Calibrating segmentation networks with margin-based label smoothing.

Despite the undeniable progress in visual recognition tasks fueled by deep neural networks, there exists recent evidence showing that these models are poorly calibrated, resulting in over-confident predictions. The standard practices of minimizing the cross-entropy loss during training promote the predicted softmax probabilities to match the one-hot label assignments. Nevertheless, this yields a pre-softmax activation of the correct class that is significantly larger than the remaining activations, which exacerbates the miscalibration problem. Recent observations from the classification literature suggest that loss functions that embed implicit or explicit maximization of the entropy of predictions yield state-of-the-art calibration performances. Despite these findings, the impact of these losses in the relevant task of calibrating medical image segmentation networks remains unexplored. In this work, we provide a unifying constrained-optimization perspective of current state-of-the-art calibration losses. Specifically, these losses could be viewed as approximations of a linear penalty (or a Lagrangian term) imposing equality constraints on logit distances. This points to an important limitation of such underlying equality constraints, whose ensuing gradients constantly push towards a non-informative solution, which might prevent from reaching the best compromise between the discriminative performance and calibration of the model during gradient-based optimization. Following our observations, we propose a simple and flexible generalization based on inequality constraints, which imposes a controllable margin on logit distances. Comprehensive experiments on a variety of public medical image segmentation benchmarks demonstrate that our method sets novel state-of-the-art results on these tasks in terms of network calibration, whereas the discriminative performance is also improved. The code is available at https://github.com/Bala93/MarginLoss.

Adversarial Robustness Via Fisher-Rao Regularization.

Adversarial robustness has become a topic of growing interest in machine learning since it was observed that neural networks tend to be brittle. We propose an information-geometric formulation of adversarial defense and introduce Fire, a new Fisher-Rao regularization for the categorical cross-entropy loss, which is based on the geodesic distance between the softmax outputs corresponding to natural and perturbed input features. Based on the information-geometric properties of the class of softmax distributions, we derive an explicit characterization of the Fisher-Rao Distance (FRD) for the binary and multiclass cases, and draw some interesting properties as well as connections with standard regularization metrics. Furthermore, we verify on a simple linear and Gaussian model, that all Pareto-optimal points in the accuracy-robustness region can be reached by Fire while other state-of-the-art methods fail. Empirically, we evaluate the performance of various classifiers trained with the proposed loss on standard datasets, showing up to a simultaneous 1% of improvement in terms of clean and robust performances while reducing the training time by 20% over the best-performing methods.

State-of-the-art retinal vessel segmentation with minimalistic models.

The segmentation of retinal vasculature from eye fundus images is a fundamental task in retinal image analysis. Over recent years, increasingly complex approaches based on sophisticated Convolutional Neural Network architectures have been pushing performance on well-established benchmark datasets. In this paper, we take a step back and analyze the real need of such complexity. We first compile and review the performance of 20 different techniques on some popular databases, and 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. We then show that a cascaded extension (W-Net) reaches outstanding performance on several popular datasets, still using orders of magnitude less learnable weights than any previously published work. 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 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 enables moderate enhancement of cross-dataset performance, indicating that there is still much room for improvement in this area. Finally, we test our approach on Artery/Vein and vessel segmentation from OCTA imaging problems, where we again achieve results well-aligned with the state-of-the-art, at a fraction of the model complexity available in recent literature. Code to reproduce the results in this paper is released.

Deep Interpretable Classification and Weakly-Supervised Segmentation of Histology Images via Max-Min Uncertainty.

