A consensus sampling technique for fast and robust model fitting

In this paper, a new algorithm is proposed to improve the efficiency and robustness of random sampling consensus (RANSAC) without prior information about the error scale. Three techniques are developed in an iterative hypothesis-and-evaluation framework. Firstly, we propose a consensus sampling technique to increase the probability of sampling inliers by exploiting the feedback information obtained from the evaluation procedure. Secondly, the preemptive multiple K-th order approximation (PMKA) is developed for efficient model evaluation with unknown error scale. Furthermore, we propose a coarse-to-fine strategy for the robust standard deviation estimation to determine the unknown error scale. Experimental results of the fundamental matrix computation on both simulated and real data are shown to demonstrate the superiority of the proposed algorithm over the previous methods.     

Using symmetry in robust model fitting

The pattern recognition and computer vision communities often employ robust methods for model fitting. In particular, high breakdown-point methods such as least median of squares (LMedS) and least trimmed squares (LTS) have often been used in situations where the data are contaminated with outliers. However, though the breakdown point of these methods can be as high as 50% (they can be robust to up to 50% contamination), they can break down at unexpectedly lower percentages when the outliers are clustered. In this paper, we demonstrate the fragility of LMedS and LTS and analyze the reasons that cause the fragility of these methods in the situation when a large percentage of clustered outliers exist in the data. We adapt the concept of “symmetry distance” to formulate an improved regression method, called the least trimmed symmetry distance (LTSD). Experimental results are presented to show that the LTSD performs better than LMedS and LTS under a large percentage of clustered outliers and large standard variance of inliers.     

Preemptive RANSAC for live structure and motion estimation

A system capable of performing robust live ego-motion estimation for perspective cameras is presented. The system is powered by random sample consensus with preemptive scoring of the motion hypotheses. A general statement of the problem of efficient preemptive scoring is given. Then a theoretical investigation of preemptive scoring under a simple inlier–outlier model is performed. A practical preemption scheme is proposed and it is shown that the preemption is powerful enough to enable robust live structure and motion estimation.Prepared through collaborative participation in the Robotics Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0012. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. David Nistér received PhD degree in computer vision, numerical analysis and computing science from the Royal Institute of Technology (KTH), Stockholm, Sweden, with the thesis ‘Automatic Dense Reconstruction from Uncalibrated Video Sequences’. He is currently an assistant professor at the Computer Science Department and the Center for Visualization and Virtual Environments, University of Kentucky, Lexington. Before joining UK, he was a researcher in the Vision Technologies Laboratory, Sarnoff Corporation, Princeton, and Visual Technology, Ericsson Research, Stockholm, Sweden. His research interests include computer vision, computer graphics, structure from motion, multiple view geometry, Bayesian formulations, tracking, recognition, image and video compression. He is a member of the IEEE and American Mensa.     

A simultaneous sample-and-filter strategy for robust multi-structure model fitting

In many robust model fitting methods, obtaining promising hypotheses is critical to the fitting process. However the sampling process unavoidably generates many irrelevant hypotheses, which can be an obstacle for accurate model fitting. In particular, the mode seeking based fitting methods are very sensitive to the proportion of good/bad hypotheses for fitting multi-structure data. To improve hypothesis generation for the mode seeking based fitting methods, we propose a novel sample-and-filter strategy to (1) identify and filter out bad hypotheses on-the-fly, and (2) use the remaining good hypotheses to guide the sampling to further expand the set of good hypotheses. The outcome is a small set of hypotheses with a high concentration of good hypotheses. Compared to other sampling methods, our method yields a significantly large proportion of good hypotheses, which greatly improves the accuracy of the mode seeking-based fitting methods.     

随机抽样一致性平面拟合及其应用研究

针对传统平面拟合算法难以拟合包含异常值点云的问题,提出结合特征值法的随机抽样一致性（RANSAC）平面拟合算法。随机选取三个点云数据直接计算平面,选择阈值统计在此平面上的内点数量,多次重复求得包含最多内点的平面,并以这些内点以特征值法进行平面拟合得到所求平面方程。对各种包含误差及异常值的平面点云进行拟合计算,并与传统算法进行比较,将其应用于双目重构得到的隧道开挖掌子面岩体三维数字模型中节理面点云平面拟合。实验结果表明该方法可以很好地适应各种误差和异常值的情况,稳定地得到较好的平面参数估计值,是一种鲁棒的平面拟合算法。     

On a fast, robust estimator of the mode: Comparisons to other robust estimators with applications

Advances in computing power enable more widespread use of the mode, which is a natural measure of central tendency since it is not influenced by the tails in the distribution. The properties of the half-sample mode, which is a simple and fast estimator of the mode of a continuous distribution, are studied. The half-sample mode is less sensitive to outliers than most other estimators of location, including many other low-bias estimators of the mode. Its breakdown point is one half, equal to that of the median. However, because of its finite rejection point, the half-sample mode is much less sensitive to outliers that are all either greater or less than the other values of the sample. This is confirmed by applying the mode estimator and the median to samples drawn from normal, lognormal, and Pareto distributions contaminated by outliers. It is also shown that the half-sample mode, in combination with a robust scale estimator, is a highly robust starting point for iterative robust location estimators such as Huber's M-estimator. The half-sample mode can easily be generalized to modal intervals containing more or less than half of the sample. An application of such an estimator to the finding of collision points in high-energy proton–proton interactions is presented.     

