study to perform speckle reduction of 3D B-mode US using deep learning. In this study, we propose a 3D dense U-Net model to process 3D US B-mode data from a clinical US system. The model's results were applied to 3D registration. We show that our deep learning framework can obtain similar suppression and mean preservation index (1.066) on speckle reduction when compared to conventional filtering approaches (0.978), while reducing the runtime by two orders of magnitude. Moreover, it is found that the speckle reduction using our deep learning model contributes to improving the 3D registration performance. The mean square error of 3D registration on 3D data using 3D U-Net speckle reduction is reduced by half compared to that with speckles.

William Le, Francisco Perdigón Romero, Samuel Kadoury

In medical imaging, radiological scans of different modalities serve to enhance different sets of features for clinical diagnosis and treatment planning. This variety enriches the source information that could be used for outcome prediction. Deep learning methods are particularly well-suited for feature extraction from high-dimensional inputs such as images. In this work, we apply a CNN classification network augmented with a FCN preprocessor sub-network to a public TCIA head and neck cancer dataset. The training goal is survival prediction of radiotherapy cases based on pre-treatment FDG PET-CT scans, acquired across 4 different hospitals. We show that the preprocessor sub-network in conjunction with aggregated residual connection leads to improvements over state-of-the-art results when combining both CT and PET input images.

Eugene Vorontsov, Pavlo Molchanov, Christopher Beckham et al.

Often in medical imaging, it is prohibitively challenging to produce enough boundary annotations to train deep neural networks for accurate tumor segmentation. We propose the use of weak labels about whether an image presents tumor or whether it is absent to extend training over images that lack these annotations. Specifically, we propose a semi-supervised framework that employs unpaired image-to-image translation between two domains, presence vs. absence of cancer, as the unsupervised objective. We conjecture that translation helps segmentation -- both require the target to be separated from the background. We encode images into two codes: one that is common to both domains and one that is unique to the presence domain. Decoding from the common code yields healthy images; decoding with the addition of the unique code produces a residual change to this image that adds cancer. Translation proceeds from presence to absence and vice versa. In the first case, the tumor is re-added to the image and we successfully exploit the residual decoder to also perform segmentation. In the second case, unique codes are sampled, producing a distribution of possible tumors. To validate the method, we created challenging synthetic tasks and tumor segmentation datasets from public BRATS (brain, MRI) and LitS (liver, CT) datasets. We show a clear improvement (0.83 Dice on brain, 0.74 on liver) over baseline semi-supervised training with autoencoding (0.73, 0.66) and a mean teacher approach (0.75, 0.69), demonstrating the ability to generalize from smaller distributions of annotated samples.

Francisco Perdigon Romero, Andre Diler, Gabriel Bisson-Gregoire et al.

Colorectal liver metastasis is one of most aggressive liver malignancies. While the definition of lesion type based on CT images determines the diagnosis and therapeutic strategy, the discrimination between cancerous and non-cancerous lesions are critical and requires highly skilled expertise, experience and time. In the present work we introduce an end-to-end deep learning approach to assist in the discrimination between liver metastases from colorectal cancer and benign cysts in abdominal CT images of the liver. Our approach incorporates the efficient feature extraction of InceptionV3 combined with residual connections and pre-trained weights from ImageNet. The architecture also includes fully connected classification layers to generate a probabilistic output of lesion type. We use an in-house clinical biobank with 230 liver lesions originating from 63 patients. With an accuracy of 0.96 and a F1-score of 0.92, the results obtained with the proposed approach surpasses state of the art methods. Our work provides the basis for incorporating machine learning tools in specialized radiology software to assist physicians in the early detection and treatment of liver lesions.

Patrick Bilic, Patrick Christ, Hongwei Bran Li et al.

