Do we really need dice? The hidden region-size biases of segmentation losses.

Most segmentation losses are arguably variants of the Cross-Entropy (CE) or Dice losses. On the surface, these two categories of losses (i.e., distribution based vs. geometry based) seem unrelated, and there is no clear consensus as to which category is a better choice, with varying performances for each across different benchmarks and applications. Furthermore, it is widely argued within the medical-imaging community that Dice and CE are complementary, which has motivated the use of compound CE-Dice losses. In this work, we provide a theoretical analysis, which shows that CE and Dice share a much deeper connection than previously thought. First, we show that, from a constrained-optimization perspective, they both decompose into two components, i.e., a similar ground-truth matching term, which pushes the predicted foreground regions towards the ground-truth, and a region-size penalty term imposing different biases on the size (or proportion) of the predicted regions. Then, we provide bound relationships and an information-theoretic analysis, which uncover hidden region-size biases: Dice has an intrinsic bias towards specific extremely imbalanced solutions, whereas CE implicitly encourages the ground-truth region proportions. Our theoretical results explain the wide experimental evidence in the medical-imaging literature, whereby Dice losses bring improvements for imbalanced segmentation. It also explains why CE dominates natural-image problems with diverse class proportions, in which case Dice might have difficulty adapting to different region-size distributions. Based on our theoretical analysis, we propose a principled and simple solution, which enables to control explicitly the region-size bias. The proposed method integrates CE with explicit terms based on L1 or the KL divergence, which encourage segmenting region proportions to match target class proportions, thereby mitigating class imbalance but without losing generality. Comprehensive experiments and ablation studies over different losses and applications validate our theoretical analysis, as well as the effectiveness of explicit and simple region-size terms. The code is available at https://github.com/by-liu/SegLossBias .

Segmentation with mixed supervision: Confidence maximization helps knowledge distillation.

Despite achieving promising results in a breadth of medical image segmentation tasks, deep neural networks (DNNs) require large training datasets with pixel-wise annotations. Obtaining these curated datasets is a cumbersome process which limits the applicability of DNNs in scenarios where annotated images are scarce. Mixed supervision is an appealing alternative for mitigating this obstacle. In this setting, only a small fraction of the data contains complete pixel-wise annotations and other images have a weaker form of supervision, e.g., only a handful of pixels are labeled. In this work, we propose a dual-branch architecture, where the upper branch (teacher) receives strong annotations, while the bottom one (student) is driven by limited supervision and guided by the upper branch. Combined with a standard cross-entropy loss over the labeled pixels, our novel formulation integrates two important terms: (i) a Shannon entropy loss defined over the less-supervised images, which encourages confident student predictions in the bottom branch; and (ii) a Kullback-Leibler (KL) divergence term, which transfers the knowledge (i.e., predictions) of the strongly supervised branch to the less-supervised branch and guides the entropy (student-confidence) term to avoid trivial solutions. We show that the synergy between the entropy and KL divergence yields substantial improvements in performance. We also discuss an interesting link between Shannon-entropy minimization and standard pseudo-mask generation, and argue that the former should be preferred over the latter for leveraging information from unlabeled pixels. We evaluate the effectiveness of the proposed formulation through a series of quantitative and qualitative experiments using two publicly available datasets. Results demonstrate that our method significantly outperforms other strategies for semantic segmentation within a mixed-supervision framework, as well as recent semi-supervised approaches. Moreover, in line with recent observations in classification, we show that the branch trained with reduced supervision and guided by the top branch largely outperforms the latter. Our code is publicly available: https://github.com/by-liu/ConfKD.

Source-free domain adaptation for image segmentation.

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 weak labels of the target samples and 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.

Annotation-efficient deep learning for automatic medical image segmentation.

Automatic medical image segmentation plays a critical role in scientific research and medical care. Existing high-performance deep learning methods typically rely on large training datasets with high-quality manual annotations, which are difficult to obtain in many clinical applications. Here, we introduce Annotation-effIcient Deep lEarning (AIDE), an open-source framework to handle imperfect training datasets. Methodological analyses and empirical evaluations are conducted, and we demonstrate that AIDE surpasses conventional fully-supervised models by presenting better performance on open datasets possessing scarce or noisy annotations. We further test AIDE in a real-life case study for breast tumor segmentation. Three datasets containing 11,852 breast images from three medical centers are employed, and AIDE, utilizing 10% training annotations, consistently produces segmentation maps comparable to those generated by fully-supervised counterparts or provided by independent radiologists. The 10-fold enhanced efficiency in utilizing expert labels has the potential to promote a wide range of biomedical applications.

