On Filtering in Markovian Term Structure Models (an approximation approach

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landmarc的基本算法流程

landmarc的基本算法流程Landmarc基本算法流程是用于定位和追踪目标的一种算法。

它是一种基于卡尔曼滤波的滤波器，通过整合视觉或其他传感器数据，将目标在三维空间中的位置和速度预测，并实时更新以提供准确的目标追踪。

Landmarc基本算法流程的步骤如下：1.初始化：- 创建Landmarc滤波器对象。

-设置初始目标状态估计，包括位置、速度和协方差矩阵。

-设置传感器的参数，例如像素尺寸、焦距等。

2.观测预测：-根据目标的速度和运动模型，在每个时间步预测目标在图像中的位置。

-使用图像特征提取算法提取目标的特征点。

3.特征匹配：-对于每个特征点，在图像帧上其在前一个帧中的对应位置。

-使用特征点匹配算法匹配特征点。

-根据匹配结果计算匹配误差。

4.状态更新：-使用卡尔曼滤波器，基于观测的位置变化和误差，更新目标的状态估计。

-通过加权平均计算目标的最终位置和速度估计。

5.目标重定位：-如果目标在图像中移动超过阈值，进行目标重定位。

-重新计算目标的状态估计，并更新卡尔曼滤波器的初始状态。

6.目标追踪：-将目标的状态估计转换为实际物理坐标。

-使用目标的状态估计进行目标追踪。

7.更新：-当新的图像帧到达时，回到步骤2，继续观测预测、特征匹配和状态更新。

Landmarc基本算法流程的关键在于观测预测和状态更新。

通过预测目标的位置，并使用特征匹配算法提取特征并匹配特征点，可以获取目标在图像中的位置变化。

然后，使用卡尔曼滤波器将观测到的位置变化和误差纳入考虑，并实时更新目标的状态估计。

Landmarc基本算法流程的优点是可以提供较为准确的目标追踪，适用于各种不同的传感器和场景。

它可以用于各种应用，例如机器人导航、自动驾驶和视频监控等。

然而，该算法也有一些局限性，例如当目标与背景颜色相似或者出现遮挡时，会导致特征匹配失败，从而影响追踪的准确性。

为了解决这些问题，还可以将其他传感器的数据（如雷达或激光）集成到Landmarc中，以提供更可靠和鲁棒的目标追踪。

A_review_of_feature_selection_techniques_in_bioinformatics

A review of feature selection techniques in bioinformaticsAbstractFeature selection techniques have become an apparent need in many bioinformatics applications. In addition to the large pool of techniques that have already been developed in the machine learning and data mining fields, specific applications in bioinformatics have led to a wealth of newly proposed techniques.In this article, we make the interested reader aware of the possibilities of feature selection, providing a basic taxonomy of feature selection techniques, and discussing their use, variety and potential in a number of both common as well as upcoming bioinformatics applications.1 INTRODUCTIONDuring the last decade, the motivation for applying feature selection (FS) techniques in bioinformatics has shifted from being an illustrative example to becoming a real prerequisite for model building. In particular, the high dimensional nature of many modelling tasks in bioinformatics, going from sequence analysis over microarray analysis to spectral analyses and literature mining has given rise to a wealth of feature selection techniques being presented in the field.In this review, we focus on the application of feature selection techniques. In contrast to other dimensionality reduction techniques like those based on projection (e.g. principal component analysis) or compression (e.g. using information theory), feature selection techniques do not alter the original representation of the variables, but merely select a subset of them. Thus, they preserve the original semantics of the variables, hence, offering the advantage of interpretability by a domain expert.While feature selection can be applied to both supervised and unsupervised learning, we focus here on the problem of supervised learning (classification), where the class labels are known beforehand. The interesting topic of feature selection for unsupervised learning (clustering) is a more complex issue, and research into this field is recently getting more attention in several communities (Liu and Yu, 2005; Varshavsky et al., 2006).The main aim of this review is to make practitioners aware of the benefits, and in some cases even the necessity of applying feature selection techniques. Therefore, we provide an overview of the different feature selection techniques for classification: we illustrate them by reviewing the most important application fields in the bioinformatics domain, highlighting the efforts done by the bioinformatics community in developing novel and adapted procedures. Finally, we also point the interested reader to some useful data mining and bioinformatics software packages that can be used for feature selection.Previous SectionNext Section2 FEATURE SELECTION TECHNIQUESAs many pattern recognition techniques were originally not designed to cope with large amounts of irrelevant features, combining them with FS techniques has become a necessity in many applications (Guyon and Elisseeff, 2003; Liu and Motoda, 1998; Liu and Yu, 2005). The objectives of feature selection are manifold, the most important ones being: (a) to avoid overfitting andimprove model performance, i.e. prediction performance in the case of supervised classification and better cluster detection in the case of clustering, (b) to provide faster and more cost-effective models and (c) to gain a deeper insight into the underlying processes that generated the data. However, the advantages of feature selection techniques come at a certain price, as the search for a subset of relevant features introduces an additional layer of complexity in the modelling task. Instead of just optimizing the parameters of the model for the full feature subset, we now need to find the optimal model parameters for the optimal feature subset, as there is no guarantee that the optimal parameters for the full feature set are equally optimal for the optimal feature subset (Daelemans et al., 2003). As a result, the search in the model hypothesis space is augmented by another dimension: the one of finding the optimal subset of relevant features. Feature selection techniques differ from each other in the way they incorporate this search in the added space of feature subsets in the model selection.In the context of classification, feature selection techniques can be organized into three categories, depending on how they combine the feature selection search with the construction of the classification model: filter methods, wrapper methods and embedded methods. Table 1 provides a common taxonomy of feature selection methods, showing for each technique the most prominent advantages and disadvantages, as well as some examples of the most influential techniques.Table 1.A taxonomy of feature selection techniques. For each feature selection type, we