430 research outputs found

    Discriminative Training of Deep Fully-connected Continuous CRF with Task-specific Loss

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    Recent works on deep conditional random fields (CRF) have set new records on many vision tasks involving structured predictions. Here we propose a fully-connected deep continuous CRF model for both discrete and continuous labelling problems. We exemplify the usefulness of the proposed model on multi-class semantic labelling (discrete) and the robust depth estimation (continuous) problems. In our framework, we model both the unary and the pairwise potential functions as deep convolutional neural networks (CNN), which are jointly learned in an end-to-end fashion. The proposed method possesses the main advantage of continuously-valued CRF, which is a closed-form solution for the Maximum a posteriori (MAP) inference. To better adapt to different tasks, instead of using the commonly employed maximum likelihood CRF parameter learning protocol, we propose task-specific loss functions for learning the CRF parameters. It enables direct optimization of the quality of the MAP estimates during the course of learning. Specifically, we optimize the multi-class classification loss for the semantic labelling task and the Turkey's biweight loss for the robust depth estimation problem. Experimental results on the semantic labelling and robust depth estimation tasks demonstrate that the proposed method compare favorably against both baseline and state-of-the-art methods. In particular, we show that although the proposed deep CRF model is continuously valued, with the equipment of task-specific loss, it achieves impressive results even on discrete labelling tasks

    Revisiting loss-specific training of filter-based MRFs for image restoration

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    It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1) probabilistic learning using sampling-based algorithms and (2) loss-specific training based on MAP estimate. After investigating existing training approaches, it turns out that the performance of the loss-specific training has been significantly underestimated in existing work. In this paper, we revisit this approach and use techniques from bi-level optimization to solve it. We show that we can get a substantial gain in the final performance by solving the lower-level problem in the bi-level framework with high accuracy using our newly proposed algorithm. As a result, our trained model is on par with highly specialized image denoising algorithms and clearly outperforms probabilistically trained MRF models. Our findings suggest that for the loss-specific training scheme, solving the lower-level problem with higher accuracy is beneficial. Our trained model comes along with the additional advantage, that inference is extremely efficient. Our GPU-based implementation takes less than 1s to produce state-of-the-art performance.Comment: 10 pages, 2 figures, appear at 35th German Conference, GCPR 2013, Saarbr\"ucken, Germany, September 3-6, 2013. Proceeding

    iPiano: Inertial Proximal Algorithm for Non-Convex Optimization

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    In this paper we study an algorithm for solving a minimization problem composed of a differentiable (possibly non-convex) and a convex (possibly non-differentiable) function. The algorithm iPiano combines forward-backward splitting with an inertial force. It can be seen as a non-smooth split version of the Heavy-ball method from Polyak. A rigorous analysis of the algorithm for the proposed class of problems yields global convergence of the function values and the arguments. This makes the algorithm robust for usage on non-convex problems. The convergence result is obtained based on the \KL inequality. This is a very weak restriction, which was used to prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic algorithm is proved, and, then iPiano is shown to satisfy the requirements of this theorem. Furthermore, a convergence rate is established for the general problem class. We demonstrate iPiano on computer vision problems: image denoising with learned priors and diffusion based image compression.Comment: 32pages, 7 figures, to appear in SIAM Journal on Imaging Science

    A Data-Driven Regularization Model for Stereo and Flow

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    Data-driven techniques can reliably build semantic correspondence among images. In this paper, we present a new regularization model for stereo or flow through transferring the shape information of the disparity or flow from semantically matched patches in the training database. Compared to previous regularization models based on image appearance alone, we can better resolve local ambiguity of the disparity or flow by considering the semantic information without explicit object modeling. We incorporate this data-driven regularization model into a standard Markov Random Field (MRF) model, inferred with a gradient descent algorithm and learned with a discriminative learning approach. Compared to prior state-of-the-art methods, our full model achieves comparable or better results on the KITTI stereo and flow datasets, and improves results on the Sintel Flow dataset under an online estimation setting.National Science Foundation (U.S.) (CGV 1212849)United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award N00014-09-1-1051
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