Efficient generic face model fitting to images and videos

In this paper we present a robust and lightweight method for the automatic fitting of deformable 3D face models on facial images. Popular fitting techniques such as those based on statistical models of shape and appearance require a training stage based on a set of facial images and their corresponding facial landmarks, which have to be manually labeled. Therefore, new images in which to fit the model cannot differ too much in shape and appearance (including illumination variation, facial hair, wrinkles, etc.) from those used for training. By contrast, our approach can fit a generic face model in two steps: (1) the detection of facial features based on local image gradient analysis and (2) the backprojection of a deformable 3D face model through the optimization of its deformation parameters. The proposed approach can retain the advantages of both learning-free and learning-based approaches. Thus, we can estimate the position, orientation, shape and actions of faces, and initialize user-specific face tracking approaches, such as Online Appearance Models (OAMs), which have shown to be more robust than generic user tracking approaches. Experimental results show that our method outperforms other fitting alternatives under challenging illumination conditions and with a computational cost that allows its implementation in devices with low hardware specifications, such as smartphones and tablets. Our proposed approach lends itself nicely to many frameworks addressing semantic inference in face images and videos.     

A neural model for the integration of stereopsis and motion parallax in structure from motion

We introduce a model for the computation of structure from motion based on the physiology of visual cortical areas MT and MST. The model assumes that the perception of depth from motion is related to the firing of a subset of MT neurons tuned to both velocity and disparity. The model's MT neurons are connected to each other laterally to form modulatory receptive-field surrounds that are gated by feedback connections from area MST. This allows the building up of a depth map from motion in area MT, even in absence of disparity in the input. Depth maps from motion and from stereo are combined by a weighted average at a final stage. The model's predictions for the interaction between motion and stereo cues agree with previous psychophysical data, both when the cues are consistent with each other or when they are contradictory. In particular, the model shows nonlinearities as a result of early interactions between motion and stereo before their depth maps are averaged. The two cues interact in a way that represents an alternative to the “modified weak fusion” model of depth–cue combination.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

基于加速健壮特征拟合算法和Chan-Vese模型的超声图像腔室分割方法

针对超声心动周期序列图的腔室自动分割过程中,弱边缘轮廓难以有效提取的问题,提出一种基于加速健壮特征(SURF)拟合算法和Chan-Vese模型的超声图像腔室分割方法。首先对序列中第一帧图像进行人工标记弱边缘轮廓;然后,提取弱边缘轮廓周围的SURF点,建立Delaunay三角网;接着,通过相邻两帧之间的特征点匹配,预测后续帧的弱边缘轮廓;之后,用Chan-Vese模型提取粗糙轮廓;最后采用区域生长算法得到精确的目标轮廓。实验结果表明,该算法能较好地完整提取超声序列图像中含弱边缘的腔室轮廓,并且与专家手动分割结果相近。     

An Iterative Multiresolution Scheme for SFM with Missing Data

Several techniques have been proposed for tackling the Structure from Motion problem through factorization in the case of missing data. However, when the percentage of unknown data is high, most of them may not perform as well as expected. Focussing on this problem, an iterative multiresolution scheme, which aims at recovering missing entries in the originally given input matrix, is proposed. Information recovered following a coarse-to-fine strategy is used for filling in the missing entries. The objective is to recover, as much as possible, missing data in the given matrix. Thus, when a factorization technique is applied to the partially or totally filled in matrix, instead of to the originally given input one, better results will be obtained. An evaluation study about the robustness to missing and noisy data is reported. Experimental results obtained with synthetic and real video sequences are presented to show the viability of the proposed approach.

Global robust output regulation of lower triangular systems with unknown control direction

This paper presents the solvability conditions for the global robust output regulation problem for lower triangular nonlinear systems assuming the control direction is unknown. The approach used is an integration of the robust stabilization technique and Nussbaum gain technique.     

Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency

Asymptotically stable, observable linear systems of order n which are not required to be minimum phase and are affected by an additive noisy biased sinusoidal disturbance with unknown bias, magnitude, phase and frequency are considered. The problem of designing an output feedback compensator which regulates the output to zero for any initial condition and for any biased sinusoidal disturbance with no noise is addressed, under the assumption that the system parameters are known. This problem is solved by a (2n+6)-order compensator which generates asymptotically convergent estimates of the biased sinusoidal disturbance and of its parameters, including frequency. The robustness of the closed loop system with respect to sufficiently small additive unmodelled noise is characterized in terms of input-to-state stability.     

