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.
While powerful, the RNN-CNN approach requires hand-designing special architecture for each new CRFl one wishes to model. This is a very difficult task, and thus far, other than CRF model with mean field optimization, there are few other examples. The only other example we are aware of is the work of @cite_28 , that describe how to implement a submodular CRF layer within a CNN architecture. Their approach is technically difficult and is limited to submodular functions.
@cite_28
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Can we incorporate discrete optimization algorithms within modern machine learning models? For example, is it possible to use in deep architectures a layer whose output is the minimal cut of a parametrized graph? Given that these models are trained end-to-end by leveraging gradient information, the introduction of such layers seems very challenging due to their non-continuous output. In this paper we focus on the problem of submodular minimization, for which we show that such layers are indeed possible. The key idea is that we can continuously relax the output without sacrificing guarantees. We provide an easily computable approximation to the Jacobian complemented with a complete theoretical analysis. Finally, these contributions let us experimentally learn probabilistic log-supermodular models via a bi-level variational inference formulation.