Results 1  10
of
52
Global Stereo Reconstruction under Second Order Smoothness Priors
"... Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express t ..."
Abstract

Cited by 127 (8 self)
 Add to MetaCart
Secondorder priors on the smoothness of 3D surfaces are a better model of typical scenes than firstorder priors. However, stereo reconstruction using global inference algorithms, such as graphcuts, has not been able to incorporate secondorder priors because the triple cliques needed to express them yield intractable (nonsubmodular) optimization problems. This paper shows that inference with triple cliques can be effectively optimized. Our optimization strategy is a development of recent extensions to αexpansion, based on the “QPBO ” algorithm [5, 14, 26]. The strategy is to repeatedly merge proposal depth maps using a novel extension of QPBO. Proposal depth maps can come from any source, for example frontoparallel planes as in αexpansion, or indeed any existing stereo algorithm, with arbitrary parameter settings. Experimental results demonstrate the usefulness of the secondorder prior and the efficacy of our optimization framework. An implementation of our stereo framework is available online [34].
Feature Correspondence via Graph Matching: Models and Global Optimization
"... Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate th ..."
Abstract

Cited by 120 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion, such as points extracted from a pair of images containing a human figure in distinct poses. We formulate this matching task as an energy minimization problem by defining a complex objective function of the appearance and the spatial arrangement of the features. Optimization of this energy is an instance of graph matching, which is in general a NPhard problem. We describe a novel graph matching optimization technique, which we refer to as dual decomposition (DD), and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms. In the majority of our examples DD is able to find the global minimum within a minute. The ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples. We show on several matching tasks that our learned model yields results superior to those of stateoftheart methods. 1
Fusion Moves for Markov Random Field Optimization
"... The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combi ..."
Abstract

Cited by 68 (5 self)
 Add to MetaCart
(Show Context)
The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph cut based algorithms (socalled QPBOgraph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph cut approaches, which allows them to be used as building block within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads; 2) for fast MRF optimization by combining cheaptocompute solutions; and 3) for the optimization of highly nonconvex continuouslabeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation).
FusionFlow: DiscreteContinuous Optimization for Optical Flow Estimation
, 2008
"... Accurate estimation of optical flow is a challenging task, which often requires addressing difficult energy optimization problems. To solve them, most topperforming methods rely on continuous optimization algorithms. The modeling accuracy of the energy in this case is often traded for its tractabil ..."
Abstract

Cited by 57 (7 self)
 Add to MetaCart
(Show Context)
Accurate estimation of optical flow is a challenging task, which often requires addressing difficult energy optimization problems. To solve them, most topperforming methods rely on continuous optimization algorithms. The modeling accuracy of the energy in this case is often traded for its tractability. This is in contrast to the related problem of narrowbaseline stereo matching, where the topperforming methods employ powerful discrete optimization algorithms such as graph cuts and messagepassing to optimize highly nonconvex energies. In this paper, we demonstrate how similar nonconvex energies can be formulated and optimized discretely in the context of optical flow estimation. Starting with a set of candidate solutions that are produced by fast continuous flow estimation algorithms, the proposed method iteratively fuses these candidate solutions by the computation of minimum cuts on graphs. The obtained continuousvalued fusion result is then further improved using local gradient descent. Experimentally, we demonstrate that the proposed energy is an accurate model and that the proposed discretecontinuous optimization scheme not only finds lower energy solutions than traditional discrete or continuous optimization techniques, but also leads to flow estimates that outperform the current stateoftheart.
Geos: Geodesic image segmentation
 ECCV '08 PROCEEDINGS OF THE 10TH EUROPEAN CONFERENCE ON COMPUTER VISION: PART I
, 2008
"... Abstract. This paper presents GeoS, a new algorithm for the efficient segmentation of ndimensional image and video data. The segmentation problem is cast as approximate energy minimization in a conditional random field. A new, parallel filtering operator built upon efficient geodesic distance compu ..."
Abstract