highlight a set of characteristics which can guide the choice for a technique suited to the goals and resources of practitioners in the fieldFilter techniques assess the relevance of features by looking only at the intrinsic properties of the data. In most cases a feature relevance score is calculated, and low-scoring features are removed. Afterwards, this subset of features is presented as input to the classification algorithm. Advantages of filter techniques are that they easily scale to very high-dimensional datasets, they are computationally simple and fast, and they are independent of the classification algorithm. As a result, feature selection needs to be performed only once, and then different classifiers can be evaluated.A common disadvantage of filter methods is that they ignore the interaction with the classifier (the search in the feature subset space is separated from the search in the hypothesis space), and that most proposed techniques are univariate. This means that each feature is considered separately, thereby ignoring feature dependencies, which may lead to worse classification performance when compared to other types of feature selection techniques. In order to overcome the problem of ignoring feature dependencies, a number of multivariate filter techniques were introduced, aiming at the incorporation of feature dependencies to some degree.Whereas filter techniques treat the problem of finding a good feature subset independently of the model selection step, wrapper methods embed the model hypothesis search within the feature subset search. In this setup, a search procedure in the space of possible feature subsets is defined, and various subsets of features are generated and evaluated. The evaluation of a specific subset of features is obtained by training and testing a specific classification model, rendering this approach tailored to a specific classification algorithm. To search the space of all feature subsets, a search algorithm is then ‘wrapped’ around the classification model. However, as the space of feature subsets grows exponentially with the number of features, heuristic search methods are used to guide the search for an optimal subset. These search methods can be divided in two classes: deterministic and randomized search algorithms. Advantages of wrapper approaches include the interaction between feature subset search and model selection, and the ability to take into account feature dependencies. A common drawback of these techniques is that they have a higher risk of overfitting than filter techniques and are very computationally intensive, especially if building the classifier has a high computational cost.In a third class of feature selection techniques, termed embedded techniques, the search for an optimal subset of features is built into the classifier construction, and can be seen as a search in the combined space of feature subsets and hypotheses. Just like wrapper approaches, embedded approaches are thus specific to a given learning algorithm. Embedded methods have the advantage that they include the interaction with the classification model, while at the same time being far less computationally intensive than wrapper methods.Previous SectionNext Section3 APPLICATIONS IN BIOINFORMATICS3.1 Feature selection for sequence analysisSequence analysis has a long-standing tradition in bioinformatics. In the context of feature selection, two types of problems can be distinguished: content and signal analysis. Content analysis focuses on the broad characteristics of a sequence, such as tendency to code for proteins or fulfillment of a certain biological function. Signal analysis on the other hand focuses on the identification of important motifs in the sequence, such as gene structural elements or regulatory elements.Apart from the basic features that just represent the nucleotide or amino acid at each position in a sequence, many other features, such as higher order combinations of these building blocks (e.g.k-mer patterns) can be derived, their number growing exponentially with the pattern length k. As many of them will be irrelevant or redundant, feature selection techniques are then applied to focus on the subset of relevant variables.3.1.1 Content analysisThe prediction of subsequences that code for proteins (coding potential prediction) has been a focus of interest since the early days of bioinformatics. Because many features can be extracted from a sequence, and most dependencies occur between adjacent positions, many variations of Markov models were developed. To deal with the high amount of possible features, and the often limited amount of samples, (Salzberg et al., 1998) introduced the interpolated Markov model (IMM), which used interpolation between different orders of the Markov model to deal with small sample sizes, and a filter method (χ2) to select only relevant features. In further work, (Delcher et al., 1999) extended the IMM framework to also deal with non-adjacent feature dependencies, resulting in the interpolated context model (ICM), which crosses a Bayesian decision tree with a filter method (χ2) to assess feature relevance. Recently, the avenue of FS techniques for coding potential prediction was further pursued by (Saeys et al., 2007), who combined different measures of coding potential prediction, and then used the Markov blanket multivariate filter approach (MBF) to retain only the relevant ones.A second class of techniques focuses on the prediction of protein function from sequence. The early work of Chuzhanova et al. (1998), who combined a genetic algorithm in combination with the Gamma test to score feature subsets for classification of large subunits of rRNA, inspired researchers to use FS techniques to focus on important subsets of amino acids that relate to the protein's; functional class (Al-Shahib et al., 2005). An