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## Feature Correspondence via Graph Matching: Models and Global Optimization

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2044 |
J.B.: ‘Network flows: theory, algorithm and applications
- AHUJA, MAGMANTI, et al.
- 1992
(Show Context)
Citation Context ...ote by the index “L”, we = 0 for (a, b) ∈ N. In such case probrequire all pairwise terms to be zero: θL ab lem (13) can be solved exactly in polynomial time, for example using the Hungarian algorithm =-=[27]-=-. (This is often known as the linear assignment problem.) We define ΦL(θL ) = minx∈M E(x | θL ). To compute this minimum, we converted the problem to an instance of a minimum cost circulation with uni... |

1809 | Shape matching and object recognition using shape contexts,”
- Belongie, Malik, et al.
- 2002
(Show Context)
Citation Context ...tal evaluation shows that the model and the algorithm presented in this paper can be applied to a wide range of image matching problems with results matching or exceeding those of existing algorithms =-=[5, 14]-=-. 1.1 Relation to Previous Work Models for feature matching Our technique is loosely related to algorithms that find correspondences by matching appearance descriptors under smooth spatial transformat... |

1533 | Gradient-based learning applied to document recognition
- LeCun, Bottou, et al.
- 1998
(Show Context)
Citation Context ...ement over the results reported in [5] where the best system had a matching error above 10%. Matching MNIST digits. Here we describe experiments on images of handwritten digits from the MNIST dataset =-=[35]-=-. For training, we randomly sampled from this dataset one image pair for each of the 10 digits. We repeated the same procedure to generate a test set of 10 pairs of same digits. From each pair we extr... |

1005 | Visual categorization with bags of keypoints.
- Csurka, Dance, et al.
- 2004
(Show Context)
Citation Context ...Vladimir Kolmogorov, and Carsten Rother Function Eapp(x) favors correspondences between features having similar appearance. We define this function as a sum of unary terms: Eapp(x) = ∑ a∈A θappa xa . =-=(3)-=- For an assignment a = (p′, p′′) ∈ A, θappa is the distance between appearance descriptors (such as Shape Context [19]) computed at points p′ and p′′ in the respective images. We have used different f... |

544 | The pyramid match kernel: Discriminative classification with sets of image features.
- Grauman, Darrell
- 2005
(Show Context)
Citation Context ...in our measure of geometric compatibility.N consists of all correspondence pairs defined over neighboring features: N={〈(p′, p′′), (q′, q′′)〉 ∈ A×A | p′ ∈ Nq′ ∨ q ′ ∈ Np′ ∨ p ′′ ∈ Nq′′ ∨ q ′′ ∈ Np′′} =-=(5)-=- where Np indicates the set of K nearest neighbors of p (computed in the set of feature p), and K is a positive integer value controlling the size of the neighborhood, which we call geometric neighbor... |

489 | Convergent Tree-reweighted Message Passing for Energy Minimization”,
- Kolmogorov
- 2006
(Show Context)
Citation Context ... [13] who decomposed the problem into a convex combination of trees and proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound (see =-=[32]-=- or review article [33]). Schlesinger and Giginyak [14, 15] and Komodakis et al. [16] proposed to use subgradient techniques [34, 11] for MRF optimization, which guarantee to converge to a vector θ gi... |

419 | Shape matching and object recognition using low distortion correspondences,”
- Berg, Berg, et al.
- 2005
(Show Context)
Citation Context ...ration after the warping. Since the objective is changed at each iteration, the convergence properties of this algorithm are not clear. Our approach is most closely related to the work of Berg et al. =-=[17]-=-, and Leordeanu and Hebert [18], who formulate visual correspondence as a graph matching problem by defining an objective including terms based on appearance similarity as well as geometric compatibil... |

400 |
Minimization Methods for Non-Differentiable Functions.
- Shor
- 1985
(Show Context)
Citation Context ...ng techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound. Schlesinger and Giginyak [9, 10] and Komodakis et al. [11] proposed to use subgradient techniques =-=[26, 6]-=- for MRF optimization, which guarantee to converge to a vector θ giving the best possible lower bound. 3.1 Graph matching via problem decomposition We now apply this approach to the graph matching pro... |

373 | A graduated assignment algorithm for graph matching.
- Gold, Rangarajan
- 1996
(Show Context)
Citation Context ...problem which received considerable attention in the literature (see [21] for a comprehensive survey of methods). Proposed techniques include the graduated assignment algorithm of Gold and Rangarajan =-=[22]-=-, spectral relaxation methods [18, 12], COMPOSE method of Duchi et al. [13]. Maciel and Costeira [23] reduce the problem to concave minimization and apply the exact method in [24]. Torr [19] and Schel... |