In this work, we report the set-up and results of the Liver Tumor Segmentation Benchmark (LiTS), which was organized in conjunction with the IEEE International Symposium on Biomedical Imaging (ISBI) 2017 and the International Conferences on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2017 and 2018. The image dataset is diverse and contains primary and secondary tumors with varied sizes and appearances with various lesion-to-background levels (hyper-/hypo-dense), created in collaboration with seven hospitals and research institutions. Seventy-five submitted liver and liver tumor segmentation algorithms were trained on a set of 131 computed tomography (CT) volumes and were tested on 70 unseen test images acquired from different patients. We found that not a single algorithm performed best for both liver and liver tumors in the three events. The best liver segmentation algorithm achieved a Dice score of 0.963, whereas, for tumor segmentation, the best algorithms achieved Dices scores of 0.674 (ISBI 2017), 0.702 (MICCAI 2017), and 0.739 (MICCAI 2018). Retrospectively, we performed additional analysis on liver tumor detection and revealed that not all top-performing segmentation algorithms worked well for tumor detection. The best liver tumor detection method achieved a lesion-wise recall of 0.458 (ISBI 2017), 0.515 (MICCAI 2017), and 0.554 (MICCAI 2018), indicating the need for further research. LiTS remains an active benchmark and resource for research, e.g., contributing the liver-related segmentation tasks in \url{http://medicaldecathlon.com/}. In addition, both data and online evaluation are accessible via \url{www.lits-challenge.com}.

Francisco Perdigon Romero, An Tang, Samuel Kadoury

Breast cancer is the most diagnosed cancer and the most predominant cause of death in women worldwide. Imaging techniques such as the breast cancer pathology helps in the diagnosis and monitoring of the disease. However identification of malignant cells can be challenging given the high heterogeneity in tissue absorbotion from staining agents. In this work, we present a novel approach for Invasive Ductal Carcinoma (IDC) cells discrimination in histopathology slides. We propose a model derived from the Inception architecture, proposing a multi-level batch normalization module between each convolutional steps. This module was used as a base block for the feature extraction in a CNN architecture. We used the open IDC dataset in which we obtained a balanced accuracy of 0.89 and an F1 score of 0.90, thus surpassing recent state of the art classification algorithms tested on this public dataset.

Marc-Antoine Boucher, Sarah Lippe, Amelie Damphousse et al.

Ultrasound (US) can be used to assess brain development in newborns, as MRI is challenging due to immobilization issues, and may require sedation. Dilatation of the lateral ventricles in the brain is a risk factor for poorer neurodevelopment outcomes in infants. Hence, 3D US has the ability to assess the volume of the lateral ventricles similar to clinically standard MRI, but manual segmentation is time consuming. The objective of this study is to develop an approach quantifying the ratio of lateral ventricular dilatation with respect to total brain volume using 3D US, which can assess the severity of macrocephaly. Automatic segmentation of the lateral ventricles is achieved with a multi-atlas deformable registration approach using locally linear correlation metrics for US-MRI fusion, followed by a refinement step using deformable mesh models. Total brain volume is estimated using a 3D ellipsoid modeling approach. Validation was performed on a cohort of 12 infants, ranging from 2 to 8.5 months old, where 3D US and MRI were used to compare brain volumes and segmented lateral ventricles. Automatically extracted volumes from 3D US show a high correlation and no statistically significant difference when compared to ground truth measurements. Differences in volume ratios was 6.0 +/- 4.8% compared to MRI, while lateral ventricular segmentation yielded a mean Dice coefficient of 70.8 +/- 3.6% and a mean absolute distance (MAD) of 0.88 +/- 0.2mm, demonstrating the clinical benefit of this tool in paediatric ultrasound.

William Mandel, Olivier Turcot, Dejan Knez et al.

