Hybrid Gromov-Wasserstein Embedding for Capsule Learning.

Capsule networks (CapsNets) aim to parse images into a hierarchy of objects, parts, and their relationships using a two-step process involving part-whole transformation and hierarchical component routing. However, this hierarchical relationship modeling is computationally expensive, which has limited the wider use of CapsNet despite its potential advantages. The current state of CapsNet models primarily focuses on comparing their performance with capsule baselines, falling short of achieving the same level of proficiency as deep convolutional neural network (CNN) variants in intricate tasks. To address this limitation, we present an efficient approach for learning capsules that surpasses canonical baseline models and even demonstrates superior performance compared with high-performing convolution models. Our contribution can be outlined in two aspects: first, we introduce a group of subcapsules onto which an input vector is projected. Subsequently, we present the hybrid Gromov-Wasserstein (HGW) framework, which initially quantifies the dissimilarity between the input and the components modeled by the subcapsules, followed by determining their alignment degree through optimal transport (OT). This innovative mechanism capitalizes on new insights into defining alignment between the input and subcapsules, based on the similarity of their respective component distributions. This approach enhances CapsNets' capacity to learn from intricate, high-dimensional data while retaining their interpretability and hierarchical structure. Our proposed model offers two distinct advantages: 1) its lightweight nature facilitates the application of capsules to more intricate vision tasks, including object detection; and 2) it outperforms baseline approaches in these demanding tasks. Our empirical findings illustrate that HGW capsules (HGWCapsules) exhibit enhanced robustness against affine transformations, scale effectively to larger datasets, and surpass CNN and CapsNet models across various vision tasks.

GEN: Generative Equivariant Networks for Diverse Image-to-Image Translation.

Image-to-image (I2I) translation has become a key asset for generative adversarial networks. Convolutional neural networks (CNNs), despite having a significant performance, are not able to capture the spatial relationships among different parts of an object and, thus, do not qualify as the ideal representative model for image translation tasks. As a remedy to this problem, capsule networks have been proposed to represent patterns for a visual object in such a way that preserves hierarchical spatial relationships. The training of capsules is constrained by learning all pairwise relationships between capsules of consecutive layers. This design would be prohibitively expensive both in time and memory. In this article, we present a new framework for capsule networks to provide a full description of the input components at various levels of semantics, which can successfully be applied to the generator-discriminator architectures without incurring computational overhead compared to the CNNs. To successfully apply the proposed capsules in the generative adversarial network, we put forth a novel Gromov-Wasserstein (GW) distance as a differentiable loss function that compares the dissimilarity between two distributions and then guides the learned distribution toward target properties, using optimal transport (OT) discrepancy. The proposed method-which is called generative equivariant network (GEN)-is an alternative architecture for GANs with equivariance capsule layers. The proposed model is evaluated through a comprehensive set of experiments on I2I translation and image generation tasks and compared with several state-of-the-art models. Results indicate that there is a principled connection between generative and capsule models that allows extracting discriminant and invariant information from image data.

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).

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.

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.

Bag-Level Aggregation for Multiple-Instance Active Learning in Instance Classification Problems.

A growing number of applications, e.g., video surveillance and medical image analysis, require training recognition systems from large amounts of weakly annotated data, while some targeted interactions with a domain expert are allowed to improve the training process. In such cases, active learning (AL) can reduce labeling costs for training a classifier by querying the expert to provide the labels of most informative instances. This paper focuses on AL methods for instance classification problems in multiple instance learning (MIL), where data are arranged into sets, called bags, which are weakly labeled. Most AL methods focus on single-instance learning problems. These methods are not suitable for MIL problems because they cannot account for the bag structure of data. In this paper, new methods for bag-level aggregation of instance informativeness are proposed for multiple instance AL (MIAL). The aggregated informativeness method identifies the most informative instances based on classifier uncertainty and queries bags incorporating the most information. The other proposed method, called cluster-based aggregative sampling, clusters data hierarchically in the instance space. The informativeness of instances is assessed by considering bag labels, inferred instance labels, and the proportion of labels that remain to be discovered in clusters. Both proposed methods significantly outperform reference methods in extensive experiments using benchmark data from several application domains. Results indicate that using an appropriate strategy to address MIAL problems yields a significant reduction in the number of queries needed to achieve the same level of performance as single-instance AL methods.

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.