365 | Computing visual correspondence with occlusions using graph cuts.
- Kolmogorov, Zabih
- 2001
(Show Context)
Citation Context ...vision and is a key ingredient in a wide range of applications including object recognition, 3D reconstruction, mosaicing, motion segmentation, and image morphing. Several robust algorithms (see e.g. =-=[1, 2]-=-) exist for registration of images of static scenes and for visual correspondence under rigid motion. These methods typically exploit powerful constraints (e.g. epipolar constraints) to reduce the sea... |

251 | A spectral technique for correspondence problems using pairwise constraints. In: - Leordeanu, Hebert - 2005 |

238 | Thirty Years of Graph Matching in Pattern Recognition,"
- Conte, Foggia, et al.
- 2004
(Show Context)
Citation Context ...mples, thus avoiding the need of manual parameter tuning. Graph matching optimization Graph matching is a challenging optimization problem which received considerable attention in the literature (see =-=[21]-=- for a comprehensive survey of methods). Proposed techniques include the graduated assignment algorithm of Gold and Rangarajan [22], spectral relaxation methods [18, 12], COMPOSE method of Duchi et al... |

199 | AP..Pentland, Modal Matching for Correspondence and Recognition.
- Sclaroff
- 1995
(Show Context)
Citation Context ...to Previous Work Models for feature matching Our technique is loosely related to algorithms that find correspondences by matching appearance descriptors under smooth spatial transformations (see e.g. =-=[15, 16]-=-). However, unlike such approaches, our method does not make a parametric assumption about the transformation relating the input images, and thus can be used in a wider range of applications. Belongie... |

197 | Discovering object categories in image collections,
- Sivic, Russell, et al.
- 2005
(Show Context)
Citation Context ...r approach in these cases is to discard the information about the spatial layout of features, and to find correspondences using appearance only. For example, many object recognition methods (see e.g. =-=[3, 4]-=-) represent images as orderless sets of local appearance descriptors, known as bags of features. Recent work [5] has suggested that for many correspondence problems, learned appearance-based models pe... |

191 | MAP estimation via agreement on trees : Message-passing and linear programming.
- Wainwright, Jaakkola, et al.
- 2005
(Show Context)
Citation Context ...ms for graph matching, however, is different from [7]. In vision the decomposition approach is probably best known in the context of the MAP-MRF inference task. It was introduced by Wainwright et al. =-=[8]-=- who decomposed the problem into a convex combination of trees and6 Lorenzo Torresani, Vladimir Kolmogorov, and Carsten Rother proposed message passing techniques for optimizing vector θ. These techn... |

178 | Recognition with local feature: the kernel recipe,
- Wallraven, Caputo, et al.
- 2003
(Show Context)
Citation Context ...neighborhood size. Egeom(x) is computed over pairs of active correspondences in the set N : Egeom(x) = ∑ (a,b)∈N θgeomab xaxb (6) where: θ geom ab = η(e δ2a,b/σ 2 l − 1) + (1 − η)(eα 2 a,b/σ 2 α − 1) =-=(7)-=- δ(p′,p′′),(q′,q′′) = |||p′ − q′|| − ||p′′ − q′′||| ||p′ − q′||+ ||p′′ − q′′|| (8) α(p′,p′′),(q′,q′′) = arccos ( p′ − q′ ||p′ − q′|| · p′′ − q′′ ||p′′ − q′′|| ) (9) Intuitively, θgeom(p′,p′′),(q′,q′′)... |

174 | A linear programming approach to maxsum problem: A review.
- Werner
- 2007
(Show Context)
Citation Context ...e problem into a convex combination of trees and proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound (see [32] or review article =-=[33]-=-). Schlesinger and Giginyak [14, 15] and Komodakis et al. [16] proposed to use subgradient techniques [34, 11] for MRF optimization, which guarantee to converge to a vector θ giving the best possible ... |

172 | Optimizing binary mrfs via extended roof duality.
- Rother, Kolmogorov, et al.
- 2007
(Show Context)
Citation Context ...gree, i.e. x ′ a = x ′′ a. Then we convert the obtained graph matching problem to a quadratic pseudo-boolean optimization problem (see [30] for conversion details). Finally, we run the QPBO-PI method =-=[33]-=- starting either with labeling x ′ if E(x ′ | ¯ θ) < E(x ′′ | ¯ θ) or with x ′′ otherwise. The produced solution x is guaranteed to have the same or smaller cost than the costs of x ′ and x ′′. BP We ... |

