Point set registration: coherent point drift

Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.     

含局部空间约束的t分布混合模型的点集配准

基于高斯混合模型（Gaussian mixture model,GMM）的点集非刚性配准算法易受重尾点和异常点影响,提出含局部空间约束的t分布混合模型的点集非刚性配准算法. 通过期望最大化（Expectation maximization,EM）框架将高斯混合模型推广为t分布混合模型;把Dirichlet分布作为浮动点的先验权重,并构造含局部空间约束性质的Dirichlet 分布参数. 使用EM算法获得配准参数的闭合解;计算浮动点的自由度,改变其概率密度分布,避免异常点水平估计误差. 实验表明,本文提出的配准算法具有配准误差小、鲁棒性好、抗干扰能力强等优点.     

一种基于概率的孤立点检测方法

现有孤立点检测方法大多数都需要预先设定孤立点个数,若设定不准确将降低孤立点检测的准确性。针对该问题,提出一种基于概率的孤立点检测方法。结合基于密度的DBSCAN算法与中位数求方差的方法,对待检测数据集进行聚类,提取出不包含在任何聚类中的可疑孤立点并进行分析,从而确定最终孤立点。该方法所检测的数据与时间因素线性无关,不必预先设定孤立点个数及聚类数,并且对噪声数据具有较强的抗干扰能力。IRIS测试数据集上的实验结果表明,该方法能够有效地识别孤立点。     

基于全局与局部相似性测度的非刚性点集配准

非刚性点集配准算法中，能否找到正确的对应关系对配准结果起着至关重要的作用，而通常两个点集中的对应点除了距离比较接近之外还具有相似的邻域结构，因此提出基于全局与局部相似性测度的非刚性点集配准算法。首先，使用一致性点漂移（CPD）算法作为配准框架，采用高斯混合模型对点集进行建模。然后，对全局局部混合距离进行改进，形成全局与局部相似性测度准则。最后，采用期望最大化（EM）算法迭代地求解对应关系和变换公式：在迭代初期局部相似性所占比重较大，从而能够尽快地找到正确的对应关系；随着迭代的进展全局相似性比重逐渐增大，从而确保得到较小的配准误差。实验结果表明，与薄板样条鲁棒点匹配（TPS-RPM）算法、高斯混合模型点集配准（GMMREG）算法、基于L₂E估计的鲁棒点匹配算法（RPM-L2E）、基于全局局部混合距离与薄板样条的点集配准算法（GLMDTPS）和CPD算法相比，所提算法的均方根误差（RMSE）分别下降了39.93%、42.45%、32.51%、22.36%和11.76%，说明该算法具有较好的配准效果。     

基于聚类的两段式孤立点检测算法

现有的大多数孤立点检测算法都需要预先设定孤立点个数,并且还缺乏对不均匀数据集的检测能力。针对以上问题,提出了基于聚类的两段式孤立点检测算法,该算法首先用DBSCAN聚类算法产生可疑孤立点集合,然后利用剪枝策略对数据集进行剪枝,并用基于改进距离的孤立点检测算法产生最可能孤立点排序集合,最终由两个集合的交集确定孤立点集合。该算法不必预先设定孤立点个数,具有较高的准确率与检测效率,并且对数据集的分布状况不敏感。数据集上的实验结果表明,该算法能够高效、准确地识别孤立点。     

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point (ICP) algorithm has the advantages of high accuracy and fast speed for point set registration, but it performs poorly when the point set has a large number of noisy outliers. To solve this problem, we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers. Firstly, we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model, which can avoid the influence of outliers. To maximize the objective function, we then propose a robust affine ICP algorithm. At each iteration of this new algorithm, we set up the index mapping of two point sets according to the known transformation, and then compute the closed-form solution of the new transformation according to the known index mapping. Similar to the traditional ICP algorithm, our algorithm converges to a local maximum monotonously for any given initial value. Finally, the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.      

Consistency Clustering: A Robust Algorithm for Group-wise Registration,Segmentation and Automatic Atlas Construction in Diffusion MRI

We propose an integrated registration and clustering algorithm, called “consistency clustering”, that automatically constructs a probabilistic white-matter atlas from a set of multi-subject diffusion weighted MR images. We formulate the atlas creation as a maximum likelihood problem which the proposed method solves using a generalized Expectation Maximization (EM) framework. Additionally, the algorithm employs an outlier rejection and denoising strategy to produce sharp probabilistic maps of certain bundles of interest. We test this algorithm on synthetic and real data, and evaluate its stability against initialization. We demonstrate labeling a novel subject using the resulting spatial atlas and evaluate the accuracy of this labeling. Consistency clustering is a viable tool for completely automatic white-matter atlas construction for sub-populations and the resulting atlas is potentially useful for making diffusion measurements in a common coordinate system to identify pathology related changes or developmental trends.     

The thin plate spline robust point matching (TPS-RPM) algorithm: A revisit

This paper reviews the TPS-RPM algorithm (Chui and Rangarajan, 2003) for robustly registering two sets of points and demonstrates from a theoretical point of view its inherent limited performance when outliers are present in both point sets simultaneously. A double-sided outlier handling approach is proposed to overcome this limitation with a rigorous mathematical proof as the underlying theoretical support. This double-sided outlier handling approach is proved to be equivalent to the original formulation of the point matching problem. For a practical application, we also extend the TPS-RPM algorithms to non-rigid image registration by registering two sets of sparse features extracted from images. The intensity information of the extracted features are incorporated into feature matching in order to reduce the impact from outliers. Our experiments demonstrate the double-sided outlier handling approach and the efficiency of intensity information in assisting outlier detection.     

基于K-means的数据流离群点检测算法

针对数据流中离群点挖掘问题,在K-means聚类算法基础上,提出了基于距离的准则进行数据间离群点判断的离群点检测DOKM算法。根据数据流概念漂移检测结果来自适应地调整滑动窗口大小,从而实现对数据流的离群点检测,与其他离群点算法的一系列实验验证和对比结果表明,DOKM算法在人工数据集和真实数据集中均可以实现对离群点的有效检测。     

A new point matching algorithm for non-rigid registration

Feature-based methods for non-rigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, feature-based non-rigid matching requires us to automatically solve for correspondences between two sets of features. In addition, there could be many features in either set that have no counterparts in the other. This outlier rejection problem further complicates an already difficult correspondence problem. We formulate feature-based non-rigid registration as a non-rigid point matching problem. After a careful review of the problem and an in-depth examination of two types of methods previously designed for rigid robust point matching (RPM), we propose a new general framework for non-rigid point matching. We consider it a general framework because it does not depend on any particular form of spatial mapping. We have also developed an algorithm—the TPS–RPM algorithm—with the thin-plate spline (TPS) as the parameterization of the non-rigid spatial mapping and the softassign for the correspondence. The performance of the TPS–RPM algorithm is demonstrated and validated in a series of carefully designed synthetic experiments. In each of these experiments, an empirical comparison with the popular iterated closest point (ICP) algorithm is also provided. Finally, we apply the algorithm to the problem of non-rigid registration of cortical anatomical structures which is required in brain mapping. While these results are somewhat preliminary, they clearly demonstrate the applicability of our approach to real world tasks involving feature-based non-rigid registration.     

基于局部密度的快速离群点检测算法

已有的密度离群点检测算法LOF不能适应数据分布异常情况离群点检测,INFLO算法虽引入反向k近邻点集有效地解决了数据分布异常情况的离群点检测问题,但存在需要对所有数据点不加区分地分析其k近邻和反向k近邻点集导致的效率降低问题。针对该问题,提出局部密度离群点检测算法--LDBO,引入强k近邻点和弱k近邻点概念,通过分析邻近数据点的离群相关性,对数据点区别对待;并提出数据点离群性预判断策略,尽可能避免不必要的反向k近邻分析,有效提高数据分布异常情况离群点检测算法的效率。理论分析和实验结果表明,LDBO算法效率优于INFLO,算法是有效可行的。     

A fast and automatic stereotactic registration with a single CT-slice

The paper presents an algorithm for the automatic registration of a stereotactic frame from a single slice captured by a computed tomography (CT) scanner. Such registration is needed in interventional radiology for CT-image guidance of a robotic assistant. Stereotactic registration is based on a set of line fiducials that produce a set of image points. Our objective is to achieve the automatic registration of a stereotactic frame in the presence of noisy data and outliers. To this end, a new formulation of the stereotactic registration problem with a single image is proposed, for any configuration of the fiducials. With very few fiducials, closed-form and numerical solutions are presented. This comes in useful for building a robust automatic line to point matching algorithm based on the RANSAC statistical method. Simulation and experimental results are presented and highlight the robustness properties of the algorithm. They show that the registration is accurate with moderate computing requirements even for a large amount of outliers.     

一种基于多示例学习的局部离群点检测算法

提出了一种基于多示例学习（multi-instance learning,MIL）的局部离群点检测算法,称之为MIL-LOF（a local outlier factor based on multi-instance learning）．算法采用MIL框架,首先将真实对象提取为多示例形式,然后运用退化策略和权重调整方法,计算综合离群点因子,最后检测离群点．在实际企业监控数据以及公共数据集上将MIL-LOF与经典局部离群点检测算法及其优化算法进行了对比实验,结果表明本文提出的MIL-LOF算法在准确性、全面性及高效性上相对其他算法均可获得较为明显的提高．     

Robust probabilistic PCA with missing data and contribution analysis for outlier detection

Principal component analysis (PCA) is a widely adopted multivariate data analysis technique, with interpretation being established on the basis of both classical linear projection and a probability model (i.e. probabilistic PCA (PPCA)). Recently robust PPCA models, by using the multivariate t-distribution, have been proposed to consider the situation where there may be outliers within the data set. This paper presents an overview of the robust PPCA technique, and further discusses the issue of missing data. An expectation-maximization (EM) algorithm is presented for the maximum likelihood estimation of the model parameters in the presence of missing data. When applying robust PPCA for outlier detection, a contribution analysis method is proposed to identify which variables contribute the most to the occurrence of outliers, providing valuable information regarding the source of outlying data. The proposed technique is demonstrated on numerical examples, and the application to outlier detection and diagnosis in an industrial fermentation process.     

A hybrid approach to outlier detection based on boundary region

In recent years, much attention has been given to the problem of outlier detection, whose aim is to detect outliers - objects who behave in an unexpected way or have abnormal properties. The identification of outliers is important for many applications such as intrusion detection, credit card fraud, criminal activities in electronic commerce, medical diagnosis and anti-terrorism, etc. In this paper, we propose a hybrid approach to outlier detection, which combines the opinions from boundary-based and distance-based methods for outlier detection ( [Jiang et al., 2005], [Jiang et al., 2009] and [Knorr and Ng, 1998]). We give a novel definition of outliers - BD (boundary and distance)-based outliers, by virtue of the notion of boundary region in rough set theory and the definitions of distance-based outliers. An algorithm to find such outliers is also given. And the effectiveness of our method for outlier detection is demonstrated on two publicly available databases.     

三维点云配准中的计算智能方法综述

随着三维数据采集设备的成熟与普及,由激光雷达、结构光传感器和立体相机等设备采集的点云数据引起了广泛关注,并以此研究出针对点云的配准、分类、分割和跟踪等算法,推动了点云相关研究领域的科研进展。点云配准是点云数据处理的一个重要研究方向,旨在找到一个刚性变换运动参数,使得运动参数作用于源点云后能够与参考点云对齐。传统的点云配准方法大多存在着对初始位姿、异常值敏感等问题,而计算智能方法在处理点云配准问题,例如去除孤立点或求解矩阵时可以有效解决这些问题,并且能够适用于点云重叠程度低的情况,表现出较强的鲁棒性和泛化性。这种方法不依赖于问题本身特性,也不需要建立精确的模型,只需要求出替代真值解的近似解,大幅简化了计算量。在计算智能中,深度学习因其强大的学习能力越来越多地应用于点云配准问题,同时由于进化计算的强大全局搜索能力以及模糊逻辑对不确定性的良好适应能力,许多研究也将这两种方法应用于配准问题。本文对点云配准领域中的计算智能方法进行全面讨论,分别从基于深度学习、进化计算和模糊逻辑的点云配准方法这 3 个方面展开论述,同时对传统的点云配准方法进行简要介绍,并对各种方法的优缺点进行了详细讨论,旨在以更全面、清晰的方式总结点云配准问题上的相关研究。     