Anterior Vertebral Body Growth Modulation (AVBGM) is a minimally invasive surgical technique that gradually corrects spine deformities while preserving lumbar motion. However the selection of potential surgical patients is currently based on clinical judgment and would be facilitated by the identification of patients responding to AVBGM prior to surgery. We introduce a statistical framework for predicting the surgical outcomes following AVBGM in adolescents with idiopathic scoliosis. A discriminant manifold is first constructed to maximize the separation between responsive and non-responsive groups of patients treated with AVBGM for scoliosis. The model then uses subject-specific correction trajectories based on articulated transformations in order to map spine correction profiles to a group-average piecewise-geodesic path. Spine correction trajectories are described in a piecewise-geodesic fashion to account for varying times at follow-up exams, regressing the curve via a quadratic optimization process. To predict the evolution of correction, a baseline reconstruction is projected onto the manifold, from which a spatiotemporal regression model is built from parallel transport curves inferred from neighboring exemplars. The model was trained on 438 reconstructions and tested on 56 subjects using 3D spine reconstructions from follow-up exams, with the probabilistic framework yielding accurate results with differences of 2.1 +/- 0.6deg in main curve angulation, and generating models similar to biomechanical simulations.

Eugene Vorontsov, An Tang, Chris Pal et al.

We propose a model for the joint segmentation of the liver and liver lesions in computed tomography (CT) volumes. We build the model from two fully convolutional networks, connected in tandem and trained together end-to-end. We evaluate our approach on the 2017 MICCAI Liver Tumour Segmentation Challenge, attaining competitive liver and liver lesion detection and segmentation scores across a wide range of metrics. Unlike other top performing methods, our model output post-processing is trivial, we do not use data external to the challenge, and we propose a simple single-stage model that is trained end-to-end. However, our method nearly matches the top lesion segmentation performance and achieves the second highest precision for lesion detection while maintaining high recall.

Michal Drozdzal, Gabriel Chartrand, Eugene Vorontsov et al.

In this paper, we introduce a simple, yet powerful pipeline for medical image segmentation that combines Fully Convolutional Networks (FCNs) with Fully Convolutional Residual Networks (FC-ResNets). We propose and examine a design that takes particular advantage of recent advances in the understanding of both Convolutional Neural Networks as well as ResNets. Our approach focuses upon the importance of a trainable pre-processing when using FC-ResNets and we show that a low-capacity FCN model can serve as a pre-processor to normalize medical input data. In our image segmentation pipeline, we use FCNs to obtain normalized images, which are then iteratively refined by means of a FC-ResNet to generate a segmentation prediction. As in other fully convolutional approaches, our pipeline can be used off-the-shelf on different image modalities. We show that using this pipeline, we exhibit state-of-the-art performance on the challenging Electron Microscopy benchmark, when compared to other 2D methods. We improve segmentation results on CT images of liver lesions, when contrasting with standard FCN methods. Moreover, when applying our 2D pipeline on a challenging 3D MRI prostate segmentation challenge we reach results that are competitive even when compared to 3D methods. The obtained results illustrate the strong potential and versatility of the pipeline by achieving highly accurate results on multi-modality images from different anatomical regions and organs.

Eugene Vorontsov, Chiheb Trabelsi, Samuel Kadoury et al.

It is well known that it is challenging to train deep neural networks and recurrent neural networks for tasks that exhibit long term dependencies. The vanishing or exploding gradient problem is a well known issue associated with these challenges. One approach to addressing vanishing and exploding gradients is to use either soft or hard constraints on weight matrices so as to encourage or enforce orthogonality. Orthogonal matrices preserve gradient norm during backpropagation and may therefore be a desirable property. This paper explores issues with optimization convergence, speed and gradient stability when encouraging or enforcing orthogonality. To perform this analysis, we propose a weight matrix factorization and parameterization strategy through which we can bound matrix norms and therein control the degree of expansivity induced during backpropagation. We find that hard constraints on orthogonality can negatively affect the speed of convergence and model performance.

Samuel Kadoury, William Mandel, Marjolaine Roy-Beaudry et al.