Boundary loss for highly unbalanced segmentation.

Widely used loss functions for CNN segmentation, e.g., Dice or cross-entropy, are based on integrals over the segmentation regions. Unfortunately, for highly unbalanced segmentations, such regional summations have values that differ by several orders of magnitude across classes, which affects training performance and stability. We propose a boundary loss, which takes the form of a distance metric on the space of contours, not regions. This can mitigate the difficulties of highly unbalanced problems because it uses integrals over the interface between regions instead of unbalanced integrals over the regions. Furthermore, a boundary loss complements regional information. Inspired by graph-based optimization techniques for computing active-contour flows, we express a non-symmetric L2 distance on the space of contours as a regional integral, which avoids completely local differential computations involving contour points. This yields a boundary loss expressed with the regional softmax probability outputs of the network, which can be easily combined with standard regional losses and implemented with any existing deep network architecture for N-D segmentation. We report comprehensive evaluations and comparisons on different unbalanced problems, showing that our boundary loss can yield significant increases in performances while improving training stability. Our code is publicly available1.

Non-uniform Label Smoothing for Diabetic Retinopathy Grading from Retinal Fundus Images with Deep Neural Networks.

Purpose: Introducing a new technique to improve deep learning (DL) models designed for automatic grading of diabetic retinopathy (DR) from retinal fundus images by enhancing predictions' consistency. Methods: A convolutional neural network (CNN) was optimized in three different manners to predict DR grade from eye fundus images. The optimization criteria were (1) the standard cross-entropy (CE) loss; (2) CE supplemented with label smoothing (LS), a regularization approach widely employed in computer vision tasks; and (3) our proposed non-uniform label smoothing (N-ULS), a modification of LS that models the underlying structure of expert annotations. Results: Performance was measured in terms of quadratic-weighted κ score (quad-κ) and average area under the receiver operating curve (AUROC), as well as with suitable metrics for analyzing diagnostic consistency, like weighted precision, recall, and F1 score, or Matthews correlation coefficient. While LS generally harmed the performance of the CNN, N-ULS statistically significantly improved performance with respect to CE in terms quad-κ score (73.17 vs. 77.69, P < 0.025), without any performance decrease in average AUROC. N-ULS achieved this while simultaneously increasing performance for all other analyzed metrics. Conclusions: For extending standard modeling approaches from DR detection to the more complex task of DR grading, it is essential to consider the underlying structure of expert annotations. The approach introduced in this article can be easily implemented in conjunction with deep neural networks to increase their consistency without sacrificing per-class performance. Translational Relevance: A straightforward modification of current standard training practices of CNNs can substantially improve consistency in DR grading, better modeling expert annotations and human variability.

Discretely-constrained deep network for weakly supervised segmentation.

An efficient strategy for weakly-supervised segmentation is to impose constraints or regularization priors on target regions. Recent efforts have focused on incorporating such constraints in the training of convolutional neural networks (CNN), however this has so far been done within a continuous optimization framework. Yet, various segmentation constraints and regularization priors can be modeled and optimized more efficiently in a discrete formulation. This paper proposes a method, based on the alternating direction method of multipliers (ADMM) algorithm, to train a CNN with discrete constraints and regularization priors. This method is applied to the segmentation of medical images with weak annotations, where both size constraints and boundary length regularization are enforced. Experiments on two benchmark datasets for medical image segmentation show our method to provide significant improvements compared to existing approaches in terms of segmentation accuracy, constraint satisfaction and convergence speed.

3D Motion Estimation of Left Ventricular Dynamics Using MRI and Track-to-Track Fusion.