White noise theory of robust nonlinear filtering with correlated state and observation noises

In the existing ‘direct’ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a ‘finitely additive’ white noise is used to model the observation noise. We remove this asymmetry by modelling the state process as the solution of a (stochastic) differential equation with a ‘finitely additive’ white noise as the input. This enables us to introduce correlation between the state and observation noises, and to obtain robust nonlinear filtering equations in the correlated noise case.     

Spherical approximation for multiple cameras in motion estimation: Its applicability and advantages

Estimating motions of a multi-camera system which may not have overlapping fields of view is generally complex and computationally expensive because of the non-zero offset between each camera’s center. It is conceivable that if we can assume that multiple cameras share a single optical center, and thus can be modeled as a spherical imaging system, motion estimation and calibration of this system would become simpler and more efficient.     

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.     

A robust dynamic programming algorithm for motion detection and estimation

A new robust algorithm for motion detection and precise evaluation of the motion vectors of moving objects in a sequence of images is presented. It is well known that the accuracy of estimating motion vectors estimation is limited by smoothness constraints and mutual occlusions of motion segments. The proposed method is a fusion of block-matching motion estimation and global optimization technique. It is robust to motion discontinuity and moving objects occlusions. To avoid some contradictions between global optimization techniques and piece-wise smooth values of sought motion vectors, a hidden segmentation model is utilized. Computer simulation and experimental results demonstrate an excellent performance of the method in terms of dynamic motion analysis. This article was translated by the authors. Mikhail Mozerov received his MS degree in Physics from the Moscow State University in 1982 and his PhD degree in Image Processing from the Institute of Information Transmission Problems, Russian Academy of Sciences, in 1995. He works at the Laboratory of Digital Optics of the Institute of Information Transmission Problems, Russian Academy of Sciences. His research interests include signal and image processing, pattern recognition, digital holography. Vitaly Kober obtained his MS degree in Applied Mathematics from the Air-Space University of Samara (Russia) in 1984, and his PhD degree in 1992 and Doctor of Sciences degree in 2004 in Image Processing from the Institute of Information Transmission Problems, Russian Academy of Sciences. Now he is a titular researcher at the Centro de Investigación Científica y de Educación Superior de Ensenada (Cicese), México. His research interests include signal and image processing, pattern recognition. Iosif A. Ovseyevich graduated from the Moscow Electrotechnical Institute of Telecommunications. Received candidate’s degree in 1953 and doctoral degree in information theory in 1972. At present, he is Emeritus Professor at the Institute of Information Transmission Problems of the Russian Academy of Sciences. His research interests include information theory, signal processing, and expert systems. He is a Member of IEEE, Popov Radio Society.     

Omnidirectional video

Omnidirectional video enables direct surround immersive viewing of a scene by warping the original image into the correct perspective given a viewing direction. However, novel views from viewpoints off the camera path can only be obtained if we solve the three-dimensional motion and calibration problem. In this paper we address the case of a parabolic catadioptric camera – a paraboloidal mirror in front of an orthographic lens – and we introduce a new representation, called the circle space, for points and lines in such images. In this circle space, we formulate an epipolar constraint involving a 4×4 fundamental matrix. We prove that the intrinsic parameters can be inferred in closed form from the two-dimensional subspace of the new fundamental matrix from two views if they are constant or from three views if they vary. Three-dimensional motion and structure can then be estimated from the decomposition of the fundamental matrix.     

The optimal projection equations for reduced-order, discrete-time state estimation for linear systems with multiplicative white noise

The optimal projection equations obtained in [2,3] for reduced-order, discrete-time state estimation are generalized to include the effects of state- and measurement-dependent noise to provide a model of parameter uncertainty. In contrast to the single matrix Riccati equation arising in the full-order (Kalman filter) case, the optimal steady-state reduced-order discrete-time estimator is characterized by three matrix equations (one modified Riccati equation and two modified Lyapunov equations) coupled by both an oblique projection and stochastic effects.     

Corner-based estimation of tire forces and vehicle velocities robust to road conditions

Recent developments in vehicle stability control and active safety systems have led to an interest in reliable vehicle state estimation on various road conditions. This paper presents a novel method for tire force and velocity estimation at each corner to monitor tire capacities individually. This is entailed for more demanding advanced vehicle stability systems and especially in full autonomous driving in harsh maneuvers. By integrating the lumped LuGre tire model and the vehicle kinematics, it is shown that the proposed corner-based estimator does not require knowledge of the road friction and is robust to model uncertainties. The stability of the time-varying longitudinal and lateral velocity estimators is explored. The proposed method is experimentally validated in several maneuvers on different road surface frictions. The experimental results confirm the accuracy and robustness of the state estimators.