Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions

This study investigates the optimization aspects of imposing hard inequality constraints on the outputs of CNNs. In the context of deep networks, constraints are commonly handled with penalties for their simplicity, and despite their well-known limitations. Lagrangian-dual optimization has been largely avoided, except for a few recent works, mainly due to the computational complexity and stability/convergence issues caused by alternating explicit dual updates/projections and stochastic optimization. Several studies showed that, surprisingly for deep CNNs, the theoretical and practical advantages of Lagrangian optimization over penalties do not materialize in practice. We propose log-barrier extensions, which approximate Lagrangian optimization of constrained-CNN problems with a sequence of unconstrained losses. Unlike standard interior-point and log-barrier methods, our formulation does not need an initial feasible solution. Furthermore, we provide a new technical result, which shows that the proposed extensions yield an upper bound on the duality gap. This generalizes the duality-gap result of standard log-barriers, yielding sub-optimality certificates for feasible solutions. While sub-optimality is not guaranteed for non-convex problems, our result shows that log-barrier extensions are a principled way to approximate Lagrangian optimization for constrained CNNs via implicit dual variables. We report comprehensive weakly supervised segmentation experiments, with various constraints, showing that our formulation outperforms substantially the existing constrained-CNN methods, both in terms of accuracy, constraint satisfaction and training stability, more so when dealing with a large number of constraints

Curriculum semi-supervised segmentation

This study investigates a curriculum-style strategy for semi-supervised CNN segmentation, which devises a regression network to learn image-level information such as the size of a target region. These regressions are used to effectively regularize the segmentation network, constraining softmax predictions of the unlabeled images to match the inferred label distributions. Our framework is based on inequality constraints that tolerate uncertainties with inferred knowledge, e.g., regressed region size, and can be employed for a large variety of region attributes. We evaluated our proposed strategy for left ventricle segmentation in magnetic resonance images (MRI), and compared it to standard proposal-based semi-supervision strategies. Our strategy leverages unlabeled data in more efficiently, and achieves very competitive results, approaching the performance of full-supervision.Comment: Accepted as paper as MICCAI 2O1

Discovering Class-Specific Pixels for Weakly-Supervised Semantic Segmentation

We propose an approach to discover class-specific pixels for the weakly-supervised semantic segmentation task. We show that properly combining saliency and attention maps allows us to obtain reliable cues capable of significantly boosting the performance. First, we propose a simple yet powerful hierarchical approach to discover the class-agnostic salient regions, obtained using a salient object detector, which otherwise would be ignored. Second, we use fully convolutional attention maps to reliably localize the class-specific regions in a given image. We combine these two cues to discover class-specific pixels which are then used as an approximate ground truth for training a CNN. While solving the weakly supervised semantic segmentation task, we ensure that the image-level classification task is also solved in order to enforce the CNN to assign at least one pixel to each object present in the image. Experimentally, on the PASCAL VOC12 val and test sets, we obtain the mIoU of 60.8% and 61.9%, achieving the performance gains of 5.1% and 5.2% compared to the published state-of-the-art results. The code is made publicly available

Seed, Expand and Constrain: Three Principles for Weakly-Supervised Image Segmentation

We introduce a new loss function for the weakly-supervised training of semantic image segmentation models based on three guiding principles: to seed with weak localization cues, to expand objects based on the information about which classes can occur in an image, and to constrain the segmentations to coincide with object boundaries. We show experimentally that training a deep convolutional neural network using the proposed loss function leads to substantially better segmentations than previous state-of-the-art methods on the challenging PASCAL VOC 2012 dataset. We furthermore give insight into the working mechanism of our method by a detailed experimental study that illustrates how the segmentation quality is affected by each term of the proposed loss function as well as their combinations.Comment: ECCV 201

From Image-level to Pixel-level Labeling with Convolutional Networks

We are interested in inferring object segmentation by leveraging only object class information, and by considering only minimal priors on the object segmentation task. This problem could be viewed as a kind of weakly supervised segmentation task, and naturally fits the Multiple Instance Learning (MIL) framework: every training image is known to have (or not) at least one pixel corresponding to the image class label, and the segmentation task can be rewritten as inferring the pixels belonging to the class of the object (given one image, and its object class). We propose a Convolutional Neural Network-based model, which is constrained during training to put more weight on pixels which are important for classifying the image. We show that at test time, the model has learned to discriminate the right pixels well enough, such that it performs very well on an existing segmentation benchmark, by adding only few smoothing priors. Our system is trained using a subset of the Imagenet dataset and the segmentation experiments are performed on the challenging Pascal VOC dataset (with no fine-tuning of the model on Pascal VOC). Our model beats the state of the art results in weakly supervised object segmentation task by a large margin. We also compare the performance of our model with state of the art fully-supervised segmentation approaches.Comment: CVPR201