OBJECTIVE: This study investigates the estimation of three dimensional (3D) left ventricular (LV) motion using the fusion of different two dimensional (2D) cine magnetic resonance (CMR) sequences acquired during routine imaging sessions. Although standard clinical cine CMR data is inherently 2D, the actual underlying LV dynamics lies in 3D space and cannot be captured entirely using single 2D CMR image sequences. By utilizing the image information from various short-axis and long-axis image sequences, the proposed method intends to estimate the dynamic state vectors consisting of the position and velocity information of the myocardial borders in 3D space. METHOD: The proposed method comprises two main components: tracking myocardial points in 2D CMR sequences and fusion of multiple trajectories correspond to the tracked points. The tracking which yields the set of corresponding temporal points representing the myocardial points is performed using a diffeomorphic nonrigid image registration approach. The trajectories obtained from each cine CMR sequence is then fused with the corresponding trajectories from other CMR views using an unscented Kalman smoother (UKS) and a track-to-track fusion algorithm. RESULTS: We evaluated the proposed method by comparing the results against CMR imaging with myocardial tagging. We report a quantitative performance analysis by projecting the state vector estimates we obtained onto 2D tagged CMR images acquired from the same subjects and comparing them against harmonic phase estimates. The proposed algorithm yielded a competitive performance with a mean root mean square error of 1.3±0.5 pixels (1.8±0.6 mm) evaluated over 118 image sequences acquired from 30 subjects. CONCLUSION: This study demonstrates that fusing the information from short and long-axis views of CMR improves the accuracy of cardiac tissue motion estimation. Clinical Impact: The proposed method demonstrates that the fusion of tissue tracking information from long and short-axis views improves the binary classification of the automated regional function assessment.

Deep CNN ensembles and suggestive annotations for infant brain MRI segmentation.

Precise 3D segmentation of infant brain tissues is an essential step towards comprehensive volumetric studies and quantitative analysis of early brain development. However, computing such segmentations is very challenging, especially for 6-month infant brain, due to the poor image quality, among other difficulties inherent to infant brain MRI, e.g., the isointense contrast between white and gray matter and the severe partial volume effect due to small brain sizes. This study investigates the problem with an ensemble of semi-dense fully convolutional neural networks (CNNs), which employs T1-weighted and T2-weighted MR images as input. We demonstrate that the ensemble agreement is highly correlated with the segmentation errors. Therefore, our method provides measures that can guide local user corrections. To the best of our knowledge, this work is the first ensemble of 3D CNNs for suggesting annotations within images. Our quasi-dense architecture allows the efficient propagation of gradients during training, while limiting the number of parameters, requiring one order of magnitude less parameters than popular medical image segmentation networks such as 3D U-Net (Çiçek, et al.). We also investigated the impact that early or late fusions of multiple image modalities might have on the performances of deep architectures. We report evaluations of our method on the public data of the MICCAI iSEG-2017 Challenge on 6-month infant brain MRI segmentation, and show very competitive results among 21 teams, ranking first or second in most metrics.

Constrained-CNN losses for weakly supervised segmentation.

Weakly-supervised learning based on, e.g., partially labelled images or image-tags, is currently attracting significant attention in CNN segmentation as it can mitigate the need for full and laborious pixel/voxel annotations. Enforcing high-order (global) inequality constraints on the network output (for instance, to constrain the size of the target region) can leverage unlabeled data, guiding the training process with domain-specific knowledge. Inequality constraints are very flexible because they do not assume exact prior knowledge. However, constrained Lagrangian dual optimization has been largely avoided in deep networks, mainly for computational tractability reasons. To the best of our knowledge, the method of Pathak et al. (2015a) is the only prior work that addresses deep CNNs with linear constraints in weakly supervised segmentation. It uses the constraints to synthesize fully-labeled training masks (proposals) from weak labels, mimicking full supervision and facilitating dual optimization. We propose to introduce a differentiable penalty, which enforces inequality constraints directly in the loss function, avoiding expensive Lagrangian dual iterates and proposal generation. From constrained-optimization perspective, our simple penalty-based approach is not optimal as there is no guarantee that the constraints are satisfied. However, surprisingly, it yields substantially better results than the Lagrangian-based constrained CNNs in Pathak et al. (2015a), while reducing the computational demand for training. By annotating only a small fraction of the pixels, the proposed approach can reach a level of segmentation performance that is comparable to full supervision on three separate tasks. While our experiments focused on basic linear constraints such as the target-region size and image tags, our framework can be easily extended to other non-linear constraints, e.g., invariant shape moments (Klodt and Cremers, 2011) and other region statistics (Lim et al., 2014). Therefore, it has the potential to close the gap between weakly and fully supervised learning in semantic medical image segmentation. Our code is publicly available.

