Results 1  10
of
52
Halfintegrality based algorithms for cosegmentation of images
 In CVPR
, 2009
"... We study the cosegmentation problem where the objective is to segment the same object (i.e., region) from a pair of images. The segmentation for each image can be cast using a partitioning/segmentation function with an additional constraint that seeks to make the histograms of the segmented regions ..."
Abstract

Cited by 52 (4 self)
 Add to MetaCart
(Show Context)
We study the cosegmentation problem where the objective is to segment the same object (i.e., region) from a pair of images. The segmentation for each image can be cast using a partitioning/segmentation function with an additional constraint that seeks to make the histograms of the segmented regions (based on intensity and texture features) similar. Using Markov Random Field (MRF) energy terms for the simultaneous segmentation of the images together with histogram consistency requirements using the squared L2 (rather than L1) distance, after linearization and adjustments, yields an optimization model with some interesting combinatorial properties. We discuss these properties which are closely related to certain relaxation strategies recently introduced in computer vision. Finally, we show experimental results of the proposed approach. 1.
Practical global optimization for multiview geometry
 IN ECCV
, 2006
"... This paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation, camera resectioning and homography estimation. Unlike traditional methods which may get trapped in local minima due to the noncon ..."
Abstract

Cited by 33 (14 self)
 Add to MetaCart
This paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation, camera resectioning and homography estimation. Unlike traditional methods which may get trapped in local minima due to the nonconvex nature of these problems, this approach provides a theoretical guarantee of global optimality. The formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard L2norm of reprojection errors which is optimal under Gaussian noise as well as the more robust L1norm which is less sensitive to outliers. The efficacy of our algorithm is empirically demonstrated by good performance on experiments for both synthetic and real data. An open source MATLAB toolbox that implements the algorithm is also made available to facilitate further research.
Global Optimization through Rotation Space Search
, 2009
"... This paper introduces a new algorithmic technique for solving certain problems in geometric computer vision. The main novelty of the method is a branchandbound search over rotation space, which is used in this paper to determine camera orientation. By searching over all possible rotations, problem ..."
Abstract

Cited by 32 (7 self)
 Add to MetaCart
This paper introduces a new algorithmic technique for solving certain problems in geometric computer vision. The main novelty of the method is a branchandbound search over rotation space, which is used in this paper to determine camera orientation. By searching over all possible rotations, problems can be reduced to known fixedrotation problems for which optimal solutions have been previously given. In particular, a method is developed for the estimation of the essential matrix, giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors. Recently convex optimization techniques have been shown to provide optimal solutions to many of the common problems in structure from motion. However, they do not apply to problems involving rotations. The search method described in this paper allows such problems to be solved optimally. Apart from the essential matrix, the algorithm is applied to the camera pose problem, providing an optimal algorithm. The approach has been implemented and tested on a number of both synthetically generated and real data sets with good performance.
Optimal algorithms in multiview geometry
 IN: ASIAN CONF. COMPUTER VISION
, 2007
"... This is a survey paper summarizing recent research aimed at finding guaranteed optimal algorithms for solving problems in Multiview Geometry. Many of the traditional problems in Multiview Geometry now have optimal solutions in terms of minimizing residual imageplane error. Success has been achieved ..."
Abstract