We introduce a novel approach for predicting the progression of adolescent idiopathic scoliosis from 3D spine models reconstructed from biplanar X-ray images. Recent progress in machine learning have allowed to improve classification and prognosis rates, but lack a probabilistic framework to measure uncertainty in the data. We propose a discriminative probabilistic manifold embedding where locally linear mappings transform data points from high-dimensional space to corresponding low-dimensional coordinates. A discriminant adjacency matrix is constructed to maximize the separation between progressive and non-progressive groups of patients diagnosed with scoliosis, while minimizing the distance in latent variables belonging to the same class. To predict the evolution of deformation, a baseline reconstruction is projected onto the manifold, from which a spatiotemporal regression model is built from parallel transport curves inferred from neighboring exemplars. Rate of progression is modulated from the spine flexibility and curve magnitude of the 3D spine deformation. The method was tested on 745 reconstructions from 133 subjects using longitudinal 3D reconstructions of the spine, with results demonstrating the discriminatory framework can identify between progressive and non-progressive of scoliotic patients with a classification rate of 81% and prediction differences of 2.1$^{o}$ in main curve angulation, outperforming other manifold learning methods. Our method achieved a higher prediction accuracy and improved the modeling of spatiotemporal morphological changes in highly deformed spines compared to other learning methods.

Michal Drozdzal, Eugene Vorontsov, Gabriel Chartrand et al.

In this paper, we study the influence of both long and short skip connections on Fully Convolutional Networks (FCN) for biomedical image segmentation. In standard FCNs, only long skip connections are used to skip features from the contracting path to the expanding path in order to recover spatial information lost during downsampling. We extend FCNs by adding short skip connections, that are similar to the ones introduced in residual networks, in order to build very deep FCNs (of hundreds of layers). A review of the gradient flow confirms that for a very deep FCN it is beneficial to have both long and short skip connections. Finally, we show that a very deep FCN can achieve near-to-state-of-the-art results on the EM dataset without any further post-processing.

Mahsa Shakeri, Enzo Ferrante, Stavros Tsogkas et al.

We propose a modular and scalable framework for dense coregistration and cosegmentation with two key characteristics: first, we substitute ground truth data with the semantic map output of a classifier; second, we combine this output with population deformable registration to improve both alignment and segmentation. Our approach deforms all volumes towards consensus, taking into account image similarities and label consistency. Our pipeline can incorporate any classifier and similarity metric. Results on two datasets, containing annotations of challenging brain structures, demonstrate the potential of our method.

Mahsa Shakeri, Stavros Tsogkas, Enzo Ferrante et al.

In this paper we propose a deep learning approach for segmenting sub-cortical structures of the human brain in Magnetic Resonance (MR) image data. We draw inspiration from a state-of-the-art Fully-Convolutional Neural Network (F-CNN) architecture for semantic segmentation of objects in natural images, and adapt it to our task. Unlike previous CNN-based methods that operate on image patches, our model is applied on a full blown 2D image, without any alignment or registration steps at testing time. We further improve segmentation results by interpreting the CNN output as potentials of a Markov Random Field (MRF), whose topology corresponds to a volumetric grid. Alpha-expansion is used to perform approximate inference imposing spatial volumetric homogeneity to the CNN priors. We compare the performance of the proposed pipeline with a similar system using Random Forest-based priors, as well as state-of-art segmentation algorithms, and show promising results on two different brain MRI datasets.

Samuel Kadoury, Eugene Vorontsov, An Tang

The early detection, diagnosis and monitoring of liver cancer progression can be achieved with the precise delineation of metastatic tumours. However, accurate automated segmentation remains challenging due to the presence of noise, inhomogeneity and the high appearance variability of malignant tissue. In this paper, we propose an unsupervised metastatic liver tumour segmentation framework using a machine learning approach based on discriminant Grassmannian manifolds which learns the appearance of tumours with respect to normal tissue. First, the framework learns within-class and between-class similarity distributions from a training set of images to discover the optimal manifold discrimination between normal and pathological tissue in the liver. Second, a conditional optimisation scheme computes nonlocal pairwise as well as pattern-based clique potentials from the manifold subspace to recognise regions with similar labelings and to incorporate global consistency in the segmentation process. The proposed framework was validated on a clinical database of 43 CT images from patients with metastatic liver cancer. Compared to state-of-the-art methods, our method achieves a better performance on two separate datasets of metastatic liver tumours from different clinical sites, yielding an overall mean Dice similarity coefficient of 90.7 +/- 2.4 in over 50 tumours with an average volume of 27.3 mm3.