Weakly-supervised learning (WSL) has recently triggered substantial interest as it mitigates the lack of pixel-wise annotations. Given global image labels, WSL methods yield pixel-level predictions (segmentations), which enable to interpret class predictions. Despite their recent success, mostly with natural images, such methods can face important challenges when the foreground and background regions have similar visual cues, yielding high false-positive rates in segmentations, as is the case in challenging histology images. WSL training is commonly driven by standard classification losses, which implicitly maximize model confidence, and locate the discriminative regions linked to classification decisions. Therefore, they lack mechanisms for modeling explicitly non-discriminative regions and reducing false-positive rates. We propose novel regularization terms, which enable the model to seek both non-discriminative and discriminative regions, while discouraging unbalanced segmentations. We introduce high uncertainty as a criterion to localize non-discriminative regions that do not affect classifier decision, and describe it with original Kullback-Leibler (KL) divergence losses evaluating the deviation of posterior predictions from the uniform distribution. Our KL terms encourage high uncertainty of the model when the latter inputs the latent non-discriminative regions. Our loss integrates: (i) a cross-entropy seeking a foreground, where model confidence about class prediction is high; (ii) a KL regularizer seeking a background, where model uncertainty is high; and (iii) log-barrier terms discouraging unbalanced segmentations. Comprehensive experiments and ablation studies over the public GlaS colon cancer data and a Camelyon16 patch-based benchmark for breast cancer show substantial improvements over state-of-the-art WSL methods, and confirm the effect of our new regularizers (our code is publicly available at https://github.com/sbelharbi/deep-wsl-histo-min-max-uncertainty).

Deep Clustering: On the Link Between Discriminative Models and K-Means.

In the context of recent deep clustering studies, discriminative models dominate the literature and report the most competitive performances. These models learn a deep discriminative neural network classifier in which the labels are latent. Typically, they use multinomial logistic regression posteriors and parameter regularization, as is very common in supervised learning. It is generally acknowledged that discriminative objective functions (e.g., those based on the mutual information or the KL divergence) are more flexible than generative approaches (e.g., K-means) in the sense that they make fewer assumptions about the data distributions and, typically, yield much better unsupervised deep learning results. On the surface, several recent discriminative models may seem unrelated to K-means. This study shows that these models are, in fact, equivalent to K-means under mild conditions and common posterior models and parameter regularization. We prove that, for the commonly used logistic regression posteriors, maximizing the L2 regularized mutual information via an approximate alternating direction method (ADM) is equivalent to minimizing a soft and regularized K-means loss. Our theoretical analysis not only connects directly several recent state-of-the-art discriminative models to K-means, but also leads to a new soft and regularized deep K-means algorithm, which yields competitive performance on several image clustering benchmarks.

Benchmark on Automatic 6-month-old Infant Brain Segmentation Algorithms: The iSeg-2017 Challenge.

Accurate segmentation of infant brain magnetic resonance (MR) images into white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) is an indispensable foundation for early studying of brain growth patterns and morphological changes in neurodevelopmental disorders. Nevertheless, in the isointense phase (approximately 6-9 months of age), due to inherent myelination and maturation process, WM and GM exhibit similar levels of intensity in both T1-weighted (T1w) and T2-weighted (T2w) MR images, making tissue segmentation very challenging. Despite many efforts were devoted to brain segmentation, only few studies have focused on the segmentation of 6-month infant brain images. With the idea of boosting methodological development in the community, iSeg-2017 challenge (http://iseg2017.web.unc.edu) provides a set of 6-month infant subjects with manual labels for training and testing the participating methods. Among the 21 automatic segmentation methods participating in iSeg-2017, we review the 8 top-ranked teams, in terms of Dice ratio, modified Hausdorff distance and average surface distance, and introduce their pipelines, implementations, as well as source codes. We further discuss limitations and possible future directions. We hope the dataset in iSeg-2017 and this review article could provide insights into methodological development for the community.

Kernel Clustering: Density Biases and Solutions.

Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the density mode isolation bias in kernel K-means for a common class of kernels. We call it Breiman's bias due to its similarity to the histogram mode isolation previously discovered by Breiman in decision tree learning with Gini impurity. We also extend our analysis to other popular kernel clustering methods, e.g., average/normalized cut or dominant sets, where density biases can take different forms. For example, splitting isolated points by cut-based criteria is essentially the sparsest subset bias, which is the opposite of the density mode bias. Our findings suggest that a principled solution for density biases in kernel clustering should directly address data inhomogeneity. We show that density equalization can be implicitly achieved using either locally adaptive weights or locally adaptive kernels. Moreover, density equalization makes many popular kernel clustering objectives equivalent. Our synthetic and real data experiments illustrate density biases and proposed solutions. We anticipate that theoretical understanding of kernel clustering limitations and their principled solutions will be important for a broad spectrum of data analysis applications across the disciplines.

