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11
Fast approximate energy minimization with label costs
, 2010
"... The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simult ..."
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Cited by 52 (6 self)
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The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simultaneously optimize “label costs ” as well. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution. Our energy is quite general, and we prove optimality bounds for our algorithm. A natural application of label costs is multimodel fitting, and we demonstrate several such applications in vision: homography detection, motion segmentation, and unsupervised image segmentation. Our C++/MATLAB implementation is publicly available.
Energy based multiple model fitting for nonrigid structure from motion
 In Proceedings of IEEE Conference on Computer Vision and Pattern
, 2007
"... In this paper we reformulate the 3D reconstruction of deformable surfaces from monocular video sequences as a labeling problem. We solve simultaneously for the assignment of feature points to multiple local deformation models and the fitting of models to points to minimize a geometric cost, subject ..."
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Cited by 7 (1 self)
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In this paper we reformulate the 3D reconstruction of deformable surfaces from monocular video sequences as a labeling problem. We solve simultaneously for the assignment of feature points to multiple local deformation models and the fitting of models to points to minimize a geometric cost, subject to a spatial constraint that neighboring points should also belong to the same model. Piecewise reconstruction methods rely on features shared between models to enforce global consistency on the 3D surface. To account for this overlap between regions, we consider a superset of the classic labeling problem in which a set of labels, instead of a single one, is assigned to each variable. We propose a mathematical formulation of this new model and show how it can be efficiently optimized with a variant of αexpansion. We demonstrate how this framework can be applied to NonRigid Structure from Motion and leads to simpler explanations of the same data. Compared to existing methods run on the same data, our approach has up to half the reconstruction error, and is more robust to overfitting and outliers. 1.
Automated articulated structure and 3d shape recovery from point correspondences
 In ICCV
, 2011
"... In this paper we propose a new method for the simultaneous segmentation and 3D reconstruction of interest point based articulated motion. We decompose a set of point tracks into rigidbodied overlapping regions which are associated with skeletal links, while joint centres can be derived from the reg ..."
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Cited by 5 (1 self)
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In this paper we propose a new method for the simultaneous segmentation and 3D reconstruction of interest point based articulated motion. We decompose a set of point tracks into rigidbodied overlapping regions which are associated with skeletal links, while joint centres can be derived from the regions of overlap. This allows us to formulate the problem of 3D reconstruction as one of model assignment, where each model corresponds to the motion and shape parameters of an articulated body part. We show how this labelling can be optimised using a combination of preexisting graphcut based inference, and robust structure from motion factorization techniques. The strength of our approach comes from viewing both the decomposition into parts, and the 3D reconstruction as the optimisation of a single cost function, namely the image reprojection error. We show results of full 3D shape recovery on challenging realworld sequences with one or more articulated bodies, in the presence of outliers and missing data. 1.
Interactive Segmentation with SuperLabels
 In Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR
, 2011
"... *authors contributed equally ..."
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DiscreteContinuous Optimization for MultiTarget Tracking
"... The problem of multitarget tracking is comprised of two distinct, but tightly coupled challenges: (i) the naturally discrete problem of data association, i.e. assigning image observations to the appropriate target; (ii) the naturally continuous problem of trajectory estimation, i.e. recovering the ..."
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Cited by 3 (0 self)
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The problem of multitarget tracking is comprised of two distinct, but tightly coupled challenges: (i) the naturally discrete problem of data association, i.e. assigning image observations to the appropriate target; (ii) the naturally continuous problem of trajectory estimation, i.e. recovering the trajectories of all targets. To go beyond simple greedy solutions for data association, recent approaches often perform multitarget tracking using discrete optimization. This has the disadvantage that trajectories need to be precomputed or represented discretely, thus limiting accuracy. In this paper we instead formulate multitarget tracking as a discretecontinuous optimization problem that handles each aspect in its natural domain and allows leveraging powerful methods for multimodel fitting. Data association is performed using discrete optimization with label costs, yielding near optimality. Trajectory estimation is posed as a continuous fitting problem with a simple closedform solution, which is used in turn to update the label costs. We demonstrate the accuracy and robustness of our approach with stateoftheart performance on several standard datasets. 1.
Dense Multibody Motion Estimation and Reconstruction from a Handheld Camera
"... Existing approaches to camera tracking and reconstruction from a single handheld camera for Augmented Reality (AR) focus on the reconstruction of static scenes. However, most real world scenarios are dynamic and contain multiple independently moving rigid objects. This paper addresses the problem of ..."