Cited by 47 (4 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents GeoS, a new algorithm for the efficient segmentation of ndimensional image and video data. The segmentation problem is cast as approximate energy minimization in a conditional random field. A new, parallel filtering operator built upon efficient geodesic distance computation is used to propose a set of spatially smooth, contrastsensitive segmentation hypotheses. An economical search algorithm finds the solution with minimum energy within a sensible and highly restricted subset of all possible labellings. Advantages include: i) computational efficiency with high segmentation accuracy; ii) the ability to estimate an approximation to the posterior over segmentations; iii) the ability to handle generally complex energy models. Comparison with maxflow indicates up to 60 times greater computational efficiency as well as greater memory efficiency. GeoS is validated quantitatively and qualitatively by thorough comparative experiments on existing and novel groundtruth data. Numerous results on interactive and automatic segmentation of photographs, video and volumetric medical image data are presented. 1
Surface Stereo with Soft Segmentation
"... This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surfacebased representation, where each pixel is assigned to a 3D surface (planes or Bsplines). This representation enables several impo ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
(Show Context)
This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surfacebased representation, where each pixel is assigned to a 3D surface (planes or Bsplines). This representation enables several important contributions: Firstly, we formulate a higherorder prior which states that pixels of similar appearance are likely to belong to the same 3D surface. This enables to incorporate the very popular color segmentation constraint in a soft and principled way. Secondly, we use a global MDL prior to penalize the number of surfaces. Thirdly, we are able to incorporate, in a simple way, a prior which favors low curvature surfaces. Fourthly, we improve the asymmetric occlusion model by disallowing pixels of the same surface to occlude each other. Finally, we use the known fusion move approach which enables a powerful optimization of our model, despite the infinite number of possible labelings (surfaces). 1.
Transformation of General Binary MRF Minimization to the First Order Case
 IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI
, 2011
"... Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction with the fusionmove and QPBO algorithms. While many computer vision problems today are formulated as energy minimization problems, they have mostly been limited to using firstorder energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higherorder interactions. Our algorithm challenges this restriction that limits the representational power of the models so that higherorder energies can be used to capture the rich statistics of natural scenes. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques. Index Terms—Energy minimization, pseudoBoolean function, higher order MRFs, graph cuts. F 1
TriangleFlow: Optical Flow with Triangulationbased HigherOrder Likelihoods
"... Abstract. We use a simple yet powerful higherorder conditional random field (CRF) to model optical flow. It consists of a standard photoconsistency cost and a prior on affine motions both modeled in terms of higherorder potential functions. Reasoning jointly over a large set of unknown variables p ..."
Abstract

Cited by 16 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We use a simple yet powerful higherorder conditional random field (CRF) to model optical flow. It consists of a standard photoconsistency cost and a prior on affine motions both modeled in terms of higherorder potential functions. Reasoning jointly over a large set of unknown variables provides more reliable motion estimates and a robust matching criterion. One of the main contributions is that unlike previous regionbased methods, we omit the assumption of constant flow. Instead, we consider local affine warps whose likelihood energy can be computed exactly without approximations. This results in a tractable, socalled, higherorder likelihood function. We realize this idea by employing triangulation meshes which immensely reduce the complexity of the problem. Optimization is performed by hierarchical QPBO moves and an adaptive mesh refinement strategy. Experiments show that we achieve highquality motion fields on several data sets including the Middlebury optical flow database. 1
Generalized roof duality and bisubmodular functions
, 2010
"... Consider a convex relaxation ˆ f of a pseudoboolean function f. We say that the relaxation is totally halfintegral if ˆ f(x) is a polyhedral function with halfintegral extreme points x, and this property is preserved after adding an arbitrary combination of constraints of the form xi = xj, xi = 1 ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
(Show Context)
Consider a convex relaxation ˆ f of a pseudoboolean function f. We say that the relaxation is totally halfintegral if ˆ f(x) is a polyhedral function with halfintegral extreme points x, and this property is preserved after adding an arbitrary combination of constraints of the form xi = xj, xi = 1 − xj, and xi = γ where γ ∈ {0, 1, 1 2} is a constant. A wellknown example is the roof duality relaxation for quadratic pseudoboolean functions f. We argue that total halfintegrality is a natural requirement for generalizations of roof duality to arbitrary pseudoboolean functions. Our contributions are as follows. First, we provide a complete characterization of totally halfintegral relaxations ˆ f by establishing a onetoone correspondence with bisubmodular functions. Second, we give a new characterization of bisubmodular functions. Finally, we show some relationships between general totally halfintegral relaxations and relaxations based on the roof duality.