Publications

2021

1. NeurIPS

   Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyond

   Đ.Khuê Lê-Huu, Karteek Alahari

   In Advances in Neural Information Processing Systems 2021

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   We introduce regularized Frank-Wolfe, a general and effective algorithm for inference and learning of dense conditional random fields (CRFs). The algorithm optimizes a nonconvex continuous relaxation of the CRF inference problem using vanilla Frank-Wolfe with approximate updates, which are equivalent to minimizing a regularized energy function. Our proposed method is a generalization of existing algorithms such as mean field or concave-convex procedure. This perspective not only offers a unified analysis of these algorithms, but also allows an easy way of exploring different variants that potentially yield better performance. We illustrate this in our empirical results on standard semantic segmentation datasets, where several instantiations of our regularized Frank-Wolfe outperform mean field inference, both as a standalone component and as an end-to-end trainable layer in a neural network. We also show that dense CRFs, coupled with our new algorithms, produce significant improvements over strong CNN baselines.

2019

1. PhD Thesis

   Nonconvex Alternating Direction Optimization for Graphs: Inference and Learning

   Đ.Khuê Lê-Huu

   2019

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2018

1. CVPR

   Continuous Relaxation of MAP Inference: A Nonconvex Perspective

   Đ.Khuê Lê-Huu, Nikos Paragios

   In IEEE Conference on Computer Vision and Pattern Recognition 2018

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   In this paper, we study a nonconvex continuous relaxation of MAP inference in discrete Markov random fields (MRFs). We show that for arbitrary MRFs, this relaxation is tight, and a discrete stationary point of it can be easily reached by a simple block coordinate descent algorithm. In addition, we study the resolution of this relaxation using popular gradient methods, and further propose a more effective solution using a multilinear decomposition framework based on the alternating direction method of multipliers (ADMM). Experiments on many real-world problems demonstrate that the proposed ADMM significantly outperforms other nonconvex relaxation based methods, and compares favorably with state of the art MRF optimization algorithms in different settings.

2017

1. CVPR

   Alternating Direction Graph Matching

   Đ.Khuê Lê-Huu, Nikos Paragios

   In IEEE Conference on Computer Vision and Pattern Recognition 2017

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   In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a decomposition of the matching constraints. Graph matching is then reformulated as a non-convex non-separable optimization problem that can be split into smaller and much-easier-to-solve subproblems, by means of the alternating direction method of multipliers. The proposed framework is modular, scalable, and can be instantiated into different variants. Two instantiations are studied exploring pairwise and higher-order constraints. Experimental results on widely adopted benchmarks involving synthetic and real examples demonstrate that the proposed solutions outperform existing pairwise graph matching methods, and competitive with the state of the art in higher-order settings.

2014

1. Dual decomposition with accelerated first-order scheme for discrete markov random field optimization

   Đ.Khuê Lê-Huu

   Technical report 2014

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   The problem of discrete Markov Random Field optimization, or MAP inference, can be reformulated as an integer linear program (ILP), which is NP-Hard in general. A usual method to approximately solve this ILP is to relax the integral constraints. Many MAP inference methods have been based on this linear programming relaxation. In this work, we propose a new decomposition scheme to solve the dual of this relaxed linear program, where the dependencies between any two nodes of the graph are relaxed using Lagrangian relaxation. Since the dual function is non-differentiable, subgradient methods are first used. The application on a stereo vision problem shows that the convergence rate of these methods, which is O(1/ε^2) in theory, is not practical. Therefore, we smooth the dual using Nesterov’s method and then use optimal first-order gradient methods to optimize the obtained smooth function, which result in a better convergence rate of O(1/ε). The method can handle any graph structures with arbitrary potential functions. As an application, a new MRF model for locally affine image registration is proposed.

2013

1. An Active Contour Model with Improved Shape Priors using Fourier Descriptors

   Fareed Ahmed, Đ.Khuê Lê-Huu, Julien Olivier, Romuald Boné

   In VISAPP 2013

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   Snakes or active contours are widely used for image segmentation. There are many different implementationsof snakes. No matter which implementation is being employed, the segmentation results suffer greatly inpresence of occlusions, noise, concavities or abnormal modification of shape. If some prior knowledge aboutthe shape of the object is available, then its addition to an existing model can greatly improve the segmentationresults. In this work inclusion of such shape constraints for explicit active contours is presented. Theseshape priors are introduced through the use of Fourier based descriptors which makes them invariant to thetranslation, scaling and rotation factors and enables the deformable model to converge towards the prior shapeeven in the presence of occlusion and context noise. These shape constraints have been computed in descriptorspace so no reconstruction is required. Experimental results clearly indicate that the inclusion of these shapepriors greatly improved the segmentation results in comparison with the original snake model.