CVPR 2014 Oral Talks
TechTalks from event: CVPR 2014 Oral Talks
Orals 4E : Optimization Methods
Second-Order Shape Optimization for Geometric Inverse Problems in VisionWe develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through an approximation of the shape Hessian, which is generally hard to compute and suffers from a series of degeneracies. Our analysis highlights the role of mean curvature motion in comparison with first-order schemes: instead of surface area, our approach penalizes deformation, either by its Dirichlet energy or total variation, and hence does not suffer from shrinkage. The latter regularizer sparks the development of an alternating direction method of multipliers on triangular meshes. Therein, a conjugate-gradient solver enables us to bypass formation of the Gaussian normal equations appearing in the course of the overall optimization. We combine all of these ideas in a versatile geometric variation-regularized Levenberg-Marquardt-type method applicable to a variety of shape functionals, depending on intrinsic properties of the surface such as normal field and curvature as well as its embedding into space. Promising experimental results are reported.
l0 Norm Based Dictionary Learning by Proximal Methods with Global ConvergenceSparse coding and dictionary learning have seen their applications in many vision tasks, which usually is formulated as a non-convex optimization problem. Many iterative methods have been proposed to tackle such an optimization problem. However, it remains an open problem to have a method that is not only practically fast but also is globally convergent. In this paper, we proposed a fast proximal method for solving `0 norm based dictionary learning problems, and we proved that the whole sequence generated by the proposed method converges to a stationary point with sub-linear convergence rate. The benefit of having a fast and convergent dictionary learning method is demonstrated in the applications of image recovery and face recognition.
Adaptive Partial Differential Equation Learning for Visual Saliency DetectionPartial Differential Equations (PDEs) have been successful in solving many low-level vision tasks. However, it is a challenging task to directly utilize PDEs for visual saliency detection due to the difficulty in incorporating human perception and high-level priors to a PDE system. Instead of designing PDEs with fixed formulation and boundary condition, this paper proposes a novel framework for adaptively learning a PDE system from an image for visual saliency detection. We assume that the saliency of image elements can be carried out from the relevances to the saliency seeds (i.e., the most representative salient elements). In this view, a general Linear Elliptic System with Dirichlet boundary (LESD) is introduced to model the diffusion from seeds to other relevant points. For a given image, we first learn a guidance map to fuse human prior knowledge to the diffusion system. Then by optimizing a discrete submodular function constrained with this LESD and a uniform matroid, the saliency seeds (i.e., boundary conditions) can be learnt for this image, thus achieving an optimal PDE system to model the evolution of visual saliency. Experimental results on various challenging image sets show the superiority of our proposed learning-based PDEs for visual saliency detection.
Robust Orthonormal Subspace Learning: Efficient Recovery of Corrupted Low-rank MatricesLow-rank matrix recovery from a corrupted observation has many applications in computer vision. Conventional methods address this problem by iterating between nuclear norm minimization and sparsity minimization. However, iterative nuclear norm minimization is computationally prohibitive for large-scale data (e.g., video) analysis. In this paper, we propose a Robust Orthogonal Subspace Learning (ROSL) method to achieve efficient low-rank recovery. Our intuition is a novel rank measure on the low-rank matrix that imposes the group sparsity of its coefficients under orthonormal subspace. We present an efficient sparse coding algorithm to minimize this rank measure and recover the low-rank matrix at quadratic complexity of the matrix size. We give theoretical proof to validate that this rank measure is lower bounded by nuclear norm and it has the same global minimum as the latter. To further accelerate ROSL to linear complexity, we also describe a faster version (ROSL+) empowered by random sampling. Our extensive experiments demonstrate that both ROSL and ROSL+ provide superior efficiency against the state-of-the-art methods at the same level of recovery accuracy.