MDPE: A Very Robust Estimator for Model Fitting and Range Image Segmentation

doi:10.1023/B:VISI.0000022287.61260.B0

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MDPE: A Very Robust Estimator for Model Fitting and Range Image Segmentation

Journal Article•DOI•

MDPE: A Very Robust Estimator for Model Fitting and Range Image Segmentation

Hanzi Wang¹, David Suter¹•Institutions (1)

Monash University, Clayton campus¹

01 Sep 2004-International Journal of Computer Vision (Kluwer Academic Publishers)-Vol. 59, Iss: 2, pp 139-166

TL;DR: A novel and highly robust estimator, called MDPE1 (Maximum Density Power Estimator), which applies nonparametric density estimation and density gradient estimation techniques in parametric estimation (“model fitting”).

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Abstract: In this paper, we propose a novel and highly robust estimator, called MDPE1 (Maximum Density Power Estimator). This estimator applies nonparametric density estimation and density gradient estimation techniques in parametric estimation (“model fitting”). MDPE optimizes an objective function that measures more than just the size of the residuals. Both the density distribution of data points in residual space and the size of the residual corresponding to the local maximum of the density distribution, are considered as important characteristics in our objective function. MDPE can tolerate more than 85% outliers. Compared with several other recently proposed similar estimators, MDPE has a higher robustness to outliers and less error variance. We also present a new range image segmentation algorithm, based on a modified version of the MDPE (Quick-MDPE), and its performance is compared to several other segmentation methods. Segmentation requires more than a simple minded application of an estimator, no matter how good that estimator is: our segmentation algorithm overcomes several difficulties faced with applying a statistical estimator to this task.

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Journal Article•DOI•

Robust adaptive-scale parametric model estimation for computer vision

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Hanzi Wang¹, David Suter¹•Institutions (1)

Monash University, Clayton campus¹

01 Nov 2004-IEEE Transactions on Pattern Analysis and Machine Intelligence

TL;DR: ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model and this work proposes two novel robust techniques: the two-step scale estimator (TSSE) and the adaptive scale sample consensus (ASSC) estimator.

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Abstract: Robust model fitting essentially requires the application of two estimators. The first is an estimator for the values of the model parameters. The second is an estimator for the scale of the noise in the (inlier) data. Indeed, we propose two novel robust techniques: the two-step scale estimator (TSSE) and the adaptive scale sample consensus (ASSC) estimator. TSSE applies nonparametric density estimation and density gradient estimation techniques, to robustly estimate the scale of the inliers. The ASSC estimator combines random sample consensus (RANSAC) and TSSE, using a modified objective function that depends upon both the number of inliers and the corresponding scale. ASSC is very robust to discontinuous signals and data with multiple structures, being able to tolerate more than 80 percent outliers. The main advantage of ASSC over RANSAC is that prior knowledge about the scale of inliers is not needed. ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model. Experiments on synthetic data show that ASSC has better robustness to heavily corrupted data than least median squares (LMedS), residual consensus (RESC), and adaptive least Kth order squares (ALKS). We also apply ASSC to two fundamental computer vision tasks: range image segmentation and robust fundamental matrix estimation. Experiments show very promising results.

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169 citations

Cites methods from "MDPE: A Very Robust Estimator for M..."

...Indeed, we propose two novel robust techniques: the Two-Step Scale estimator (TSSE) and the Adaptive Scale Sample Consensus (ASSC) estimator....
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...In this section, we investigate the behavior of several robust scale estimators that are widely used in computer vision community: showing some of the weaknesses of these scale estimation techniques....
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...By employing TSSE in a RANSAC like procedure, we propose a highly robust estimator: Adaptive Scale Sample Consensus (ASSC) estimator....
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...In the next section, we will propose a new robust estimator—Adaptive Scale Sample Consensus (ASSC) estimator, which can estimate the parameters and the scale simultaneously....
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...Index Terms—Robust model fitting, random sample consensus, least-median-of-squares, residual consensus, adaptive least kth order squares, kernel density estimation, mean shift, range image segmentation, fundamental matrix estimation....
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Proceedings Article•DOI•

Robust Statistical Estimation and Segmentation of Multiple Subspaces

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Allen Y. Yang¹, Shankar R. Rao¹, Yi Ma¹•Institutions (1)

University of Illinois at Urbana–Champaign¹

17 Jun 2006

TL;DR: A comprehensive survey of robust statistical techniques in the literature is provided, and three main approaches for detecting and rejecting outliers are identified: random sample consensus, the influence function, and multivariate trimming.