interesting technique is described in Zavaljevsky et al. (2002), using selective kernel scaling for support vector machines (SVM) as a way to asses feature weights, and subsequently remove features with low weights.The use of FS techniques in the domain of sequence analysis is also emerging in a number of more recent applications, such as the recognition of promoter regions (Conilione and Wang, 2005), and the prediction of microRNA targets (Kim et al., 2006).3.1.2 Signal analysisMany sequence analysis methodologies involve the recognition of short, more or less conserved signals in the sequence, representing mainly binding sites for various proteins or protein complexes. A common approach to find regulatory motifs, is to relate motifs to gene expressionlevels using a regression approach. Feature selection can then be used to search for the motifs that maximize the fit to the regression model (Keles et al., 2002; Tadesse et al.,2004). In Sinha (2003), a classification approach is chosen to find discriminative motifs. The method is inspired by Ben-Dor et al. (2000) who use the threshold number of misclassification (TNoM, see further in the section on microarray analysis) to score genes for relevance to tissue classification. From the TNoM score, a P-value is calculated that represents the significance of each motif. Motifs are then sorted according to their P-value.Another line of research is performed in the context of the gene prediction setting, where structural elements such as the translation initiation site (TIS) and splice sites are modelled as specific classification problems. The problem of feature selection for structural element recognition was pioneered in Degroeve et al. (2002) for the problem of splice site prediction, combining a sequential backward method together with an embedded SVM evaluation criterion to assess feature relevance. In Saeys et al. (2004), an estimation of distribution algorithm (EDA, a generalization of genetic algorithms) was used to gain more insight in the relevant features for splice site prediction. Similarly, the prediction of TIS is a suitable problem to apply feature selection techniques. In Liu et al. (2004), the authors demonstrate the advantages of using feature selection for this problem, using the feature-class entropy as a filter measure to remove irrelevant features.In future research, FS techniques can be expected to be useful for a number of challenging prediction tasks, such as identifying relevant features related to alternative splice sites and alternative TIS.3.2 Feature selection for microarray analysisDuring the last decade, the advent of microarray datasets stimulated a new line of research in bioinformatics. Microarray data pose a great challenge for computational techniques, because of their large dimensionality (up to several tens of thousands of genes) and their small sample sizes (Somorjai et al., 2003). Furthermore, additional experimental complications like noise and variability render the analysis of microarray data an exciting domain.In order to deal with these particular characteristics of microarray data, the obvious need for dimension reduction techniques was realized (Alon et al., 1999; Ben-Dor et al., 2000; Golub et al., 1999; Ross et al., 2000), and soon their application became a de facto standard in the field. Whereas in 2001, the field of microarray analysis was still claimed to be in its infancy (Efron et al., 2001), a considerable and valuable effort has since been done to contribute new and adapt known FS methodologies (Jafari and Azuaje, 2006). A general overview of the most influential techniques, organized according to the general FS taxonomy of Section 2, is shown in Table 2.Table 2.Key references for each type of feature selection technique in the microarray domain3.2.1 The univariate filter paradigm: simple yet efficientBecause of the high dimensionality of most microarray analyses, fast and efficient FS techniques such as univariate filter methods have attracted most attention. The prevalence of these univariate techniques has dominated the field, and up to now comparative evaluations of different classification and FS techniques over DNA microarray datasets only focused on the univariate case (Dudoit et al., 2002; Lee et al., 2005; Li et al., 2004; Statnikov et al., 2005). This domination of the univariate approach can be explained by a number of reasons:the output provided by univariate feature rankings is intuitive and easy to understand;the gene ranking output could fulfill the objectives and expectations that bio-domain experts have when wanting to subsequently validate the result by laboratory techniques or in order to explore literature searches. The experts could not feel the need for selection techniques that take into account gene interactions;the possible unawareness of subgroups of gene expression domain experts about the existence of data analysis techniques to select genes in a multivariate way;the extra computation time needed by multivariate gene selection techniques.Some of the simplest heuristics for the identification of differentially expressed genes include setting a threshold on the observed fold-change differences in gene expression between the states under study, and the detection of the threshold point in each gene that minimizes the number of training sample misclassification (threshold number of misclassification, TNoM (Ben-Dor etal.,2000)). However, a wide range of new or adapted univariate feature ranking techniques has since then been developed. These techniques can be divided into two classes: parametric and model-free methods (see Table 2).Parametric methods assume a given distribution from which the samples (observations) have been generated. The two sample t-test and ANOVA are among the most widely used techniques in microarray studies, although the usage