Combining CNN with CRF for modeling dependencies between pixel labels is a popular research direction. This task is far from trivial, especially if end-to-end training is desired. In this paper, we propose a novel simple approach to CNN+CRF combination. In particular, we propose to simulate a CRF regularizer with a trainable module that has standard CNN architecture. We call this module a CRF Simulator. We can automatically generate an unlimited amount of ground truth for training such CRF Simulator without any user interaction, provided we have an efficient algorithm for optimization of the actual CRF regularizer. After our CRF Simulator is trained, it can be directly incorporated as part of any larger CNN architecture, enabling a seamless end-to-end training. In particular, the other modules can learn parameters that are more attuned to the performance of the CRF Simulator module. We demonstrate the effectiveness of our approach on the task of salient object segmentation regularized with the standard binary CRF energy. In contrast to previous work we do not need to develop and implement the complex mechanics of optimizing a specific CRF as part of CNN. In fact, our approach can be easily extended to other CRF energies, including multi-label. To the best of our knowledge we are the first to study the question of whether the output of CNNs can have regularization properties of CRFs.
An alternative approach is to incorporate regularization directly into the loss function. For example the approach in @cite_8 incorporates normalized cut regularization into the loss function for the problem of weakly supervised learning. However, incorporating length regularization into loss during fully supervised learning suprisingly leads to inferior performance compared with unregularized loss function Private communication with the authors , also confirmed by our experiments.
@cite_8
2963687373 2909986471 2963198662 2151532749
Minimization of regularized losses is a principled approach to weak supervision well-established in deep learning, in general. However, it is largely overlooked in semantic segmentation currently dominated by methods mimicking full supervision via “fake” fully-labeled masks (proposals) generated from available partial input. To obtain such full masks the typical methods explicitly use standard regularization techniques for “shallow” segmentation, e.g. graph cuts or dense CRFs. In contrast, we integrate such standard regularizers directly into the loss functions over partial input. This approach simplifies weakly-supervised training by avoiding extra MRF CRF inference steps or layers explicitly generating full masks, while improving both the quality and efficiency of training. This paper proposes and experimentally compares different losses integrating MRF CRF regularization terms. We juxtapose our regularized losses with earlier proposal-generation methods. Our approach achieves state-of-the-art accuracy in semantic segmentation with near full-supervision quality. The recently proposed semi-supervised learning methods exploit consistency loss between different predictions under random perturbations. Typically, a student model is trained to predict consistently with the targets generated by a noisy teacher. However, they ignore the fact that not all training data provide meaningful and reliable information in terms of consistency. For misclassified data, blindly minimizing the consistency loss around them can hinder learning. In this paper, we propose a novel certainty-driven consistency loss (CCL) to dynamically select data samples that have relatively low uncertainty. Specifically, we measure the variance or entropy of multiple predictions under random augmentations and dropout as an estimation of uncertainty. Then, we introduce two approaches, i.e. Filtering CCL and Temperature CCL to guide the student learn more meaningful and certain reliable targets, and hence improve the quality of the gradients backpropagated to the student. Experiments demonstrate the advantages of the proposed method over the state-of-the-art semi-supervised deep learning methods on three benchmark datasets: SVHN, CIFAR10, and CIFAR100. Our method also shows robustness to noisy labels. Most recent semantic segmentation methods train deep convolutional neural networks with fully annotated masks requiring pixel-accuracy for good quality training. Common weakly-supervised approaches generate full masks from partial input (e.g. scribbles or seeds) using standard interactive segmentation methods as preprocessing. But, errors in such masks result in poorer training since standard loss functions (e.g. cross-entropy) do not distinguish seeds from potentially mislabeled other pixels. Inspired by the general ideas in semi-supervised learning, we address these problems via a new principled loss function evaluating network output with criteria standard in "shallow" segmentation, e.g. normalized cut. Unlike prior work, the cross entropy part of our loss evaluates only seeds where labels are known while normalized cut softly evaluates consistency of all pixels. We focus on normalized cut loss where dense Gaussian kernel is efficiently implemented in linear time by fast Bilateral filtering. Our normalized cut loss approach to segmentation brings the quality of weakly-supervised training significantly closer to fully supervised methods. Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, @math -loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers.