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Keywords
(6)
Combinatorial Problems
Convex Optimization
Image Analysis
Operator Splitting
Total Variation
rudin osher fatemi
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Convex Multiclass Image Labeling by SimplexConstrained Total Variation
Convex Multiclass Image Labeling by SimplexConstrained Total Variation,10.1007/9783642022562_13,Jan Lellmann,Jörg H. Kappes,Jing Yuan,Florian Be
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Convex Multiclass Image Labeling by SimplexConstrained Total Variation
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Citations: 21
)
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Jan Lellmann
,
Jörg H. Kappes
,
Jing Yuan
,
Florian Becker
,
Christoph Schnörr
Multiclass labeling is one of the core problems in image analysis. We show how this combinatorial problem can be approximately solved using tools from convex optimization. We suggest a novel functional based on a multidimensional
total variation
formulation, allowing for a broad range of data terms. Optimization is carried out in the
operator splitting
framework using DouglasRachford Splitting. In this connection, we compare two methods to solve the RudinOsherFatemi type subproblems and demonstrate the performance of our approach on single and multichannel images.
Conference:
ScaleSpace Theories in Computer Vision  ScaleSpace
, pp. 150162, 2009
DOI:
10.1007/9783642022562_13
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Citation Context
(18)
...Recently, similar convex formulations have also been proposed for the continuous Potts model with more than two labels (Zach et al. 2008;
Lellmann et al. 2009;
Pock et al. 2009), by relaxing the integrability constraint of the labeling function...
...Some other relaxations closely related to (Zach et al. 2008;
Lellmann et al. 2009
) have later been proposed in (Brown et al. 2009, 2010)...
...This paper builds on the work of Zach et al. (2008) and
Lellmann et al. (2009)
...
...A new algorithm derived from the smoothed dual formulation is shown to be significantly more efficient than the state of art works (Zach et al. 2008;
Lellmann et al. 2009
)...
...This work builds on the convex relaxation method of the nonconvex Potts model (Zach et al. 2008;
Lellmann et al. 2009
)...
...Zach et al. (2008) and
Lellmann et al. (2009)
proposed to use the indicator function of the largest component ui as an approximate binary solution, i.e...
...Secondly, we evaluate quality and efficiency with the approaches of (Zach et al. 2008;
Lellmann et al. 2009
)...
...7 and 8 was first used by
Lellmann et al. (2009)
...
...Observe also that our approach can obtain solutions of lower energy than the approaches (Zach et al. 2008;
Lellmann et al. 2009
)...
...This benefit can also be observed in the energy plots of Fig. 10: we can obtain binary solutions of lower energy than the approaches of Zach et al. (2008),
Lellmann et al. (2009)
...
...We will now compare the cpu time and convergence with the approaches (Zach et al. 2008;
Lellmann et al. 2009
)...
...Furthermore, each iteration of this loop has a computational cost approximately equal to one inner loop iteration of (Zach et al. 2008;
Lellmann et al. 2009
)...
...between 0 and 1. The approaches (
Lellmann et al. 2009;
Zach et al. 2008) require more parameters, like the outer time step τ , inner time step, accuracy of solving inner problem etc...
...Another algorithm was derived which was shown to converge faster than the approaches of
Lellmann et al. (2009)
, Zach et al. (2008)...
Egil Bae
,
et al.
Global Minimization for Continuous Multiphase Partitioning Problems Us...
...Recently, Chan’s model (1) was extended to more than two regions in [18,
16
, 4], which proposes multiway cuts in a continuous configuration and was applied to solve multilabeling problems...
Jing Yuan
,
et al.
A study on continuous maxflow and mincut approaches
...However, by relaxing the original problem to a convex constraint set, good solutions for the original problem can be recovered using convex optimization [22,4,
13
,14]...
Jan Lellmann
,
et al.
Fast and Exact PrimalDual Iterations for Variational Problems in Comp...
...[3,18,19,20,21,
22
]. Compared to level set methods, great advantages in numerics can be achieved, e.g...
...In [18,
22
], such convex minimization problem is computed directly through the minimization over the labeling functions, i.e...
...Experiments show that our maxflow algorithm is much more efficient than the state of art of computational methods [18,
22
]...
...Our experiments show it is around 4 times faster than the previous methods [18,
22
]...
...Clearly, the Potts model (4) is nonconvex due to the binary configuration of each function ui(x) ∈{ 0, 1} .T heconvex relaxed Potts model [20,
22
,21] proposes to relax such binary constraints to the convex interval [0, 1] and approximates (4) by the reduced convex optimization problem:...
...In [
22
], a DouglasRachford splitting algorithm was proposed to solve a quite similar problem as (5), where a variant of the totalvariation term is considered:...
...In contrast to [18,
22
,20,27], [21] did not try to tackle the labeling function of the continuous mincut problem (5) directly, but solved its equivalent dual formulation:...