of their basic form, possibly without justification of their main assumptions, is not advisable (Jafari and Azuaje, 2006). Modifications of the standard t-test to better deal with the small sample size and inherent noise of gene expression datasets include a number of t- or t-test like statistics (differing primarily in the way the variance is estimated) and a number of Bayesian frameworks (Baldi and Long, 2001; Fox and Dimmic, 2006). Although Gaussian assumptions have dominated the field, other types of parametrical approaches can also be found in the literature, such as regression modelling approaches (Thomas et al., 2001) and Gamma distribution models (Newton et al.,2001).Due to the uncertainty about the true underlying distribution of many gene expression scenarios, and the difficulties to validate distributional assumptions because of small sample sizes,non-parametric or model-free methods have been widely proposed as an attractive alternative to make less stringent distributional assumptions (Troyanskaya et al., 2002). Many model-free metrics, frequently borrowed from the statistics field, have demonstrated their usefulness in many gene expression studies, including the Wilcoxon rank-sum test (Thomas et al., 2001), the between-within classes sum of squares (BSS/WSS) (Dudoit et al., 2002) and the rank products method (Breitling et al., 2004).A specific class of model-free methods estimates the reference distribution of the statistic using random permutations of the data, allowing the computation of a model-free version of the associated parametric tests. These techniques have emerged as a solid alternative to deal with the specificities of DNA microarray data, and do not depend on strong parametric assumptions (Efron et al., 2001; Pan, 2003; Park et al., 2001; Tusher et al., 2001). Their permutation principle partly alleviates the problem of small sample sizes in microarray studies, enhancing the robustness against outliers.We also mention promising types of non-parametric metrics which, instead of trying to identify differentially expressed genes at the whole population level (e.g. comparison of sample means), are able to capture genes which are significantly disregulated in only a subset of samples (Lyons-Weiler et al., 2004; Pavlidis and Poirazi, 2006). These types of methods offer a more patient specific approach for the identification of markers, and can select genes exhibiting complex patterns that are missed by metrics that work under the classical comparison of two prelabelled phenotypic groups. In addition, we also point out the importance of procedures for controlling the different types of errors that arise in this complex multiple testing scenario of thousands of genes (Dudoit et al., 2003; Ploner et al., 2006; Pounds and Cheng, 2004; Storey, 2002), with a special focus on contributions for controlling the false discovery rate (FDR).3.2.2 Towards more advanced models: the multivariate paradigm for filter, wrapperand embedded techniquesUnivariate selection methods have certain restrictions and may lead to less accurate classifiers by, e.g. not taking into account gene–gene interactions. Thus, researchers have proposed techniques that try to capture these correlations between genes.The application of multivariate filter methods ranges from simple bivariate interactions (Bø and Jonassen, 2002) towards more advanced solutions exploring higher order interactions, such as correlation-based feature selection (CFS) (Wang et al., 2005; Yeoh et al., 2002) and several variants of the Markov blanket filter method (Gevaert et al., 2006; Mamitsuka, 2006; Xing et al., 2001). The Minimum Redundancy-Maximum Relevance (MRMR) (Ding and Peng, 2003) and Uncorrelated Shrunken Centroid (USC) (Yeung and Bumgarner, 2003) algorithms are two other solid multivariate filter procedures, highlighting the advantage of using multivariate methods over univariate procedures in the gene expression domain.Feature selection using wrapper or embedded methods offers an alternative way to perform a multivariate gene subset selection, incorporating the classifier's; bias into the search and thus offering an opportunity to construct more accurate classifiers. In the context of microarray analysis, most wrapper methods use population-based, randomized search heuristics (Blanco et al., 2004; Jirapech-Umpai and Aitken, 2005; Li et al., 2001; Ooi and Tan, 2003), although also a few examples use sequential search techniques (Inza et al., 2004; Xiong et al., 2001). An interesting hybrid filter-wrapper approach is introduced in (Ruiz et al., 2006), crossing a univariatelypre-ordered gene ranking with an incrementally augmenting wrapper method.Another characteristic of any wrapper procedure concerns the scoring function used to evaluate each gene subset found. As the 0–1 accuracy measure allows for comparison with previous works, the vast majority of papers uses this measure. However, recent proposals advocate the use of methods for the approximation of the area under the ROC curve (Ma and Huang, 2005), or the optimization of the LASSO (Least Absolute Shrinkage and Selection Operator) model (Ghosh and Chinnaiyan, 2005). ROC curves certainly provide an interesting evaluation measure, especially suited to the demand for screening different types of errors in many biomedical scenarios.The embedded capacity of several classifiers to discard input features and thus propose a subset of discriminative genes, has been exploited by several authors. Examples include the use of random forests (a classifier that combines many single decision trees) in an embedded way to calculate the importance of each gene (Díaz-Uriarte and Alvarez de Andrés, 2006; Jiang et al., 2004). Another line of embedded FS techniques uses the weights of each feature in linear classifiers, such as SVMs (Guyon et al., 2002) and logistic regression (Ma and Huang, 2005). These weights are used to reflect the relevance of each gene in a multivariate way, and thus allow for the removal of genes with very small weights.Partially due to the higher computational complexity of wrapper and to a lesser degree embedded approaches, these techniques have not received as much interest as filter proposals. However, an advisable practice is to pre-reduce the search space using a univariate filter method, and only then apply wrapper or embedded methods, hence fitting the computation time to the available resources.3.3 Mass spectra analysisMass spectrometry technology (MS) is emerging as a new and attractive framework for disease diagnosis and protein-based biomarker profiling (Petricoin and Liotta, 2003). A mass spectrum sample is characterized by thousands of different mass/charge (m / z) ratios on the x-axis, each with their corresponding signal intensity value on the y-axis. A typical MALDI-TOF low-resolution proteomic profile can contain up to 15 500 data points in the spectrum between 500 and 20 000 m / z, and the number of points even grows using higher resolution instruments.For data mining and bioinformatics purposes, it can initially be assumed that each m / z ratio represents a distinct variable whose value is the intensity. As Somorjai et al. (2003) explain, the data analysis step is severely constrained by both high-dimensional input spaces and their inherent sparseness, just as it is the case with gene expression datasets. Although the amount of publications on mass spectrometry based data mining is not comparable to the level of maturity reached in the microarray analysis domain, an interesting collection of methods has been presented in the last 4–5 years (see Hilario et al., 2006; Shin and Markey, 2006 for recent reviews) since the pioneering work of Petricoin et al.(2002).Starting from the raw data, and after an initial step to reduce noise and normalize the spectra from different samples (Coombes et al., 2007), the following crucial step is to extract the variables that will constitute the initial pool of candidate discriminative features. Some studies employ the simplest approach of considering every measured value as a predictive feature, thus applying FS techniques over initial huge pools of about 15 000 variables (Li et al., 2004; Petricoin et al., 2002), up to around 100 000 variables (Ball et al.,2002). On the other hand, a great deal of the current studies performs aggressive feature extraction procedures using elaborated peak detection and alignment techniques (see Coombes et al., 2007; Hilario et al., 2006; Shin and Markey, 2006 for a detailed description of these techniques). These procedures tend to seed the dimensionality from which supervised FS techniques will start their work in less than 500 variables (Bhanot et al., 2006; Ressom et al., 2007; Tibshirani et al., 2004). A feature extraction step is thus advisable to set the computational costs of many FS techniques to a feasible size in these MS scenarios. Table 3 presents an overview of FS techniques used in the domain of mass spectrometry. Similar to the domain of microarray analysis, univariate filter techniques seem to be the most common techniques used, although the use of embedded techniques is certainly emerging as an alternative. Although the t-test maintains a high level of popularity (Liu et al., 2002; Wu et al., 2003), other parametric measures such as F-test (Bhanot et al., 2006), and a notable variety of non-parametric scores (Tibshirani et al., 2004; Yu et al., 2005) have also been used in several MS studies. Multivariate filter techniques on the other hand, are still somewhat underrepresented (Liu et al., 2002; Prados et al., 2004).Table 3.Key references for each type of feature selection technique in the domain of mass pectrometryWrapper approaches have demonstrated their usefulness in MS studies by a group of influential works. Different types of population-based randomized heuristics are used as search engines in the major part of these papers: genetic algorithms (Li et al., 2004; Petricoin et al., 2002), particle swarm optimization (Ressom et al., 2005) and ant colony procedures (Ressom et al., 2007). It is worth noting that while the first two references start the search procedure in ∼ 15 000 dimensions by considering each m / z ratio as an initial predictive feature, aggressive peak detection and alignment processes reduce the initial dimension to about 300 variables in the last two references (Ressom et al., 2005; Ressom et al., 2007).An increasing number of papers uses the embedded capacity of several classifiers to discard input features. Variations of the popular method originally proposed for gene expression domains by Guyon et al. (2002), using the weights of the variables in the SVM-formulation to discard features with small weights, have been broadly and successfully applied in the MS domain (Jong et al., 2004; Prados et al., 2004; Zhang et al., 2006). Based on a similar framework, the weights of the input masses in a neural network classifier have been used to rank the features'importance in Ball et al. (2002). The embedded capacity of random forests (Wu et al., 2003) and other types of decision tree-based algorithms (Geurts et al., 2005) constitutes an alternative embedded FS strategy.Previous SectionNext Section4 DEALING WITH SMALL SAMPLE DOMAINSSmall sample sizes, and their inherent risk of imprecision and overfitting, pose a great challenge for many modelling problems in bioinformatics (Braga-Neto and Dougherty, 2004; Molinaro et al., 2005; Sima and Dougherty, 2006). In the context of feature selection, two initiatives have emerged in response to this novel experimental situation: the use of adequate evaluation criteria, and the use of stable and robust feature selection models.4.1 Adequate evaluation criteria。

牛顿-拉夫逊潮流计算中检测雅可比矩阵奇异性和网络孤岛的新方法

由（式可得：Ｉ【０由于Ｄ是对角矩３）＝阵，，因此至少有一对角元素为０。因为Ｕ＝ＵＬＤＤ，ＶＬ设该潮流计算是ｎ节点系统。所以（）２）２或（工ａｂ弋有一个成立，Ｕ中有一Ｈ子矩阵奇异，那么Ｈ矩阵各个列向量线性相即ｎ一１零行或中有一零列。ｕ中行为零，是行相关隋况；丰中列为关，：这Ｌ即－＝（不全为０ｑ０）零，这是列相关隋况。其中：是Ｈ矩阵的列向量，１是相关系ｃＴＡ矩阵奇异，那么Ａ矩阵行向量、向量线列数。由潮流雅可比矩阵元素计算可知：性相关，即：对同一节点，素和Ｊ素的计算具有完Ｈ元元全相似的表达式，因此，矩阵的各个列向量也Ｊ（ａ４）应满足（，即：
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Ｉ言。在日常生活中，前由于停水时忘记关闭阀门，水时也没能及时关闭阀门，来造成水资源浪费甚至形成安全隐患的情况屡见不鲜。着全民节水概念不断深入人心，一问随这题引起各方关注。因此急需设计一款可以在停水时自动关闭的水阀，它能够在停水后即使人们忘记关闭水龙头也能实现自动关闭，而再次来水时不至于出现水患的情况，能够有效的节约水资源。要实现自动关闭功能首先要有动力，这方面可以借助磁性元件的磁力、弹性元件的弹力、力等外力，时考虑供水和停水时的重同水压变化，通过联动机构实现。２停水自动关闭阀的结构及特点。利用水压、力等力学特性，过一系列的实验、重经改进，发出一种简单、行的带有停水自锁研可机构的水阀。款水阀为纯机械构造，阀体这以为主体框架，有阀芯、封圈、心轮以及配密偏手柄，无弹性元件，作状况不受环境和时间工的限制，构简单，价低廉并方便拆换，结造整体可靠性高。停水自动关闭阀结构原理如图１示，所实物如图２所示。序号ｌ水阀的偏心轮，为２为０型密封圈，为Ｖ型密封圈，阀体，３４为５为阀芯，销轴，手柄。阀体４是主框６为７为架，来装配其它元件，进水口和出水口；用有阀芯５的顶端与末端分别装有Ｖ型密封圈３和０型密封圈２ｖ型密封圈３利用其锥面，与阀体４内部锥面配合实现停水时密封，而０型密封圈２与阀体４内壁的接触实现来水时对水阀末端的密封，在阀芯５的中部开两

Embedding Motion in Model-Based Stochastic Tracking

algorithms that keep only one conﬁguration state [5], which are therefore sensitive to single failures in the presence of ambiguities or fast or erratic motion. In this paper, we address two important issues related to tracking with a particle ﬁlter. The ﬁrst issue refers to the speciﬁc form of the observation likelihood, that relies on the conditional independence of observations given the state sequence. The second one refers to the choice of an appropriate proposal distribution, which, unlike the prior dynamical model, should take into account the new observations. To handle these issues, we propose a new particle ﬁlter tracking method based on visual motion. Our method relies on a new graphical model allowing for the natural introduction of implicit or explicit motion information in the likelihood term, and on the exploitation of explicit motion measurements in the proposal distribution. the above issues, our approach, and their beneﬁts, is given in the following paragraphs. The deﬁnition of the observation likelihood distribution is perhaps the most important element in visual tracking with a particle ﬁlter. This distribution allows for the evaluation of the likelihood of the current observation given the current object state, and relies on the speciﬁc object representation. The object representation corresponds to all the information that characterizes the object like the target position, geometry, appearance, color, etc. Parametrized shapes like splines [2] or ellipses [6], and color distributions [5]–[8], are often used as target representation. One drawback of these generic representations is that they can be quite unspeciﬁc, which augments the chances of ambiguities. One way to improve the robustness of a tracker consists of combining low-level measurements such as shape and color [6]. The generic conditional form of the likelihood term relies on a standard hypothesis in probabilistic visual tracking, namely the independence of observations given the state sequence [2], [6], [9]–[13]. In this paper, we argue that this assumption can be inaccurate in the case of visual tracking. As a remedy, we propose a new model that assumes that the current observation depends on the current and previous object conﬁgurations as well as on the past observation. We show that under this more general assumption, the obtained particle ﬁltering algorithm has similar equations than the algorithm based on the standard hypothesis. To our knowledge, this has not been shown before, and so it represents the ﬁrst contribution of this article. The new assumption can thus be used to naturally introduce implicit or explicit motion information in the observation likelihood term. The introduction of such data correlation between successive images will turn generic trackers like shape or color histogram trackers into more speciﬁ in Model-Based Stochastic Tracking

纹理物体缺陷的视觉检测算法研究--优秀毕业论文

摘要
在竞争激烈的工业自动化生产过程中，机器视觉对产品质量的把关起着举足轻重的作用，机器视觉在缺陷检测技术方面的应用也逐渐普遍起来。与常规的检测技术相比，自动化的视觉检测系统更加经济、快捷、高效与安全。纹理物体在工业生产中广泛存在，像用于半导体装配和封装底板和发光二极管，现代化电子系统中的印制电路板，以及纺织行业中的布匹和织物等都可认为是含有纹理特征的物体。本论文主要致力于纹理物体的缺陷检测技术研究，为纹理物体的自动化检测提供高效而可靠的检测算法。纹理是描述图像内容的重要特征，纹理分析也已经被成功的应用与纹理分割和纹理分类当中。本研究提出了一种基于纹理分析技术和参考比较方式的缺陷检测算法。这种算法能容忍物体变形引起的图像配准误差，对纹理的影响也具有鲁棒性。本算法旨在为检测出的缺陷区域提供丰富而重要的物理意义，如缺陷区域的大小、形状、亮度对比度及空间分布等。同时，在参考图像可行的情况下，本算法可用于同质纹理物体和非同质纹理物体的检测，对非纹理物体的检测也可取得不错的效果。在整个检测过程中，我们采用了可调控金字塔的纹理分析和重构技术。与传统的小波纹理分析技术不同，我们在小波域中加入处理物体变形和纹理影响的容忍度控制算法，来实现容忍物体变形和对纹理影响鲁棒的目的。最后可调控金字塔的重构保证了缺陷区域物理意义恢复的准确性。实验阶段，我们检测了一系列具有实际应用价值的图像。实验结果表明本文提出的纹理物体缺陷检测算法具有高效性和易于实现性。关键字: 缺陷检测；纹理；物体变形；可调控金字塔；重构
Keywords: defect detection, texture, object distortion, steerable pyramid, reconstruction
II

马尔可夫链蒙特卡洛采样中的收敛诊断技巧(九)