Quantitative Identification of Nonmuscle-Invasive and Muscle-Invasive Bladder Carcinomas: A Multiparametric MRI Radiomics Analysis.

BACKGROUND: Preoperative discrimination between nonmuscle-invasive bladder carcinomas (NMIBC) and the muscle-invasive ones (MIBC) is very crucial in the management of patients with bladder cancer (BC). PURPOSE: To evaluate the discriminative performance of multiparametric MRI radiomics features for precise differentiation of NMIBC from MIBC, preoperatively. STUDY TYPE: Retrospective, radiomics. POPULATION: Fifty-four patients with postoperative pathologically proven BC lesions (24 in NMIBC and 30 in MIBC groups) were included. FIELD STRENGTH/SEQUENCE: 3.0T MRI/T2 -weighted (T2 W) and multi-b-value diffusion-weighted (DW) sequences. ASSESSMENT: A total of 1104 radiomics features were extracted from carcinomatous regions of interest on T2 W and DW images, and the apparent diffusion coefficient maps. Support vector machine with recursive feature elimination (SVM-RFE) and synthetic minority oversampling technique (SMOTE) were used to construct an optimal discriminative model, and its performance was evaluated and compared with that of using visual diagnoses by experts. STATISTICAL TESTS: Chi-square test and Student's t-test were applied on clinical characteristics to analyze the significant differences between patient groups. RESULTS: Of the 1104 features, an optimal subset involving 19 features was selected from T2 W and DW sequences, which outperformed the other two subsets selected from T2 W or DW sequence in muscle invasion discrimination. The best performance for the differentiation task was achieved by the SVM-RFE+SMOTE classifier, with averaged sensitivity, specificity, accuracy, and area under the curve of receiver operating characteristic of 92.60%, 100%, 96.30%, and 0.9857, respectively, which outperformed the diagnostic accuracy by experts. DATA CONCLUSION: The proposed radiomics approach has potential for the accurate differentiation of muscle invasion in BC, preoperatively. The optimal feature subset selected from multiparametric MR images demonstrated better performance in identifying muscle invasiveness when compared with that from T2 W sequence or DW sequence only. LEVEL OF EVIDENCE: 3 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2019;49:1489-1498.

Local Submodularization for Binary Pairwise Energies.

Many computer vision problems require optimization of binary non-submodular energies. We propose a general optimization framework based on local submodular approximations (LSA). Unlike standard LP relaxation methods that linearize the whole energy globally, our approach iteratively approximates the energy locally. On the other hand, unlike standard local optimization methods (e.g., gradient descent or projection techniques) we use non-linear submodular approximations and optimize them without leaving the domain of integer solutions. We discuss two specific LSA algorithms based on trust region and auxiliary function principles, LSA-TR and LSA-AUX. The proposed methods obtain state-of-the-art results on a wide range of applications such as binary deconvolution, curvature regularization, inpainting, segmentation with repulsion and two types of shape priors. Finally, we discuss a move-making extension to the LSA-TR approach. While our paper is focused on pairwise energies, our ideas extend to higher-order problems. The code is available online.

3D multimodal MRI brain glioma tumor and edema segmentation: a graph cut distribution matching approach.

This study investigates a fast distribution-matching, data-driven algorithm for 3D multimodal MRI brain glioma tumor and edema segmentation in different modalities. We learn non-parametric model distributions which characterize the normal regions in the current data. Then, we state our segmentation problems as the optimization of several cost functions of the same form, each containing two terms: (i) a distribution matching prior, which evaluates a global similarity between distributions, and (ii) a smoothness prior to avoid the occurrence of small, isolated regions in the solution. Obtained following recent bound-relaxation results, the optima of the cost functions yield the complement of the tumor region or edema region in nearly real-time. Based on global rather than pixel wise information, the proposed algorithm does not require an external learning from a large, manually-segmented training set, as is the case of the existing methods. Therefore, the ensuing results are independent of the choice of a training set. Quantitative evaluations over the publicly available training and testing data set from the MICCAI multimodal brain tumor segmentation challenge (BraTS 2012) demonstrated that our algorithm yields a highly competitive performance for complete edema and tumor segmentation, among nine existing competing methods, with an interesting computing execution time (less than 0.5s per image).