Cited by 27 (7 self)
 Add to MetaCart
(Show Context)
This is a survey paper summarizing recent research aimed at finding guaranteed optimal algorithms for solving problems in Multiview Geometry. Many of the traditional problems in Multiview Geometry now have optimal solutions in terms of minimizing residual imageplane error. Success has been achieved in minimizing L2 (leastsquares) or L∞ (smallest maximum error) norm. The main methods involve Second Order Cone Programming, or quasiconvex optimization, and Branchandbound. The paper gives an overview of the subject while avoiding as far as possible the mathematical details, which can be found in the original papers.
Improving numerical accuracy in gröbner basis polynomial equation solvers
 In International Conference on Computer Vision
, 2007
"... This paper presents techniques for improving the numerical stability of Gröbner basis solvers for polynomial equations. Recently Gröbner basis methods have been used succesfully to solve polynomial equations arising in global optimization e.g. three view triangulation and in many important minimal c ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
(Show Context)
This paper presents techniques for improving the numerical stability of Gröbner basis solvers for polynomial equations. Recently Gröbner basis methods have been used succesfully to solve polynomial equations arising in global optimization e.g. three view triangulation and in many important minimal cases of structure from motion. Such methods work extremely well for problems of reasonably low degree, involving a few variables. Currently, the limiting factor in using these methods for larger and more demanding problems is numerical difficulties. In the paper we (i) show how to change basis in the quotient space R[x]/I and propose a strategy for selecting a basis which improves the conditioning of a crucial elimination step, (ii) use this technique to devise a Gröbner basis with improved precision and (iii) show how solving for the eigenvalues instead of eigenvectors can be used to improve precision further while retaining the same speed. We study these methods on some of the latest reported uses of Gröbner basis methods and demonstrate dramatically improved numerical precision using these new techniques making it possible to solve a larger class of problems than previously. 1.
Multiple view geometry under the L∞norm
 IEEE Trans. Pattern Analysis and Machine Intelligence
"... This paper presents a new framework for solving geometric structure and motion problems based on L∞norm. Instead of using the common sumofsquares cost function, that is, the L2norm, the modelfitting errors are measured using the L∞norm. Unlike traditional methods based on L2, our framework all ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
(Show Context)
This paper presents a new framework for solving geometric structure and motion problems based on L∞norm. Instead of using the common sumofsquares cost function, that is, the L2norm, the modelfitting errors are measured using the L∞norm. Unlike traditional methods based on L2, our framework allows for efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as quasiconvex optimization problems within this framework. These problems can be efficiently solved using SecondOrder Cone Programming (SOCP) which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance. 1
A simple solution to the sixpoint twoview focallength problem
 In European Conference on Computer Vision
, 2006
"... National ICT Australia. Abstract. This paper presents a simple and practical solution to the 6point 2view focallength estimation problem. Based on the hiddenvariable technique we have derived a 15th degree polynomial in the unknown focallength. During this course, a simple and constructive algor ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
(Show Context)
National ICT Australia. Abstract. This paper presents a simple and practical solution to the 6point 2view focallength estimation problem. Based on the hiddenvariable technique we have derived a 15th degree polynomial in the unknown focallength. During this course, a simple and constructive algorithm is established. To make use of multiple redundant measurements and then select the best solution, we suggest a kernelvoting scheme. The algorithm has been tested on both synthetic data and real images. Satisfactory results are obtained for both cases. For reference purpose we include our Matlab implementation in the paper, which is quite concise, consisting of 20 lines of code only. The result of this paper will make a small but useful module in many computer vision systems. 1
A practical algorithm for l∞ triangulation with outliers
 In Proc. Conf. Computer Vision and Pattern Recognition
, 2007
"... This paper addresses the problem of robust optimal multiview triangulation. We propose an abstract framework, as well as a practical algorithm, which finds the best 3D reconstruction with guaranteed global optimality even in the presence of outliers. Our algorithm is founded on the theory of LPtyp ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
(Show Context)
This paper addresses the problem of robust optimal multiview triangulation. We propose an abstract framework, as well as a practical algorithm, which finds the best 3D reconstruction with guaranteed global optimality even in the presence of outliers. Our algorithm is founded on the theory of LPtype problem. We have recognized that the L ∞ triangulation is a concrete example of the LPtype problems. We propose a set of nontrivial basis operation subroutines that actually implement the idea. Experiments have validated the effectiveness and efficiency of the proposed algorithm. 1. Backgrounds The triangulation problem. Triangulation is the process of computing 3D structure from known camera matrices.
MultipleView Geometry under the L∞norm
, 2008
"... This paper presents a new framework for solving geometric structure and motion problems based on the L∞norm. Instead of using the common sumofsquares cost function, that is, the L2norm, the modelfitting errors are measured using the L∞norm. Unlike traditional methods based on L2, our framework ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
This paper presents a new framework for solving geometric structure and motion problems based on the L∞norm. Instead of using the common sumofsquares cost function, that is, the L2norm, the modelfitting errors are measured using the L∞norm. Unlike traditional methods based on L2, our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasiconvex optimization problems within this framework. These problems can be efficiently solved using secondorder cone programming (SOCP), which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance.