Coarse-to-Fine Minimization of Some Common Nonconvexities

Mobahi, Hossein; Fisher, John W.

doi:10.1007/978-3-319-14612-6_6

Cited by 6 publications

(8 citation statements)

References 26 publications

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“…To deal with more severe nuisances, several works [60,109] proposed to use discontinuous functions, such as ℓ 0 or inlier count. Instead of using a single function, many works propose to use continuation methods to deform the cost function as the optimization progresses in order to increase robustness and reduce the chance of getting caught in bad local minima [16,72]. In practice, however, it is a challenge to decide which penalty function is suitable for the problem at hand.…”

Section: Optimization In Computer Visionmentioning

confidence: 99%

Discriminative Optimization: Theory and Applications to Computer Vision

Vongkulbhisal

Torre

Costeira

2019

IEEE Trans. Pattern Anal. Mach. Intell.

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Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: designing a cost function with a local optimum at an acceptable solution, and developing an efficient numerical method to search for this optimum. While designing such functions is feasible in the noiseless case, the stability and location of local optima are mostly unknown under noise, occlusion, or missing data. In practice, this can result in undesirable local optima or not having a local optimum in the expected place. On the other hand, numerical optimization algorithms in high-dimensional spaces are typically local and often rely on expensive first or second order information to guide the search. To overcome these limitations, we propose Discriminative Optimization (DO), a method that learns search directions from data without the need of a cost function. DO explicitly learns a sequence of updates in the search space that leads to stationary points that correspond to the desired solutions. We provide a formal analysis of DO and illustrate its benefits in the problem of 3D registration, camera pose estimation, and image denoising. We show that DO outperformed or matched state-of-the-art algorithms in terms of accuracy, robustness, and computational efficiency.

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Section: Optimization In Computer Visionmentioning

confidence: 99%

Discriminative Optimization: Theory and Applications to Computer Vision

Vongkulbhisal

Torre

Costeira

2019

IEEE Trans. Pattern Anal. Mach. Intell.

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“…However, without additional heuristics such as restricting the finer solution to be around the solution of the coarse problem, there is no guarantee that coarse structure is preserved when solving the finer problem. Recently, [33] provided analysis and derived closed form solutions for the smoothing of the objective in problems of point cloud matching. Our method uses a single energy integrating over a continuum of scales in parallel, rather than a sequential approach where multiple energies from coarse to fine are solved.…”

Section: Related Workmentioning

confidence: 99%

“…First, most segmentation methods (e.g., [6,25,2]) based on scale spaces consider global scale spaces that are computed on the whole image, which does not capture the fact that there exist multiple regions of the segmentation at different scales, and this could lead to the removal and/or displacement of important structures in the image, for instance, when large structures are blurred across small ones, leading to an inaccurate segmentation. Second, algorithms that use a coarse-to-fine principle (e.g., [5,33]) do so sequentially (see Figure 1) so that the algorithm operates at the coarser scale and then uses the result to initialize computation at a finer scale. While this warm start may influence the finer scale result, there is no guarantee that the coarse structure of the segmentation is preserved in the final solution.…”

Section: Introductionmentioning

confidence: 99%

Coarse-to-Fine Segmentation with Shape-Tailored Continuum Scale Spaces

Khan

Hong

Yezzi

et al. 2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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“…However, without additional heuristics such as restricting the finer solution to be around the solution of the coarse problem, there is no guarantee that coarse structure is preserved when solving the finer problem. Recently, [10] provided analysis and derived closed form solutions for the smoothing of the objective in problems of point cloud matching. Our method uses a single energy integrating over a continuum of scales in parallel, and we optimize this energy directly.…”

Section: Related Workmentioning

confidence: 99%

“…First, most segmentation methods (e.g., [5,6,7,8]) based on scale spaces consider scale spaces that are globally computed on the whole image, which does not capture the fact that there exist multiple regions of the segmentation at different scales, and this could lead to the removal and/or displacement of important structures in the image, for instance, when large structures are blurred across small ones, leading to an inaccurate segmentation. Second, algorithms that use a coarse-to-fine principle (e.g., [9,10]) do so sequentially (see Figure 2) so that the algorithm operates at the coarser scale and then uses the result to initialize computation at a finer scale. While this warm start may influence the finer scale result, there is no guarantee that the coarse structure of the segmentation is preserved in the final solution.…”

Section: Introductionmentioning

confidence: 99%

Coarse-to-Fine Segmentation With Shape-Tailored Scale Spaces

Sundaramoorthi¹,

Khan²,

Hong³

2016

Preprint

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We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.

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Coarse-to-Fine Minimization of Some Common Nonconvexities

Cited by 6 publications

References 26 publications

Discriminative Optimization: Theory and Applications to Computer Vision

Discriminative Optimization: Theory and Applications to Computer Vision

Coarse-to-Fine Segmentation with Shape-Tailored Continuum Scale Spaces

Coarse-to-Fine Segmentation With Shape-Tailored Scale Spaces

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