Performance Metrics for Probabilistic Ordinal Classifiers

Ordinal classification models assign higher penalties to predictions further away from the true class. As a result, they are appropriate for relevant diagnostic tasks like disease progression prediction or medical image grading. The consensus for assessing their categorical predictions dictates the use of distance-sensitive metrics like the Quadratic-Weighted Kappa score or the Expected Cost. However, there has been little discussion regarding how to measure performance of probabilistic predictions for ordinal classifiers. In conventional classification, common measures for probabilistic predictions are Proper Scoring Rules (PSR) like the Brier score, or Calibration Errors like the ECE, yet these are not optimal choices for ordinal classification. A PSR named Ranked Probability Score (RPS), widely popular in the forecasting field, is more suitable for this task, but it has received no attention in the image analysis community. This paper advocates the use of the RPS for image grading tasks. In addition, we demonstrate a counter-intuitive and questionable behavior of this score, and propose a simple fix for it. Comprehensive experiments on four large-scale biomedical image grading problems over three different datasets show that the RPS is a more suitable performance metric for probabilistic ordinal predictions. Code to reproduce our experiments can be found at https://github.com/agaldran/prob_ord_metrics .Comment: Accepted to MICCAI 202

Visibility Recovery on Images Acquired in Attenuating Media. Application to Underwater, Fog, and Mammographic Imaging

When acquired in attenuating media, digital images often suffer from a particularly complex degradation that reduces their visual quality, hindering their suitability for further computational applications, or simply decreasing the visual pleasantness for the user. In these cases, mathematical image processing reveals itself as an ideal tool to recover some of the information lost during the degradation process. In this dissertation, we deal with three of such practical scenarios in which this problematic is specially relevant, namely, underwater image enhancement, fog removal and mammographic image processing. In the case of digital mammograms, X-ray beams traverse human tissue, and electronic detectors capture them as they reach the other side. However, the superposition on a bidimensional image of three-dimensional structures produces lowcontrasted images in which structures of interest suffer from a diminished visibility, obstructing diagnosis tasks. Regarding fog removal, the loss of contrast is produced by the atmospheric conditions, and white colour takes over the scene uniformly as distance increases, also reducing visibility. For underwater images, there is an added difficulty, since colour is not lost uniformly; instead, red colours decay the fastest, and green and blue colours typically dominate the acquired images. To address all these challenges, in this dissertation we develop new methodologies that rely on: a) physical models of the observed degradation, and b) the calculus of variations. Equipped with this powerful machinery, we design novel theoretical and computational tools, including image-dependent functional energies that capture the particularities of each degradation model. These energies are composed of different integral terms that are simultaneously minimized by means of efficient numerical schemes, producing a clean, visually-pleasant and useful output image, with better contrast and increased visibility. In every considered application, we provide comprehensive qualitative (visual) and quantitative experimental results to validate our methods, confirming that the developed techniques outperform other existing approaches in the literature

The Devil is in the Margin: Margin-based Label Smoothing for Network Calibration

In spite of the dominant performances of deep neural networks, recent works have shown that they are poorly calibrated, resulting in over-confident predictions. Miscalibration can be exacerbated by overfitting due to the minimization of the cross-entropy during training, as it promotes the predicted softmax probabilities to match the one-hot label assignments. This yields a pre-softmax activation of the correct class that is significantly larger than the remaining activations. Recent evidence from the literature suggests that loss functions that embed implicit or explicit maximization of the entropy of predictions yield state-of-the-art calibration performances. 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) 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 image classification, semantic segmentation and NLP benchmarks demonstrate that our method sets novel state-of-the-art results on these tasks in terms of network calibration, without affecting the discriminative performance. The code is available at https://github.com/by-liu/MbLS .Comment: To Appear at CVPR 2022. Code: https://github.com/by-liu/MbL

Class Adaptive Network Calibration

Recent studies have revealed that, beyond conventional accuracy, calibration should also be considered for training modern deep neural networks. To address miscalibration during learning, some methods have explored different penalty functions as part of the learning objective, alongside a standard classification loss, with a hyper-parameter controlling the relative contribution of each term. Nevertheless, these methods share two major drawbacks: 1) the scalar balancing weight is the same for all classes, hindering the ability to address different intrinsic difficulties or imbalance among classes; and 2) the balancing weight is usually fixed without an adaptive strategy, which may prevent from reaching the best compromise between accuracy and calibration, and requires hyper-parameter search for each application. We propose Class Adaptive Label Smoothing (CALS) for calibrating deep networks, which allows to learn class-wise multipliers during training, yielding a powerful alternative to common label smoothing penalties. Our method builds on a general Augmented Lagrangian approach, a well-established technique in constrained optimization, but we introduce several modifications to tailor it for large-scale, class-adaptive training. Comprehensive evaluation and multiple comparisons on a variety of benchmarks, including standard and long-tailed image classification, semantic segmentation, and text classification, demonstrate the superiority of the proposed method. The code is available at https://github.com/by-liu/CALS.Comment: Code: https://github.com/by-liu/CAL

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.Comment: Under review. The code is available at https://github.com/Bala93/MarginLoss. arXiv admin note: substantial text overlap with arXiv:2111.1543

The Little W-Net That Could: State-of-the-Art Retinal Vessel Segmentation with Minimalistic Models

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

Automatic Red-Channel underwater image restoration.

Underwater images typically exhibit color distortion and low contrast as a result of the exponential decay that light suffers as it travels. Moreover, colors associated to different wavelengths have different attenuation rates, being the red wavelength the one that attenuates the fastest. To restore underwater images, we propose a Red Channel method, where colors associated to short wavelengths are recovered, as expected for underwater images, leading to a recovery of the lost contrast. The Red Channel method can be interpreted as a variant of the Dark Channel method used for images degraded by the atmosphere when exposed to haze. Experimental results show that our technique handles gracefully artificially illuminated areas, and achieves a natural color correction and superior or equivalent visibility improvement when compared to other state-of-the-art methods