Efficient MRF Deformation Model for Non-Rigid Image Matching

Shekhovtsov, Alexander; Kovtun, Ivan; Hlaváč, Václav

doi:10.1109/cvpr.2007.383205

Cited by 83 publications

(124 citation statements)

References 8 publications

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“…Different from the usual formulation of optical flow [11], [12], the smoothness term in Eqn. 3 is decoupled, which allows us to separate the horizontal flow u(p) from the vertical flow v(p) in message passing, as suggested by [47]. As a result, the complexity of the algorithm is reduced from O(L 4 ) to O(L 2 ) at one iteration of message passing.…”

Section: Matching Objectivementioning

confidence: 97%

“…The recent studies show that optimization tools such as belief propagation, tree-reweighted belief propagation and graph cuts can achieve very good local optimum for these optimization problems [52]. In [47], a dual-layer formulation is proposed to apply tree-reweighted BP to estimate optical flow fields. These advances in inference on MRF's allow us to solve dense scene matching problems effectively.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

SIFT Flow: Dense Correspondence Across Scenes and Its Applications

Liu¹,

Yuen²,

Torralba³

2016

Dense Image Correspondences for Computer Vision

458

855

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Abstract-While image alignment has been studied in different areas of computer vision for decades, aligning images depicting different scenes remains a challenging problem. Analogous to optical flow where an image is aligned to its temporally adjacent frame, we propose SIFT flow, a method to align an image to its nearest neighbors in a large image corpus containing a variety of scenes. The SIFT flow algorithm consists of matching densely sampled, pixel-wise SIFT features between two images, while preserving spatial discontinuities. The SIFT features allow robust matching across different scene/object appearances, whereas the discontinuitypreserving spatial model allows matching of objects located at different parts of the scene. Experiments show that the proposed approach robustly aligns complex scene pairs containing significant spatial differences. Based on SIFT flow, we propose an alignmentbased large database framework for image analysis and synthesis, where image information is transferred from the nearest neighbors to a query image according to the dense scene correspondence. This framework is demonstrated through concrete applications, such as motion field prediction from a single image, motion synthesis via object transfer, satellite image registration and face recognition.

show abstract

Section: Matching Objectivementioning

confidence: 97%

Section: Related Workmentioning

confidence: 99%

SIFT Flow: Dense Correspondence Across Scenes and Its Applications

Liu¹,

Yuen²,

Torralba³

2016

Dense Image Correspondences for Computer Vision

458

855

View full text Add to dashboard Cite

show abstract

“…Such a term penalizes high curvature in the displacement field, is invariant to linear transformations, and thus, favors deformations which are piecewise linear. Recently, labeling of discrete Markov Random Fields has become an attractive approach for solving the problem of non-rigid image registration [4][5][6]. We will give a short introduction into the general framework in Section 2.…”

Section: Introductionmentioning

confidence: 99%

“…The assumption is that neighboring nodes should follow a similar motion. A more robust measure is used in [4,5] which allows more freedom on the deformation. However, this measure is still based on the gradient approximation.…”

Section: Introductionmentioning

confidence: 99%

Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Glocker

Komodakis

Paragios

et al. 2009

Advances in Visual Computing

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Abstract. Labeling of discrete Markov Random Fields (MRFs) has become an attractive approach for solving the problem of non-rigid image registration. Here, regularization plays an important role in order to obtain smooth deformations for the inherent ill-posed problem. Smoothness is achieved by penalizing the derivatives of the displacement field. However, efficient optimization strategies (based on iterative graph-cuts) are only available for first-order MRFs which contain cliques of size up to two. Higher-order cliques require graph modifications and insertion of auxiliary nodes, while pairwise interactions actually allow only regularization based on the first-order derivatives. In this paper, we propose an approximated curvature penalty using second-order derivatives defined on the MRF pairwise potentials. In our experiments, we demonstrate that our approximated term has similar properties as higher-order approaches (invariance to linear transformations), while the computational efficiency of pairwise models is preserved.

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“…But the algorithm may still be trapped within local optima. A Markov Random Field can also be used to model image deformation [28], but the underlying combinatorial problem is NP-hard and approximate inference techniques, such as linear programming relaxation or Tree-reweighted Message Passing, have to be used to obtain an locally optimal solution. Recently, to address the problem of local optima, a convex approximation to the objective function has been learned [19,36], but whether it remains faithful under large distortions is unclear.…”

Section: Related Workmentioning

confidence: 99%

Globally Optimal Estimation of Nonrigid Image Distortion

Tian

Narasimhan

2011

Int J Comput Vis

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Image alignment in the presence of non-rigid distortions is a challenging task. Typically, this involves estimating the parameters of a dense deformation field that warps a distorted image back to its undistorted template. Generative approaches based on parameter optimization such as Lucas-Kanade can get trapped within local minima. On the other hand, discriminative approaches like nearestneighbor require a large number of training samples that grows exponentially with respect to the dimension of the parameter space, and polynomially with the desired accuracy 1/ . In this work, we develop a novel data-driven iterative algorithm that combines the best of both generative and discriminative approaches. For this, we introduce the notion of a "pull-back" operation that enables us to predict the parameters of the test image using training samples that are not in its neighborhood (not -close) in the parameter space. We prove that our algorithm converges to the global optimum using a significantly lower number of training samples that grows only logarithmically with the desired accuracy. We analyze the behavior of our algorithm extensively using synthetic data and demonstrate successful results on experiments with complex deformations due to water and clothing.

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Efficient MRF Deformation Model for Non-Rigid Image Matching

Cited by 83 publications

References 8 publications

SIFT Flow: Dense Correspondence Across Scenes and Its Applications

SIFT Flow: Dense Correspondence Across Scenes and Its Applications

Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Globally Optimal Estimation of Nonrigid Image Distortion

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