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Abstract: We study the problem of estimating a mixed geometric model of multiple subspaces in the presence of a significant amount of outliers. The estimation of multiple subspaces is an important problem in computer vision, particularly for segmenting multiple motions in an image sequence. We first provide a comprehensive survey of robust statistical techniques in the literature, and identify three main approaches for detecting and rejecting outliers. Through a careful examination of these approaches, we propose and investigate three principled methods for robustly estimating mixed subspace models: random sample consensus, the influence function, and multivariate trimming. Using a benchmark synthetic experiment and a set of real image sequences, we conduct a thorough comparison of the three methods

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103 citations

Cites methods from "MDPE: A Very Robust Estimator for M..."

...In the computer vision literature, the latter approach dominates most applications [2, 4, 21, 25, 30] because applying RANSAC on individual simple geometric models has been well studied, and the algorithm complexity is much lower....
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Journal Article•DOI•

A Novel Subpixel Phase Correlation Method Using Singular Value Decomposition and Unified Random Sample Consensus

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Xiaohua Tong¹, Zhen Ye¹, Yusheng Xu¹, Shijie Liu¹, Lingyun Li¹, Huan Xie¹, Li Tianpeng¹ - Show less +3 more•Institutions (1)

Tongji University¹

11 Feb 2015-IEEE Transactions on Geoscience and Remote Sensing

TL;DR: A novel subpixel phase correlation method using singular value decomposition (SVD) and the unified random sample consensus (RANSAC) algorithm and the pixel locking effect was found to be significantly weakened by the proposed method, as compared with the original Hoge's method.

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Abstract: Subpixel translation estimation using phase correlation is a fundamental task for numerous applications in the remote sensing community. The major drawback of the existing subpixel phase correlation methods lies in their sensitivity to corruption, including aliasing and noise, as well as the poor performance in the case of practical remote sensing data. This paper presents a novel subpixel phase correlation method using singular value decomposition (SVD) and the unified random sample consensus (RANSAC) algorithm. In the proposed method, SVD theoretically converts the translation estimation problem to one dimensions for simplicity and efficiency, and the unified RANSAC algorithm acts as a robust estimator for the line fitting, in this case for the high accuracy, stability, and robustness. The proposed method integrates the advantages of Hoge's method and the RANSAC algorithm and avoids the corresponding shortfalls of the original phase correlation method based only on SVD. A pixel-to-pixel dense matching scheme on the basis of the proposed method is also developed for practical image registration. Experiments with both simulated and real data were carried out to test the proposed method. In the simulated case, the comparative results estimated from the generated synthetic image pairs indicate that the proposed method outperforms the other existing methods in the presence of both aliasing and noise, in both accuracy and robustness. Moreover, the pixel locking effect that commonly occurs in subpixel matching was also investigated. The degree of pixel locking effect was found to be significantly weakened by the proposed method, as compared with the original Hoge's method. In the real data case, experiments using different bands of ZY-3 multispectral sensor-corrected images demonstrate the promising performance and feasibility of the proposed method, which is able to identify seams of the image stitching between sub-charge-coupled device units.

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97 citations

Cites methods from "MDPE: A Very Robust Estimator for M..."

...RANSAC is performed in a randomized, hypothesize-andverify manner, which can yield good-quality estimates even when more than 50% of sample points are considered as gross errors [44], [45]....
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Book Chapter•DOI•

Nonparametric estimation of multiple structures with outliers

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Wei Zhang¹, Jana Kosecka¹•Institutions (1)

George Mason University¹

13 May 2006

TL;DR: A novel nonparametric sampling based method for estimating the number of models and their parameters, capable of handling data with a large fraction of outliers and showing that the modes of the residual distributions directly reveal the presence of multiple models and facilitate the recovery of the individual models.

