Removing outliers by minimizing the sum of infeasibilities

Lee, Hyunjung; Seo, Yongduek; Lee, Sang Wook

doi:10.1016/j.imavis.2009.11.004

Cited by 3 publications

(5 citation statements)

References 16 publications

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“…2 a and b. On the other hand, the SOI method [1] found significantly fewer inliers as shown in Figs. 2 c and d .…”

Section: Resultsmentioning

confidence: 99%

“…One hundred points were generated with Gaussian noise and 70% of them are randomly generated outliers. To the point data, a 2D line ( y = θ 1 x + θ 2 ) is fitted using the MILP MaxFS, QMaxFS and SOI [1] algorithms. The MILP MaxFS formulation of this problem using the Big‐M method is

\underset{θ, s}{normalmin} \sum_{i = 1}^{k} s_{i} s . t . {(||, θ_{1} x_{i} + θ_{2} - y_{i})}_{1} \leq ε + M s_{i}, normal∀ i

Fig.…”

Section: Resultsmentioning

confidence: 99%

“…SOI has been used for the robust parameter estimation of geometric vision problems under the L ∞ optimisation formulation [1, 2]. SOI examines the sum of violations over all constraints, which is formulated as a convex programming problem.…”

Section: Introductionmentioning

confidence: 99%

“…Recently several geometric vision problems, such as triangulation, camera re-sectioning, homography and structure from motion, have been defined as quasi-convex problems formulated as the L ∞ -norm optimisation problem, which yields the globally optimal solution with a geometrically meaningful cost function. In [1][2][3][4], the outlier removal problem is considered as an infeasibility measurement problem. The two most common measures of the infeasibility of a set of constraints are the number of infeasibilities (NOIs) and sum of infeasibilities (SOIs) [5].…”

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confidence: 99%

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Quasi‐maximum feasible subsystem for geometric computer vision problems

Lee

2015

Electron. lett.

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A robust fitting algorithm for geometric computer vision problems under the L ∞-norm optimisation framework is presented. It is essentially based on the maximum feasible subsystem (MaxFS) but it overcomes the computational limitation of the MaxFS for large data by finding only a quasi-maximum feasible subset. Experimental results demonstrate that the algorithm removes outliers more effectively than the other parameter estimation methods recently developed when the outlier-to-inlier ratio in a data set is high.

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“…2 a and b. On the other hand, the SOI method [1] found significantly fewer inliers as shown in Figs. 2 c and d .…”

Section: Resultsmentioning

confidence: 99%

\underset{θ, s}{normalmin} \sum_{i = 1}^{k} s_{i} s . t . {(||, θ_{1} x_{i} + θ_{2} - y_{i})}_{1} \leq ε + M s_{i}, normal∀ i

Fig.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Quasi‐maximum feasible subsystem for geometric computer vision problems

Lee

2015

Electron. lett.

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“…Lee et al removes outliers by solving a convex sum-ofinfeasibilities [12] problem. Olsson et al [13] improved the method of [6] by considering Lagrange dual problem of the ℓ ∞ minimization problem in [6], the advantage being that less number of inliers are mistakenly removed by solving the dual problem.…”

Section: Prior Workmentioning

confidence: 99%

Approximate Least Trimmed Sum of Squares Fitting and Applications in Image Analysis

Shen

Hengel

et al. 2013

IEEE Trans. on Image Process.

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The least trimmed sum of squares (LTS) regression estimation criterion is a robust statistical method for model fitting in the presence of outliers. Compared with the classical least squares estimator, which uses the entire data set for regression and is consequently sensitive to outliers, LTS identifies the outliers and fits to the remaining data points for improved accuracy. Exactly solving an LTS problem is NP-hard, but as we show here, LTS can be formulated as a concave minimization problem. Since it is usually tractable to globally solve a convex minimization or concave maximization problem in polynomial time, inspired by , we instead solve LTS' approximate complementary problem, which is convex minimization. We show that this complementary problem can be efficiently solved as a second order cone program. We thus propose an iterative procedure to approximately solve the original LTS problem. Our extensive experiments demonstrate that the proposed method is robust, efficient and scalable in dealing with problems where data are contaminated with outliers. We show several applications of our method in image analysis.

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Separability and Tight Enclosure of Point Sets

Veelaert

2012

Digital Geometry Algorithms

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Removing outliers by minimizing the sum of infeasibilities

Cited by 3 publications

References 16 publications

Quasi‐maximum feasible subsystem for geometric computer vision problems

Quasi‐maximum feasible subsystem for geometric computer vision problems

Approximate Least Trimmed Sum of Squares Fitting and Applications in Image Analysis

Separability and Tight Enclosure of Point Sets

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