158 | Selection of Scale-Invariant Parts for Object Class Recognition,”
- Dorko, Schmid
- 2003
(Show Context)
Citation Context ...r approach in these cases is to discard the information about the spatial layout of features, and to find correspondences using appearance only. For example, many object recognition methods (see e.g. =-=[3, 4]-=-) represent images as orderless sets of local appearance descriptors, known as bags of features. Recent work [5] has suggested that for many correspondence problems, learned appearance-based models pe... |

138 | Geometric motion segmentation and model selection.
- Torr
- 1998
(Show Context)
Citation Context ...nal parameter vector ¯ θ [8], i.e. ∑ ρσθ σ = ¯ θ (14) σ∈I For each subproblem σ we will define a lower bound Φσ(θ σ ) which satisfies It is easy to see that the function Φσ(θ σ ) ≤ min x∈M E(x | θσ ) =-=(15)-=- Φ(θ) = ∑ ρσΦσ(θ σ ) (16) σ∈I is a lower bound on the original function. Indeed, if x∗ is an optimal solution of (13) then from (14)-(16) we get Φ(θ) ≤ ∑ ρσ min x∈M E(x | θσ ) ≤ ∑ ρσE(x ∗ | θ σ ) = E(... |

127 | Learning physics-based motion style with nonlinear inverse optimization.
- Liu, Hertzmann, et al.
- 2005
(Show Context)
Citation Context ...etric penalty functions defined in local neighborhoods provide more accurate correspondences than global geometric costs, such as those used in [17] and [18]. Finally, we use the method of Liu et al. =-=[20]-=- to learn the parameter values for the model from examples, thus avoiding the need of manual parameter tuning. Graph matching optimization Graph matching is a challenging optimization problem which re... |

124 | Incremental Subgradient Methods for Nondifferential Optimization“,
- Nedic, Bertsekas
- 2001
(Show Context)
Citation Context .... the corresponding term is submodular) and xMab = 0.5 if θMab > 0. Step size An important issue in the subgradient method is the choice of the step size λ. We used an adaptive technique described in =-=[39, 11]-=-. We set λ = α(Φ(θ∗) + δ − Φ(θ))/||g||2 where α is a constant (1 in our experiments), θ∗ is the best vector found so far (i.e. the vector giving the best lower bound), and δ is a positive number which... |

117 | Mrf optimization via dual decomposition: message-passing revisited,” in ICCV,
- Komodakis, Paragios, et al.
- 2007
(Show Context)
Citation Context ...v, and Carsten Rother proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound. Schlesinger and Giginyak [9, 10] and Komodakis et al. =-=[11]-=- proposed to use subgradient techniques [26, 6] for MRF optimization, which guarantee to converge to a vector θ giving the best possible lower bound. 3.1 Graph matching via problem decomposition We no... |

110 | Residual belief propagation: Informed scheduling for asynchronous message passing.
- Elidan, McGraw, et al.
- 2006
(Show Context)
Citation Context ...{“occlusion′′} to each point p ′ ∈ P ′. Min-marginals for the linear subnetwork were computed via O(|A| + |P ′|) calls to the Dijkstra algorithm. As in [13], we used Residual Belief Propagation (RPB) =-=[34]-=- with damping=0.3 for computing pseudo min-marginals for the “smoothness” subnetwork containing pairwise terms θabxaxb. However, in our experiments messages did not converge, so we set an additional t... |

93 | Categorizing nine visual classes using local appearance descriptors. In:
- Willamowski, Arregui, et al.
- 2004
(Show Context)
Citation Context ...e set N : Egeom(x) = ∑ (a,b)∈N θgeomab xaxb (6) where: θ geom ab = η(e δ2a,b/σ 2 l − 1) + (1 − η)(eα 2 a,b/σ 2 α − 1) (7) δ(p′,p′′),(q′,q′′) = |||p′ − q′|| − ||p′′ − q′′||| ||p′ − q′||+ ||p′′ − q′′|| =-=(8)-=- α(p′,p′′),(q′,q′′) = arccos ( p′ − q′ ||p′ − q′|| · p′′ − q′′ ||p′′ − q′′|| ) (9) Intuitively, θgeom(p′,p′′),(q′,q′′) computes the geometric agreement between neighboring correspondences (p′, p′′),(q... |