...In numerics, its great advantages over previous works are: it avoids pointwise projections onto the simplex constraint S within each outer loop as [18,
22
]; in comparison to [21,26], it exactly solves (6) without any smoothing procedure; it is globally optimized based on an efficient and reliable multiplierbased maxflow algorithm, in contrast to the PDEdescent method [20,27] whose convergence may suffer from uncareful stepsizes resulting ...
... onto the simplex constraint S within each outer loop as [18,22]; in comparison to [21,26], it exactly solves (6) without any smoothing procedure; it is globally optimized based on an efficient and reliable multiplierbased maxflow algorithm, in contrast to the PDEdescent method [20,27] whose convergence may suffer from uncareful stepsizes resulting in suboptimums; experiments show a faster convergence rate, about 4 times, than [18,
22
]...
...The quality of the relaxation (5) has been evaluated extensively in [18,
22
,21] where it has been shown to be competitive to several state of the art methods from discrete optimization like alpha expansion and alpha betaswap [2] for approximately minimizing the Pott’s energy...
...The DouglasRachford splitting approach given in [
22
] can also be proved to converge (in the discrete setting), but we experienced that our approach was more efficient than both these approaches...
...However, in contrast to [18,
22
] our approach avoids iterative projections to the convex set S and consequently require much less outer iterations...
...E∗ . For the three images (see Fig. 2), dif ferent precision � are taken and the total number of iterations to reach convergence is evaluated, see Tab 1: clearly, our method is about 4 times faster than the DouglasRachfordsplitting [
22
], the approach in [18] is even slower and failed to reach such a low precision...
...Table 1. Comparisons between algorithms: Zach et al [18], Lellmann [
22
] and the proposed maxflow algorithm: for the three images (see Fig. 2), different precision � are taken and the total number of iterations to reach convergence is evaluated...
...Zach et al [18] fail to reach such a precision Lellmann et al [
22
] 421 iter...
Jing Yuan
,
et al.
A Continuous MaxFlow Approach to Potts Model
...(a) Input image (b) Lellmann et al. [
22
] (c) Zach et al. [30] (d) Proposed relaxation...
...More recently, Lellman et al. in [
22
] proposed a qualitatively comparable approach with a slightly different length term...
...Figure 3 shows a comparison of the proposed approach to the relaxation approach of [30] and [
22
] by means of a simple threelabel segmentation problem...
...The solution of our approach achieves an energy ofE = 13975 which is clearly aboveE = 13972 achieved by [30] andE = 13960 achieved by [
22
]...
Thomas Pock
,
et al.
A convex relaxation approach for computing minimal partitions
References
(30)
An Experimental Comparison of Mincut/Maxflow Algorithms for Energy Minimization in Vision
(
Citations: 600
)
Yuri Boykov
,
Vladimir Kolmogorov
Conference:
Energy Minimization Methods in Computer Vision and Pattern Recognition  EMMCVPR
, pp. 359374, 2001
Nonlinear total variation based noise removal algorithms
(
Citations: 2321
)
Leonid I. Rudin
,
Stanley Osher
,
Emad Fatemi
Conference:
International Symposium on Physical Design  ISPD
, 1992
Maximal flow through a domain
(
Citations: 68
)
Gilbert Strang
Journal:
Mathematical Programming
, vol. 26, no. 2, pp. 123143, 1983
Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models
(
Citations: 160
)
Mila Nikolova
,
Selim Esedoglu
,
Tony F. Chan
Journal:
Siam Journal on Applied Mathematics  SIAMAM
, vol. 66, no. 5, pp. 16321648, 2006
A Convex Formulation of Continuous Multilabel Problems
(
Citations: 30
)
Thomas Pock
,
Thomas Schoenemann
,
Gottfried Graber
,
Horst Bischof
,
Daniel Cremers
Conference:
European Conference on Computer Vision  ECCV
, pp. 792805, 2008
Sort by:
Citations
(21)
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
(
Citations: 2
)
Egil Bae
,
Jing Yuan
,
XueCheng Tai
Journal:
International Journal of Computer Vision  IJCV
, vol. 92, no. 1, pp. 112129, 2011
A study on continuous maxflow and mincut approaches
(
Citations: 4
)
Jing Yuan
,
Egil Bae
,
XueCheng Tai
Conference:
Computer Vision and Pattern Recognition  CVPR
, pp. 22172224, 2010
Fast and Exact PrimalDual Iterations for Variational Problems in Computer Vision
(
Citations: 2
)
Jan Lellmann
,
Dirk Breitenreicher
,
Christoph Schnörr
Conference:
European Conference on Computer Vision  ECCV
, pp. 494505, 2010
A Continuous MaxFlow Approach to Potts Model
(
Citations: 2
)
Jing Yuan
,
Egil Bae
,
XueCheng Tai
,
Yuri Boykov
Conference:
European Conference on Computer Vision  ECCV
, pp. 379392, 2010
A convex relaxation approach for computing minimal partitions
(
Citations: 20
)
Thomas Pock
,
Antonin Chambolle
,
Daniel Cremers
,
Horst Bischof
Conference:
Computer Vision and Pattern Recognition  CVPR
, pp. 810817, 2009