Right ventricle segmentation from cardiac MRI: a collation study.

Magnetic Resonance Imaging (MRI), a reference examination for cardiac morphology and function in humans, allows to image the cardiac right ventricle (RV) with high spatial resolution. The segmentation of the RV is a difficult task due to the variable shape of the RV and its ill-defined borders in these images. The aim of this paper is to evaluate several RV segmentation algorithms on common data. More precisely, we report here the results of the Right Ventricle Segmentation Challenge (RVSC), concretized during the MICCAI'12 Conference with an on-site competition. Seven automated and semi-automated methods have been considered, along them three atlas-based methods, two prior based methods, and two prior-free, image-driven methods that make use of cardiac motion. The obtained contours were compared against a manual tracing by an expert cardiac radiologist, taken as a reference, using Dice metric and Hausdorff distance. We herein describe the cardiac data composed of 48 patients, the evaluation protocol and the results. Best results show that an average 80% Dice accuracy and a 1cm Hausdorff distance can be expected from semi-automated algorithms for this challenging task on the datasets, and that an automated algorithm can reach similar performance, at the expense of a high computational burden. Data are now publicly available and the website remains open for new submissions (http://www.litislab.eu/rvsc/).

Left ventricle segmentation in MRI via convex relaxed distribution matching.

A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm requires about 3.87 s for a typical cardiac MRI volume, a speed-up of about five times compared to a standard implementation. We report a performance evaluation over 400 volumes acquired from 20 subjects, which shows that the obtained 3D surfaces correlate with independent manual delineations. We further demonstrate experimentally that (1) the performance of the algorithm is not significantly affected by the choice of the training subject and (2) the shape description we use does not change significantly from one subject to another. These results support the fact that a single subject is sufficient for training the proposed algorithm.

Right ventricle segmentation with probability product kernel constraints.

We propose a fast algorithm for 3D segmentation of the right ventricle (RV) in MRI using shape and appearance constraints based on probability product kernels (PPK). The proposed constraints remove the need for large, manually-segmented training sets and costly pose estimation (or registration) procedures, as is the case of the existing algorithms. We report comprehensive experiments, which demonstrate that the proposed algorithm (i) requires only a single subject for training; and (ii) yields a performance that is not significantly affected by the choice of the training data. Our PPK constraints are non-linear (high-order) functionals, which are not directly amenable to standard optimizers. We split the problem into several surrogate-functional optimizations, each solved via an efficient convex relaxation that is amenable to parallel implementations. We further introduce a scale variable that we optimize with fast fixed-point computations, thereby achieving pose invariance in real-time. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm can yield a real-time solution for typical cardiac MRI volumes, with a speed-up of more than 20 times compared to the CPU version. We report a comprehensive experimental validations over 400 volumes acquired from 20 subjects, and demonstrate that the obtained 3D surfaces correlate with independent manual delineations.

Effective level set image segmentation with a kernel induced data term.

This study investigates level set multiphase image segmentation by kernel mapping and piecewise constant modeling of the image data thereof. A kernel function maps implicitly the original data into data of a higher dimension so that the piecewise constant model becomes applicable. This leads to a flexible and effective alternative to complex modeling of the image data. The method uses an active curve objective functional with two terms: an original term which evaluates the deviation of the mapped image data within each segmentation region from the piecewise constant model and a classic length regularization term for smooth region boundaries. Functional minimization is carried out by iterations of two consecutive steps: 1) minimization with respect to the segmentation by curve evolution via Euler-Lagrange descent equations and 2) minimization with respect to the regions parameters via fixed point iterations. Using a common kernel function, this step amounts to a mean shift parameter update. We verified the effectiveness of the method by a quantitative and comparative performance evaluation over a large number of experiments on synthetic images, as well as experiments with a variety of real images such as medical, satellite, and natural images, as well as motion maps.