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Abstract: Common problem encountered in the analysis of dynamic scene is the problem of simultaneous estimation of the number of models and their parameters. This problem becomes difficult as the measurement noise in the data increases and the data are further corrupted by outliers. This is especially the case in a variety of motion estimation problems, where the displacement between the views is large and the process of establishing correspondences is difficult. In this paper we propose a novel nonparametric sampling based method for estimating the number of models and their parameters. The main novelty of the proposed method lies in the analysis of the distribution of residuals of individual data points with respect to the set of hypotheses, generated by a RANSAC-like sampling process. We will show that the modes of the residual distributions directly reveal the presence of multiple models and facilitate the recovery of the individual models, without making any assumptions about the distribution of the outliers or the noise process. The proposed approach is capable of handling data with a large fraction of outliers. Experiments with both synthetic data and image pairs related by different motion models are presented to demonstrate the effectiveness of the proposed approach.

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90 citations

Cites background or methods from "MDPE: A Very Robust Estimator for M..."

...Instead of studying the distribution of N residuals per hypothesis as in [7] when trying to determine the threshold for inlier classification, we propose to study the distribution of M residuals for each data point xi....
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...In [7] the authors propose a novel MDPE estimator (Maximal Density Power Estimator), which selects a hypothesis, whose corresponding density of residuals is maximal, with the mean close to zero....
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...According to the result of [7], existing robust estimators are likely to fail in this case....
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...The approach described here shares some features of the method proposed in [7], but differs in significant ways, which enable significant extensions to estimation of multiple models....
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Journal Article•DOI•

Fast Global Kernel Density Mode Seeking: Applications to Localization and Tracking

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Chunhua Shen¹, Michael J. Brooks¹, A. van den Hengel¹•Institutions (1)

University of Adelaide¹

01 May 2007-IEEE Transactions on Image Processing

TL;DR: This work proposes a novel multibandwidth MS procedure which converges to the global mode of the density function, regardless of the initialization point, and observes that an over-smoothed density function with a sufficiently large bandwidth is unimodal.

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Abstract: Tracking objects in video using the mean shift (MS) technique has been the subject of considerable attention. In this work, we aim to remedy one of its shortcomings. MS, like other gradient ascent optimization methods, is designed to find local modes. In many situations, however, we seek the global mode of a density function. The standard MS tracker assumes that the initialization point falls within the basin of attraction of the desired mode. When tracking objects in video this assumption may not hold, particularly when the target's displacement between successive frames is large. In this case, the local and global modes do not correspond and the tracker is likely to fail. A novel multibandwidth MS procedure is proposed which converges to the global mode of the density function, regardless of the initialization point. We term the procedure annealed MS, as it shares similarities with the annealed importance sampling procedure. The bandwidth of the procedure plays the same role as the temperature in conventional annealing. We observe that an over-smoothed density function with a sufficiently large bandwidth is unimodal. Using a continuation principle, the influence of the global peak in the density function is introduced gradually. In this way, the global maximum is more reliably located. Since it is imperative that the computational complexity is minimal for real-time applications, such as visual tracking, we also propose an accelerated version of the algorithm. This significantly decreases the number of iterations required to achieve convergence. We show on various data sets that the proposed algorithm offers considerable promise in reliably and rapidly finding the true object location when initialized from a distant point

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87 citations

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References

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Journal Article•DOI•

Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

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Martin A. Fischler¹, Robert C. Bolles¹•Institutions (1)

SRI International¹

01 Jun 1981-Communications of The ACM

TL;DR: New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.

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Abstract: A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing

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23,396 citations

"MDPE: A Very Robust Estimator for M..." refers methods in this paper

...Experiments, presented next, show the MDPE is a very powerful method for data with a large percentage of outliers....
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...RANSAC (Fischler and Rolles, 1981) applies criterion (1) into its optimization process and outputs the results with the highest number of data points within an error bound; The Least squares method uses criterion (2) as its objective function, but minimizes the residuals of all data points without…...
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Book•DOI•

Density estimation for statistics and data analysis

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Bernard W. Silverman

01 Jan 1986

TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.