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Existing approaches to camera tracking and reconstruction from a single handheld camera for Augmented Reality (AR) focus on the reconstruction of static scenes. However, most real world scenarios are dynamic and contain multiple independently moving rigid objects. This paper addresses the problem of simultaneous segmentation, motion estimation and dense 3D reconstruction of dynamic scenes. We propose a dense solution to all three elements of this problem: depth estimation, motion label assignment and rigid transformation estimation directly from the raw video by optimizing a single cost function using a hillclimbing approach. We do not require prior knowledge of the number of objects present in the scene – the number of independent motion models and their parameters are automatically estimated. The resulting inference method combines the best techniques in discrete and continuous optimization: a state of the art variational approach is used to estimate the dense depth maps while the motion segmentation is achieved using discrete graphcut based optimization. For the rigid motion estimation of the independently moving objects we propose a novel tracking approach designed to cope with the small fields of view they induce and agile motion. Our experimental results on real sequences show how accurate segmentations and dense depth maps can be obtained in a completely automated way and used in markerfree AR applications. 1
BoykovJolly Ours
"... user scribbles label 1 appearance models superlabel 1 sublabeling appearance models Fig. 1. Given user scribbles, typical MRF segmentation (BoykovJolly) uses a GMM to model the appearance of each object label. This makes the strong assumption that pixels inside each object are i.i.d. In contrast, ..."
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user scribbles label 1 appearance models superlabel 1 sublabeling appearance models Fig. 1. Given user scribbles, typical MRF segmentation (BoykovJolly) uses a GMM to model the appearance of each object label. This makes the strong assumption that pixels inside each object are i.i.d. In contrast, we define a twolevel MRF to encourage interobject coherence among superlabels and intraobject coherence among sublabels. Abstract. In interactive segmentation, the most common way to model object appearance is by GMM or histogram, while MRFs are used to encourage spatial coherence among the object labels. This makes the strong assumption that pixels within each object are i.i.d. when in fact most objects have multiple distinct appearances and exhibit strong spatial correlation among their pixels. At the very least, this calls for an MRFbased appearance model within each object itself and yet, to the best of our knowledge, such a “twolevel MRF ” has never been proposed. We propose a novel segmentation energy that can model complex appearance. We represent the appearance of each object by a set of distinct spatially coherent models. This results in a twolevel MRF with “superlabels” at the top level that are partitioned into “sublabels ” at the bottom. We introduce the hierarchical Potts (hPotts) prior to govern spatial coherence within each level. Finally, we introduce a novel algorithm with EMstyle alternation of proposal, αexpansion and reestimation steps. Our experiments demonstrate the conceptual and qualitative improvement that a twolevel MRF can provide. We show applications in binary segmentation, multiclass segmentation, and interactive cosegmentation. Finally, our energy and algorithm have interesting interpretations in terms of semisupervised learning. 1
CurvatureBased Regularization for Surface Approximation
"... We propose an energybased framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers. Our energy assigns a tangent plane to each (noisy) data point by minimizing the squared distances to the points and the irregularity of the surface implicitly defined b ..."
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We propose an energybased framework for approximating surfaces from a cloud of point measurements corrupted by noise and outliers. Our energy assigns a tangent plane to each (noisy) data point by minimizing the squared distances to the points and the irregularity of the surface implicitly defined by the tangent planes. In order to avoid the wellknown ”shrinking ” bias associated with firstorder surface regularization, we choose a robust smoothing term that approximates curvature of the underlying surface. In contrast to a number of recent publications estimating curvature using discrete (e.g. binary) labellings with triplecliques we use higherdimensional labels that allows modeling curvature with only pairwise interactions. Hence, many standard optimization algorithms (e.g. message passing, graph cut, etc) can minimize the proposed curvaturebased regularization functional. The accuracy of our approach for representing curvature is demonstrated by theoretical and empirical results on synthetic and real data sets from multiview reconstruction and stereo. 1 1.
Author manuscript, published in "Discrete Geometry for Computer Imagery, Sevilla: Spain (2013)" DOI: 10.1007/9783642370670_21 O(n 3 log n) time complexity for the Optimal Consensus Set computation for Andres and
, 2013
"... Abstract. This paper presents a method for fitting Andres circles as well as 4connected digital circles to a given set of points in 2D images in the presence of noise by maximizing the number of inliers, namely the optimal consensus set, while fixing the thickness. Our approach based on one or seve ..."
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Abstract. This paper presents a method for fitting Andres circles as well as 4connected digital circles to a given set of points in 2D images in the presence of noise by maximizing the number of inliers, namely the optimal consensus set, while fixing the thickness. Our approach based on one or several parameter spaces has a O(n 3 logn) time complexity, O(n) space complexity, n being the number of points, which is lower than previous known methods while still guaranteeing optimal solution(s).
Noname manuscript No. (will be inserted by the editor) Demisting the Hough Transform for 3D Shape Recognition and Registration
"... Abstract InapplyingtheHoughtransformtotheproblem of 3D shape recognition and registration, we develop two new and powerful improvements to this popularinferencemethod.Thefirst, intrinsic Hough,solves the problem of exponential memory requirements of the standard Hough transform by exploiting the spa ..."
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Abstract InapplyingtheHoughtransformtotheproblem of 3D shape recognition and registration, we develop two new and powerful improvements to this popularinferencemethod.Thefirst, intrinsic Hough,solves the problem of exponential memory requirements of the standard Hough transform by exploiting the sparsity of the Hough space. The second, minimumentropy Hough, explains away incorrect votes, substantially reducing the number of modes in the posterior distribution of class and pose, and improving precision. Our experimentsdemonstratethatthesecontributionsmake the Hough transform not only tractable but also highly accurate for our example application. Both contributions can be applied to other tasks that already use the standard Hough transform. 1