HyperDense-Net: A Hyper-Densely Connected CNN for Multi-Modal Image Segmentation.

Recently, dense connections have attracted substantial attention in computer vision because they facilitate gradient flow and implicit deep supervision during training. Particularly, DenseNet that connects each layer to every other layer in a feed-forward fashion and has shown impressive performances in natural image classification tasks. We propose HyperDenseNet, a 3-D 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 six 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.

Multiregion segmentation of bladder cancer structures in MRI with progressive dilated convolutional networks.

PURPOSE: Precise segmentation of bladder walls and tumor regions is an essential step toward noninvasive identification of tumor stage and grade, which is critical for treatment decision and prognosis of patients with bladder cancer (BC). However, the automatic delineation of bladder walls and tumor in magnetic resonance images (MRI) is a challenging task, due to important bladder shape variations, strong intensity inhomogeneity in urine, and very high variability across the population, particularly on tumors' appearance. To tackle these issues, we propose to leverage the representation capacity of deep fully convolutional neural networks. METHODS: The proposed network includes dilated convolutions to increase the receptive field without incurring extra cost or degrading its performance. Furthermore, we introduce progressive dilations in each convolutional block, thereby enabling extensive receptive fields without the need for large dilation rates. The proposed network is evaluated on 3.0T T2-weighted MRI scans from 60 pathologically confirmed patients with BC. RESULTS: Experiments show the proposed model to achieve a higher level of accuracy than state-of-the-art methods, with a mean Dice similarity coefficient of 0.98, 0.84, and 0.69 for inner wall, outer wall, and tumor region segmentation, respectively. These results represent a strong agreement with reference contours and an increase in performance compared to existing methods. In addition, inference times are less than a second for a whole three-dimensional (3D) volume, which is between two and three orders of magnitude faster than related state-of-the-art methods for this application. CONCLUSION: We showed that a CNN can yield precise segmentation of bladder walls and tumors in BC patients on MRI. The whole segmentation process is fully automatic and yields results similar to the reference standard, demonstrating the viability of deep learning models for the automatic multiregion segmentation of bladder cancer MRI images.

Comparing fully automated state-of-the-art cerebellum parcellation from magnetic resonance images.

The human cerebellum plays an essential role in motor control, is involved in cognitive function (i.e., attention, working memory, and language), and helps to regulate emotional responses. Quantitative in-vivo assessment of the cerebellum is important in the study of several neurological diseases including cerebellar ataxia, autism, and schizophrenia. Different structural subdivisions of the cerebellum have been shown to correlate with differing pathologies. To further understand these pathologies, it is helpful to automatically parcellate the cerebellum at the highest fidelity possible. In this paper, we coordinated with colleagues around the world to evaluate automated cerebellum parcellation algorithms on two clinical cohorts showing that the cerebellum can be parcellated to a high accuracy by newer methods. We characterize these various methods at four hierarchical levels: coarse (i.e., whole cerebellum and gross structures), lobe, subdivisions of the vermis, and the lobules. Due to the number of labels, the hierarchy of labels, the number of algorithms, and the two cohorts, we have restricted our analyses to the Dice measure of overlap. Under these conditions, machine learning based methods provide a collection of strategies that are efficient and deliver parcellations of a high standard across both cohorts, surpassing previous work in the area. In conjunction with the rank-sum computation, we identified an overall winning method.

3D fully convolutional networks for subcortical segmentation in MRI: A large-scale study.

This study investigates a 3D and fully convolutional neural network (CNN) for subcortical brain structure segmentation in MRI. 3D CNN architectures have been generally avoided due to their computational and memory requirements during inference. We address the problem via small kernels, allowing deeper architectures. We further model both local and global context by embedding intermediate-layer outputs in the final prediction, which encourages consistency between features extracted at different scales and embeds fine-grained information directly in the segmentation process. Our model is efficiently trained end-to-end on a graphics processing unit (GPU), in a single stage, exploiting the dense inference capabilities of fully CNNs. We performed comprehensive experiments over two publicly available datasets. First, we demonstrate a state-of-the-art performance on the ISBR dataset. Then, we report a large-scale multi-site evaluation over 1112 unregistered subject datasets acquired from 17 different sites (ABIDE dataset), with ages ranging from 7 to 64 years, showing that our method is robust to various acquisition protocols, demographics and clinical factors. Our method yielded segmentations that are highly consistent with a standard atlas-based approach, while running in a fraction of the time needed by atlas-based methods and avoiding registration/normalization steps. This makes it convenient for massive multi-site neuroanatomical imaging studies. To the best of our knowledge, our work is the first to study subcortical structure segmentation on such large-scale and heterogeneous data.

Esophagus segmentation in CT via 3D fully convolutional neural network and random walk.

PURPOSE: Precise delineation of organs at risk is a crucial task in radiotherapy treatment planning for delivering high doses to the tumor while sparing healthy tissues. In recent years, automated segmentation methods have shown an increasingly high performance for the delineation of various anatomical structures. However, this task remains challenging for organs like the esophagus, which have a versatile shape and poor contrast to neighboring tissues. For human experts, segmenting the esophagus from CT images is a time-consuming and error-prone process. To tackle these issues, we propose a random walker approach driven by a 3D fully convolutional neural network (CNN) to automatically segment the esophagus from CT images. METHODS: First, a soft probability map is generated by the CNN. Then, an active contour model (ACM) is fitted to the CNN soft probability map to get a first estimation of the esophagus location. The outputs of the CNN and ACM are then used in conjunction with a probability model based on CT Hounsfield (HU) values to drive the random walker. Training and evaluation were done on 50 CTs from two different datasets, with clinically used peer-reviewed esophagus contours. Results were assessed regarding spatial overlap and shape similarity. RESULTS: The esophagus contours generated by the proposed algorithm showed a mean Dice coefficient of 0.76 ± 0.11, an average symmetric square distance of 1.36 ± 0.90 mm, and an average Hausdorff distance of 11.68 ± 6.80, compared to the reference contours. These results translate to a very good agreement with reference contours and an increase in accuracy compared to existing methods. Furthermore, when considering the results reported in the literature for the publicly available Synapse dataset, our method outperformed all existing approaches, which suggests that the proposed method represents the current state-of-the-art for automatic esophagus segmentation. CONCLUSION: We show that a CNN can yield accurate estimations of esophagus location, and that the results of this model can be refined by a random walk step taking pixel intensities and neighborhood relationships into account. One of the main advantages of our network over previous methods is that it performs 3D convolutions, thus fully exploiting the 3D spatial context and performing an efficient volume-wise prediction. The whole segmentation process is fully automatic and yields esophagus delineations in very good agreement with the gold standard, showing that it can compete with previously published methods.

Spine labeling in axial magnetic resonance imaging via integral kernels.

This study investigates a fast integral-kernel algorithm for classifying (labeling) the vertebra and disc structures in axial magnetic resonance images (MRI). The method is based on a hierarchy of feature levels, where pixel classifications via non-linear probability product kernels (PPKs) are followed by classifications of 2D slices, individual 3D structures and groups of 3D structures. The algorithm further embeds geometric priors based on anatomical measurements of the spine. Our classifier requires evaluations of computationally expensive integrals at each pixel, and direct evaluations of such integrals would be prohibitively time consuming. We propose an efficient computation of kernel density estimates and PPK evaluations for large images and arbitrary local window sizes via integral kernels. Our method requires a single user click for a whole 3D MRI volume, runs nearly in real-time, and does not require an intensive external training. Comprehensive evaluations over T1-weighted axial lumbar spine data sets from 32 patients demonstrate a competitive structure classification accuracy of 99%, along with a 2D slice classification accuracy of 88%. To the best of our knowledge, such a structure classification accuracy has not been reached by the existing spine labeling algorithms. Furthermore, we believe our work is the first to use integral kernels in the context of medical images.

Detecting left ventricular impaired relaxation in cardiac MRI using moving mesh correspondences.