89 | Balanced graph matching
- Cour, Srinivasan, et al.
- 2007
(Show Context)
Citation Context ...f our examples DD finds the global minimum in reasonable time, and otherwise provides a solution whose cost is very close to the optimum. In contrast, previously proposed optimization methods such as =-=[12, 13]-=- often fail to compute good solutions for our energy function. Our experimental evaluation shows that the model and the algorithm presented in this paper can be applied to a wide range of image matchi... |

89 |
Roof duality complementation and persistency in quadratic 0-1 optimization",
- Hammer, Hansen, et al.
- 1984
(Show Context)
Citation Context ...npositive for all pairwise terms (a, b) ∈ N), then we can compute a global minimum using a maxflow algorithm. With arbitrary θM ab the problem becomes NP-hard [28]. We use the roof duality relaxation =-=[29]-=- to get a lower bound ΦM(θM ) on the problem. It can be defined as the optimal value of the following linear program: ΦM(θ M ) = min ∑ a∈A θ M a xa + ∑ (a,b)∈N θ M abxab (17) subject to { 0 ≤ xa ≤ 1 ∀... |

82 | Learning graph matching,
- Caetano, McAuley, et al.
- 2009
(Show Context)
Citation Context ...dences using appearance only. For example, many object recognition methods (see e.g. [3, 4]) represent images as orderless sets of local appearance descriptors, known as bags of features. Recent work =-=[5]-=- has suggested that for many correspondence problems, learned appearance-based models perform similarly or better than state-of-the-art structural models exploiting information about spatial arrangeme... |

72 | A global solution to sparse correspondence problems,”
- Maciel, Costeira
- 2003
(Show Context)
Citation Context ...of methods). Proposed techniques include the graduated assignment algorithm of Gold and Rangarajan [22], spectral relaxation methods [18, 12], COMPOSE method of Duchi et al. [13]. Maciel and Costeira =-=[23]-=- reduce the problem to concave minimization and apply the exact method in [24]. Torr [19] and Schellewald and Schnörr [25] useFeature Correspondence via Graph Matching: Models and Global Optimization... |

52 | Logcut - efficient graph cut optimization for markov random fields
- Lempitsky, Rother, et al.
- 2007
(Show Context)
Citation Context ...on 9 other subproblems σ. We used a maximum of 10000 iterations, and stopped earlier if the gap between the lower bound and the cost became smaller than 10−6 . FUSION This technique was introduced in =-=[32]-=- for MRF optimization with multiple labels. We propose to use it for graph matching as follows. First, we generate 256 solutions by applying one pass of coordinate descent (ICM) to zero labeling using... |

48 | Using combinatorial optimization within max-product belief propagation
- Duchi, Tarlow, et al.
(Show Context)
Citation Context ...f our examples DD finds the global minimum in reasonable time, and otherwise provides a solution whose cost is very close to the optimum. In contrast, previously proposed optimization methods such as =-=[12, 13]-=- often fail to compute good solutions for our energy function. Our experimental evaluation shows that the model and the algorithm presented in this paper can be applied to a wide range of image matchi... |

43 | A binocular stereo algorithm for reconstructing sloping, creased, and broken surfaces, in the presence of halfocclusion,”
- Belhumeur
- 1993
(Show Context)
Citation Context ...vision and is a key ingredient in a wide range of applications including object recognition, 3D reconstruction, mosaicing, motion segmentation, and image morphing. Several robust algorithms (see e.g. =-=[1, 2]-=-) exist for registration of images of static scenes and for visual correspondence under rigid motion. These methods typically exploit powerful constraints (e.g. epipolar constraints) to reduce the sea... |

33 |
Local Features and Kernels for Classifcation of Texture and Object Categories:
- Zhang, Marszalek, et al.
- 2007
(Show Context)
Citation Context ... − 1) + (1 − η)(eα 2 a,b/σ 2 α − 1) (7) δ(p′,p′′),(q′,q′′) = |||p′ − q′|| − ||p′′ − q′′||| ||p′ − q′||+ ||p′′ − q′′|| (8) α(p′,p′′),(q′,q′′) = arccos ( p′ − q′ ||p′ − q′|| · p′′ − q′′ ||p′′ − q′′|| ) =-=(9)-=- Intuitively, θgeom(p′,p′′),(q′,q′′) computes the geometric agreement between neighboring correspondences (p′, p′′),(q′, q′′) by evaluating how well the segment p′q′ matches the Feature Correspondence... |