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Abstract: Introduction. Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods. Density Estimation in Action.

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15,499 citations

Journal Article•DOI•

Mean shift: a robust approach toward feature space analysis

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Dorin Comaniciu¹, Peter Meer¹•Institutions (1)

Princeton University¹

01 May 2002-IEEE Transactions on Pattern Analysis and Machine Intelligence

TL;DR: It is proved the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density.

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Abstract: A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

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11,727 citations

"MDPE: A Very Robust Estimator for M..." refers background or methods in this paper

...Experiment 4 The problem of the choice of window radius in the means shift, i.e., bandwidth selection, has been widely investigated during the past decades (Silverman, 1986; Wand and Jones, 1995; Comaniciu and Meer, 1999, 2002; Comaniciu et al., 2001)....
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...Comaniciu and Meer (2002) suggested several techniques for the choice of window radius: (1) The optimal bandwidth should be the one that minimizes AMISE; (2) The choice of the bandwidth can be taken as the center of the largest operating range over which the same results are obtained for the same…...
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...The proof of the convergence of the mean shift algorithm can be found in Comaniciu and Meer (1999, 2002)....
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...Since its introduction by Fukunaga and Hostetler (1975), the mean shift method has been extensively exploited and applied in low level computer vision tasks (Cheng, 1995; Comaniciu and Meer, 1997, 1999, 2002) for its ease and efficiency....
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Book•

Introduction to Statistical Pattern Recognition

[...]

Keinosuke Fukunaga

01 Jan 1972

TL;DR: This completely revised second edition presents an introduction to statistical pattern recognition, which is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field.

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Abstract: This completely revised second edition presents an introduction to statistical pattern recognition Pattern recognition in general covers a wide range of problems: it is applied to engineering problems, such as character readers and wave form analysis as well as to brain modeling in biology and psychology Statistical decision and estimation, which are the main subjects of this book, are regarded as fundamental to the study of pattern recognition This book is appropriate as a text for introductory courses in pattern recognition and as a reference book for workers in the field Each chapter contains computer projects as well as exercises

...read moreread less

10,526 citations

Book•

Robust Regression and Outlier Detection

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Peter J. Rousseeuw, Annick M. Leroy

01 Jan 1987

TL;DR: This paper presents the results of a two-year study of the statistical treatment of outliers in the context of one-Dimensional Location and its applications to discrete-time reinforcement learning.

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Abstract: 1. Introduction. 2. Simple Regression. 3. Multiple Regression. 4. The Special Case of One-Dimensional Location. 5. Algorithms. 6. Outlier Diagnostics. 7. Related Statistical Techniques. References. Table of Data Sets. Index.

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6,955 citations

"MDPE: A Very Robust Estimator for M..." refers background or methods in this paper

...In order to improve the statistical efficiency, a weighted least square procedure (Rousseeuw and Leroy, 1987, p. 202) can be carried out after the initial MDPE fit....
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...Moreover, though there is a formal proof of high breakdown point (0.5, see Rousseeuw and Leroy, 1987, p. 125), this proof only applies to the exact LMedS and not the approximate method (using random sampling) that has to be used in practice....
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...In the statistical literature (Huber, 1981; Rousseeuw and Leroy, 1987), there are a number of precise definitions of robustness and of robust properties: including the aforementioned “breakdown point”—which is an attempt to characterize the tolerance of an estimator to large percentages of outliers....
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...The breakdown point of an estimator may be roughly defined as the smallest percentage of outlier contamination that can cause the estimator to produce arbitrarily large values (Rousseeuw and Leroy, 1987, p. 9)....
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...Although the breakdown point in statistics is proved to be bounded by 0.5 (Rousseeuw and Leroy, 1987, p. 125), the proof shows that they require the robust estimator has a unique solution (more technically, they require affine equivariance)....
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