UNLABELLED: Anatomical cine cardiovascular magnetic resonance (CMR) imaging is widely used to assess the systolic cardiac function because of its high soft tissue contrast. Assessment of diastolic LV function has not regularly been performed due the complex and time consuming procedures. This study presents a semi-automated assessment of the left ventricular (LV) diastolic function using anatomical short-axis cine CMR images. The proposed method is based on three main steps: (1) non-rigid registration, which yields a sequence of endocardial boundary points over the cardiac cycle based on a user-provided contour on the first frame; (2) LV volume and filling rate computations over the cardiac cycle; and (3) automated detection of the peak values of early (E) and late ventricular (A) filling waves. In 47 patients cine CMR imaging and Doppler-echocardiographic imaging were performed. CMR measurements of peak values of the E and A waves as well as the deceleration time were compared with the corresponding values obtained in Doppler-Echocardiography. For the E/A ratio the proposed algorithm for CMR yielded a Cohen's kappa measure of 0.70 and a Gwet's AC1 coefficient of 0.70. CONCLUSION: Semi-automated assessment of the left ventricular (LV) diastolic function using anatomical short-axis cine CMR images provides mitral inflow measurements comparable to Doppler-Echocardiography.

Distribution Matching with the Bhattacharyya Similarity: A Bound Optimization Framework.

We present efficient graph cut algorithms for three problems: (1) finding a region in an image, so that the histogram (or distribution) of an image feature within the region most closely matches a given model; (2) co-segmentation of image pairs and (3) interactive image segmentation with a user-provided bounding box. Each algorithm seeks the optimum of a global cost function based on the Bhattacharyya measure, a convenient alternative to other matching measures such as the Kullback-Leibler divergence. Our functionals are not directly amenable to graph cut optimization as they contain non-linear functions of fractional terms, which make the ensuing optimization problems challenging. We first derive a family of parametric bounds of the Bhattacharyya measure by introducing an auxiliary labeling. Then, we show that these bounds are auxiliary functions of the Bhattacharyya measure, a result which allows us to solve each problem efficiently via graph cuts. We show that the proposed optimization procedures converge within very few graph cut iterations. Comprehensive and various experiments, including quantitative and comparative evaluations over two databases, demonstrate the advantages of the proposed algorithms over related works in regard to optimality, computational load, accuracy and flexibility.

Right ventricular segmentation in cardiac MRI with moving mesh correspondences.

This study investigates automatic propagation of the right ventricle (RV) endocardial and epicardial boundaries in 4D (3D+time) magnetic resonance imaging (MRI) sequences. Based on a moving mesh (or grid generation) framework, the proposed algorithm detects the endocardium and epicardium within each cardiac phase via point-to-point correspondences. The proposed method has the following advantages over prior RV segmentation works: (1) it removes the need for a time-consuming, manually built training set; (2) it does not make prior assumptions as to the intensity distributions or shape; (3) it provides a sequence of corresponding points over time, a comprehensive input that can be very useful in cardiac applications other than segmentation, e.g., regional wall motion analysis; and (4) it is more flexible for congenital heart disease where the RV undergoes high variations in shape. Furthermore, the proposed method allows comprehensive RV volumetric analysis over the complete cardiac cycle as well as automatic detections of end-systolic and end-diastolic phases because it provides a segmentation for each time step. Evaluated quantitatively over the 48-subject data set of the MICCAI 2012 RV segmentation challenge, the proposed method yielded an average Dice score of 0.84±0.11 for the epicardium and 0.79±0.17 for the endocardium. Further, quantitative evaluations of the proposed approach in comparisons to manual contours over 23 infant hypoplastic left heart syndrome patients yielded a Dice score of 0.82±0.14, which demonstrates the robustness of the algorithm.

TRIC: trust region for invariant compactness and its application to abdominal aorta segmentation.

This study investigates segmentation with a novel invariant compactness constraint. The proposed prior is a high-order fractional term, which is not directly amenable to powerful optimizers. We derive first-order Gateâux derivative approximations of our compactness term and adopt an iterative trust region paradigm by splitting our problem into constrained sub-problems, each solving the approximation globally via a Lagrangian formulation and a graph cut. We apply our algorithm to the challenging task of abdominal aorta segmentation in 3D MRI volumes, and report quantitative evaluations over 30 subjects, which demonstrate that the results correlate well with independent manual segmentations. We further show the use of our method in several other medical applications and demonstrate that, in comparison to a standard level-set optimization, our algorithm is one order of magnitude faster.