32 | Probabilistic subgraph matching based on convex relaxation. In Energy minimization methods in computer vision and pattern recognition
- Schellewald, Schnörr
- 2005
(Show Context)
Citation Context ...on methods [18, 12], COMPOSE method of Duchi et al. [13]. Maciel and Costeira [23] reduce the problem to concave minimization and apply the exact method in [24]. Torr [19] and Schellewald and Schnörr =-=[25]-=- useFeature Correspondence via Graph Matching: Models and Global Optimization 3 semi-definite programming (SDP) relaxation for graph matching. Among these papers, only [23] and [25] report obtaining ... |

30 | Solving markov random fields using semi definite programming
- Torr
- 2003
(Show Context)
Citation Context ...n [17] and [18] handle outliers by removing low-confidence correspondences from the obtained solutions. Instead, we include in our energy an explicit occlusion cost, as for example previously done in =-=[19]-=-. Thus our algorithm solves for the outliers as part of the optimization. We add to the objective a spatial coherence term, favoring spatial aggregation of matched features, which reduces the correspo... |

30 | Preprocessing of unconstrained quadratic binary optimization
- Boros, Hammer, et al.
- 2006
(Show Context)
Citation Context ...mparison between different optimization methods using our energy model. (e) Mismatch error using different energy models. responding to active correspondences. We also tried to apply the PROBE method =-=[45, 42]-=- to get more labeled nodes. However, in practice we were unable to do so, due to the high computational cost of running PROBE on our problem instances. Figure 2(c) shows minimization performance as a ... |

21 |
Network flows and minimization of quadratic pseudo-Boolean functions
- Boros, Hammer, et al.
- 1991
(Show Context)
Citation Context ... a ∈ A xab ≤ xa, xab ≤ xb, xab ≥ xa + xb − 1, xab ≥ 0 ∀ (a, b) ∈ N This relaxation can be solved in polynomial time by computing a maximum flow in a graph with 2(|A|+ 1) nodes and O(|A| + |N |) edges =-=[38, 36]-=-. Local subproblems For our last set of subproblems we use an exhaustive search to compute the global minimum (see Appendix A for details). Thus, we need to make sure that subproblems are sufficiently... |

19 |
A decomposition method for quadratic zero-one programming
- Chardaire, Sutter
- 1994
(Show Context)
Citation Context ...ometimes it is referred to as “dual decomposition” [6]. It was applied to quadratic pseudo-boolean functions (i.e. functions of binary variables with unary and pairwise terms) by Chardaire and Sutter =-=[7]-=-. Their work is perhaps the closest to the method in this paper. As in [7], we use “small” subproblems for which the global minimum can be computed exactly in reasonable time. Our choice of subproblem... |

19 |
Solution to structural recognition (MAX,+)-problems by their equivalent transformations
- Schlesinger, Giginyak
- 2007
(Show Context)
Citation Context ...Torresani, Vladimir Kolmogorov, and Carsten Rother proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound. Schlesinger and Giginyak =-=[9, 10]-=- and Komodakis et al. [11] proposed to use subgradient techniques [26, 6] for MRF optimization, which guarantee to converge to a vector θ giving the best possible lower bound. 3.1 Graph matching via p... |

13 | Multi-Level Shape Representation Using Global Deformations and Locally Adaptive Finite Elements
- Metaxas
- 1997
(Show Context)
Citation Context ...sumption is not appropriate for deformable objects, such as human faces, or for different instances of an object class, such as different cars, related by highly non-linear mappings. Other approaches =-=[21, 22]-=- have proposed to constrain the correspondence problem by learning or hand-coding explicit models of how an object is allowed to deform using parametric 2D or 3D representations, such as linear eigens... |

10 |
Solving certain nonconvex quadratic minimization problems by ranking extreme points
- Cabot, Francis
- 1970
(Show Context)
Citation Context ... Gold and Rangarajan [22], spectral relaxation methods [18, 12], COMPOSE method of Duchi et al. [13]. Maciel and Costeira [23] reduce the problem to concave minimization and apply the exact method in =-=[24]-=-. Torr [19] and Schellewald and Schnörr [25] useFeature Correspondence via Graph Matching: Models and Global Optimization 3 semi-definite programming (SDP) relaxation for graph matching. Among these ... |

7 |
Convergence and Computational Analyses for Some Variable Target Value and Subgradient Deflection Methods
- Sherali, Lim
(Show Context)
Citation Context ...rtain factor (1.5 in our experiments), otherwise it is decreased by a certain factor (0.95). Restarting the subgradient method In our implementation we also used the following technique borrowed from =-=[40]-=-. If the best value of the lower bound Φ(θ∗) has not Feature Correspondence via Graph Matching: Models and Global Optimization 9 changed during γ iterations then we replace θ with θ∗. In the beginning... |