1-Point-RANSAC Structure from Motion for Vehicle-Mounted Cameras by Exploiting Non-holonomic Constraints

This paper presents a new method to estimate the relative motion of a vehicle from images of a single camera. The computational cost of the algorithm is limited only by the feature extraction and matching process, as the outlier removal and the motion estimation steps take less than a fraction of millisecond with a normal laptop computer. The biggest problem in visual motion estimation is data association; matched points contain many outliers that must be detected and removed for the motion to be accurately estimated. In the last few years, a very established method for removing outliers has been the “5-point RANSAC” algorithm which needs a minimum of 5 point correspondences to estimate the model hypotheses. Because of this, however, it can require up to several hundreds of iterations to find a set of points free of outliers. In this paper, we show that by exploiting the nonholonomic constraints of wheeled vehicles it is possible to use a restrictive motion model which allows us to parameterize the motion with only 1 point correspondence. Using a single feature correspondence for motion estimation is the lowest model parameterization possible and results in the two most efficient algorithms for removing outliers: 1-point RANSAC and histogram voting. To support our method we run many experiments on both synthetic and real data and compare the performance with a state-of-the-art approach. Finally, we show an application of our method to visual odometry by recovering a 3 Km trajectory in a cluttered urban environment and in real-time.     

基于数学形态学的模糊异常点检测

异常点检测作为数据挖掘的一项重要任务,可能会导致意想不到的知识发现.但传统的异常点检测技术都忽略了数据的自然结构,即异常点与簇的联系.然而,把异常点得分和聚类方法结合起来有利于对异常点与簇的联系的研究.提出基于数学形态学的模糊异常点检测与分析,把数学形态学技术和基于连接的异常点检测方法集成到一个模糊模型中,从异常隶属度和模糊隶属度这两个方面来分析对象与簇集的模糊关系.通过充分的实验证明,该算法能够对复杂面状和变密度的数据集,正确、高效地找出异常点,同时发现与异常点相关联的簇信息,探索异常点与簇核的关联深度,对异常点本身的意义具有启发作用.     

一种鲁棒的城市复杂动态场景点云配准方法

针对城市道路环境中面临的动态目标繁多、遮挡严重、以及GPS （全球定位系统）误差较大的问题,提出了一种无需检测动态目标且可以适应不同初始位置误差的快速、鲁棒的配准方法.首先,使用区域生长方法对去除地面的障碍物点云进行目标分割,并通过设定约束条件优化分割效果,生成点云的目标重心点集合;然后,提出了一种多层嵌套的RANSAC （随机抽样一致性）算法架构,迭代地更新配准结果,实现重心点集的粗配准并去除外点;最后,利用ICP （迭代最近点）进行点云的精确配准.与传统RANSAC方法的对比实验表明,该方法能够在复杂的动态场景和较大的初始位置误差下完成精确可靠的点云配准,且其配准成功率和配准速度明显高于传统方法.     

Bounded Influence Support Vector Regression for Robust Single-Model Estimation

Support vector regression (SVR) is now a well-established method for estimating real-valued functions. However, the standard SVR is not effective to deal with severe outlier contamination of both response and predictor variables commonly encountered in numerous real applications. In this paper, we present a bounded influence SVR, which downweights the influence of outliers in all the regression variables. The proposed approach adopts an adaptive weighting strategy, which is based on both a robust adaptive scale estimator for large regression residuals and the statistic of a “kernelized” hat matrix for leverage point removal. Thus, our algorithm has the ability to accurately extract the dominant subset in corrupted data sets. Simulated linear and nonlinear data sets show the robustness of our algorithm against outliers. Last, chemical and astronomical data sets that exhibit severe outlier contamination are used to demonstrate the performance of the proposed approach in real situations.