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Projection Based MEstimators
, 2009
"... Random Sample Consensus (RANSAC) is the most widely used robust regression algorithm in computer vision. However, RANSAC has a few drawbacks which make it difficult to use for practical applications. Some of these problems have been addressed through improved sampling algorithms or better cost funct ..."
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Cited by 8 (2 self)
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Random Sample Consensus (RANSAC) is the most widely used robust regression algorithm in computer vision. However, RANSAC has a few drawbacks which make it difficult to use for practical applications. Some of these problems have been addressed through improved sampling algorithms or better cost functions, but an important difficulty still remains. The algorithm is not user independent, and requires knowledge of the scale of the inlier noise. We propose a new robust regression algorithm, the projection based Mestimator (pbM). The pbM algorithm is derived by building a connection to the theory of kernel density estimation and this leads to an improved cost function, which gives better performance. Furthermore, pbM is user independent and does not require any knowledge of the scale of noise corrupting the inliers. We propose a general framework for the pbM algorithm which can handle heteroscedastic data and multiple linear constraints on each data point through the use of Grassmann manifold theory. The performance of pbM is compared with RANSAC and MEstimator Sample Consensus (MSAC) on various real problems. It is shown that pbM gives better results than RANSAC and MSAC in spite of being user independent.
Balanced exploration and exploitation model search for efficient epipolar geometry estimation
 In ECCV
, 2006
"... Abstract. The estimation of the epipolar geometry is especially difficult where the putative correspondences include a low percentage of inlier correspondences and/or a large subset of the inliers is consistent with a degenerate configuration of the epipolar geometry that is totally incorrect. This ..."
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Cited by 6 (1 self)
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Abstract. The estimation of the epipolar geometry is especially difficult where the putative correspondences include a low percentage of inlier correspondences and/or a large subset of the inliers is consistent with a degenerate configuration of the epipolar geometry that is totally incorrect. This work presents the Balanced Exploration and Exploitation Model Search (BEEM) algorithm that works very well especially for these difficult scenes. The BEEM algorithm handles the above two difficult cases in a unified manner. The algorithm includes the following main features: (1) Balanced use of three search techniques: global random exploration, local exploration near the current best solution and local exploitation to improve the quality of the model. (2) Exploits available prior information to accelerate the search process. (3) Uses the best found model to guide the search process, escape from degenerate models and to define an efficient stopping criterion. (4) Presents a simple and efficient method to estimate the epipolar geometry from two SIFT correspondences. (5) Uses the localitysensitive hashing (LSH) approximate nearest neighbor algorithm for fast putative correspondences generation. The resulting algorithm when tested on real images with or without degenerate configurations gives quality estimations and achieves significant speedups compared to the state of the art algorithms! 1
Guided sampling via weak motion models and outlier sample generation for epipolar geometry estimation
 In Proceedings of the CVPR
, 2005
"... The problem of automatic robust estimation of the epipolar geometry in cases where the correspondences are contaminated with a high percentage of outliers is addressed. This situation often occurs when the images have undergone a significant deformation, either due to large rotation or wide baseline ..."
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Cited by 5 (1 self)
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The problem of automatic robust estimation of the epipolar geometry in cases where the correspondences are contaminated with a high percentage of outliers is addressed. This situation often occurs when the images have undergone a significant deformation, either due to large rotation or wide baseline of the cameras. An accelerated algorithm for the identification of the false matches between the views is presented. The algorithm generates a set of weak motion models (WMMs). Each WMM roughly approximates the motion of correspondences from one image to the other. The algorithm represents the distribution of the median of the geometric distances of a correspondence to the WMMs as a mixture model of outlier correspondences and inlier correspondences. The algorithm generates a sample of outlier correspondences from the data. This sample is used to estimate the outlier rate and to estimate the outlier pdf. Using these two pdfs the probability that each correspondence is an inlier is estimated. These probabilities enable guided sampling. In the RANSAC process this guided sampling accelerates the search process. The resulting algorithm when tested on real images achieves a speedup of between one or two orders of magnitude. 1.
A Generalized Kernel Consensus Based Robust Estimator
, 2009
"... In this paper, we present a new Adaptive Scale Kernel Consensus (ASKC) robust estimator as a generalization of the popular and stateoftheart robust estimators such as RANSAC (RANdom SAmple Consensus), ASSC (Adaptive Scale Sample Consensus) and MKDE (Maximum Kernel Density Estimator). The ASKC fra ..."
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Cited by 5 (3 self)
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In this paper, we present a new Adaptive Scale Kernel Consensus (ASKC) robust estimator as a generalization of the popular and stateoftheart robust estimators such as RANSAC (RANdom SAmple Consensus), ASSC (Adaptive Scale Sample Consensus) and MKDE (Maximum Kernel Density Estimator). The ASKC framework is grounded on and unifies these robust estimators using nonparametric kernel density estimation theory. In particular, we show that each of these methods is a special case of ASKC using a specific kernel. Like these methods, ASKC can tolerate more than 50 percent outliers, but it can also automatically estimate the scale of inliers. We apply ASKC to two important areas in computer vision: robust motion estimation and pose estimation, and show comparative results on both synthetic and real data.
MAXIMUM KERNEL DENSITY ESTIMATOR FOR ROBUST FITTING
"... Robust model fitting plays an important role in many computer vision applications. In this paper, we propose a new robust estimator — Maximum Kernel Density Estimator (MKDE) based on the nonparametric kernel density estimation technique. It can be viewed as an improved version of our previously prop ..."
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Cited by 1 (1 self)
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Robust model fitting plays an important role in many computer vision applications. In this paper, we propose a new robust estimator — Maximum Kernel Density Estimator (MKDE) based on the nonparametric kernel density estimation technique. It can be viewed as an improved version of our previously proposed Quick Maximum Density Power Estimator (QMDPE) [15]. Compared with QMDPE, MKDE does not require running the mean shift algorithm for each candidate fit. Thus, the computational complexity of MKDE is greatly reduced while the accuracy of MKDE is comparable to QMDPE and outperforms that of other popular robust estimators such as LMedS and RANSAC. We evaluate MKDE in robust line fitting and fundamental matrix estimation. Experiments show that MKDE has achieved promising results. Index Terms — machine vision, robustness, model fitting, kernel density estimation, algorithms 1.
Robust Statistics over Riemannian Manifolds for Computer Vision
"... The nonlinear nature of many compute vision tasks involves analysis over curved nonlinear spaces embedded in higher dimensional Euclidean spaces. Such spaces are known as manifolds and can be studied using the theory of differential geometry. In this thesis we develop two algorithms which can be app ..."
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The nonlinear nature of many compute vision tasks involves analysis over curved nonlinear spaces embedded in higher dimensional Euclidean spaces. Such spaces are known as manifolds and can be studied using the theory of differential geometry. In this thesis we develop two algorithms which can be applied over manifolds. The nonlinear mean shift algorithm is a generalization of the original mean shift, a popular feature space analysis method for vector spaces. Nonlinear mean shift can be applied to any Riemannian manifold and is provably convergent to the local maxima of an appropriate kernel density. This algorithm is used for motion segmentation with different motion models and for the filtering of complex image data. The projection based Mestimator is a robust regression algorithm which does not require a user supplied estimate of the scale, the level of noise corrupting the inliers. We build on the connections between kernel density estimation and robust Mestimators and develop data driven rules for scale estimation. The method can be generalized to handle heteroscedastic data and subspace estimation. The results of using pbM for