在概率论和统计学中，马尔可夫链蒙特卡洛（MCMC）采样是一种常见的随机模拟方法，用于从复杂的分布中抽样。

MCMC采样主要用于贝叶斯推断、机器学习和统计模型中的参数估计。

然而，MCMC采样中的一个关键问题是如何评估采样算法是否收敛到目标分布。

本文将讨论MCMC采样中的收敛诊断技巧。

首先，MCMC采样的一个常见算法是Metropolis-Hastings算法，该算法基于马尔可夫链，在一系列状态之间进行转移。

MCMC采样的核心思想是通过一系列状态转移，使得最终的样本分布接近目标分布。

然而，由于MCMC采样是一种随机模拟方法，无法保证每次采样都能收敛到目标分布。

因此，评估MCMC采样的收敛性是非常重要的。

评估MCMC采样的收敛性可以通过多种技巧来实现。

其中，一个常见的方法是通过观察MCMC采样的轨迹，即观察随机变量在状态空间中的移动情况。

如果MCMC采样已经收敛到目标分布，那么随机变量的轨迹将呈现出稳定的特征。

例如，可以通过绘制MCMC采样的轨迹图来观察其收敛情况。

另外，一种常见的收敛诊断技巧是Gelman-Rubin统计量。

该统计量通过比较多个MCMC链之间的变异性和内部变异性来评估MCMC采样的收敛性。

当Gelman-Rubin统计量接近于1时，说明MCMC采样已经收敛到目标分布。

因此，可以通过计算Gelman-Rubin统计量来评估MCMC采样的收敛情况。

除了Gelman-Rubin统计量，还有一些其他常见的收敛诊断技巧，例如自相关函数和似然比检验。

自相关函数通过评估MCMC采样序列之间的相关性来判断其收敛性。

如果MCMC采样已经收敛到目标分布，那么其序列之间的相关性将迅速减小。

似然比检验则通过比较两个不同参数下的似然函数值来评估MCMC采样的收敛情况。

总之，MCMC采样是一种常见的随机模拟方法，用于从复杂的分布中抽样。

然而，MCMC采样的一个关键问题是如何评估其收敛性。

本文介绍了MCMC采样中的一些收敛诊断技巧，包括观察轨迹、Gelman-Rubin统计量、自相关函数和似然比检验。

卡尔曼滤波算法英文

卡尔曼滤波算法英文Kalman Filter AlgorithmThe Kalman filter is a powerful algorithm used for estimating the state of a dynamic system from a series of measurements. It is widely used in various applicationssuch as navigation, control systems, signal processing, and data fusion. The Kalman filter is an optimal estimator, meaning it provides the best estimate of the system's state given the available measurements and the system's dynamics.The Kalman filter algorithm consists of two main steps: the prediction step and the update step. In the prediction step, the algorithm uses the system's dynamics to estimate the current state of the system based on the previous state. In the update step, the algorithm incorporates the new measurement to refine the estimate and reduce the uncertainty.The Kalman filter algorithm can be summarized as follows:1. Prediction Step:- State Prediction: The algorithm uses the system's dynamics to predict the current state of the system based on the previous state.- Covariance Prediction: The algorithm also predicts the covariance of the estimated state, which represents the uncertainty in the estimate.2. Update Step:- Kalman Gain Calculation: The algorithm calculates the Kalman gain, which determines the weight given to the new measurement in the update step.- State Update: The algorithm updates the estimated state by combining the predicted state and the new measurement, using the Kalman gain.- Covariance Update: The algorithm updates the covariance of the estimated state, reflecting the reduced uncertainty after incorporating the new measurement.The Kalman filter algorithm is recursive, meaning it can be implemented in an efficient and computationally-feasible manner. The algorithm only requires the current state and measurement, and it does not need to store or process allthe previous data. This makes the Kalman filterparticularly useful for real-time applications where computational resources are limited.The Kalman filter algorithm has several key properties that make it widely applicable:1. Optimality: The Kalman filter provides the optimal estimate of the system's state, given the available measurements and the system's dynamics.2. Robustness: The Kalman filter is robust to noise and uncertainties in the measurements and the system's dynamics.3. Versatility: The Kalman filter can be applied to a wide range of linear systems, including those with multiple inputs and outputs.4. Computational Efficiency: The Kalman filter algorithm can be implemented efficiently, making it suitable forreal-time applications.The Kalman filter algorithm has been extensively studied and applied in various fields, including:- Navigation: Kalman filters are used in GPS, inertial navigation systems, and autonomous vehicles to estimate the position, velocity, and orientation of the system.- Control Systems: Kalman filters are used to estimatethe state of a system and provide feedback for control algorithms, improving the system's performance andstability.- Signal Processing: Kalman filters are used to filter and smooth signals, removing noise and improving thesignal-to-noise ratio.- Data Fusion: Kalman filters are used to combinemultiple sources of information, such as sensors, toprovide a more accurate and reliable estimate of thesystem's state.Overall, the Kalman filter algorithm is a powerful and widely-used tool for estimating the state of dynamic systems. Its optimality, robustness, and computational efficiency make it a valuable asset in various applications.卡尔曼滤波算法卡尔曼滤波是一种用于估计动态系统状态的强大算法。

FastSLAM A factored solution to the simultaneous localization and mapping problem

FastSLAM:A Factored Solution to the Simultaneous Localization and Mapping ProblemMichael Montemerlo and Sebastian Thrun School of Computer ScienceCarnegie Mellon UniversityPittsburgh,PA15213mmde@,thrun@ Daphne Koller and Ben Wegbreit Computer Science DepartmentStanford UniversityStanford,CA94305-9010koller@,ben@AbstractThe ability to simultaneously localize a robot and ac-curately map its surroundings is considered by many tobe a key prerequisite of truly autonomous robots.How-ever,few approaches to this problem scale up to handlethe very large number of landmarks present in real envi-ronments.Kalmanﬁlter-based algorithms,for example,require time quadratic in the number of landmarks to in-corporate each sensor observation.This paper presentsFastSLAM,an algorithm that recursively estimates thefull posterior distribution over robot pose and landmarklocations,yet scales logarithmically with the number oflandmarks in the map.This algorithm is based on an ex-act factorization of the posterior into a product of con-ditional landmark distributions and a distribution overrobot paths.The algorithm has been run successfullyon as many as50,000landmarks,environments far be-yond the reach of previous approaches.Experimentalresults demonstrate the advantages and limitations ofthe FastSLAM algorithm on both simulated and real-world data.IntroductionThe problem of simultaneous localization and mapping,also known as SLAM,has attracted immense attention in the mo-bile robotics literature.SLAM addresses the problem of building a map of an environment from a sequence of land-mark measurements obtained from a moving robot.Since robot motion is subject to error,the mapping problem neces-sarily induces a robot localization problem—hence the name SLAM.The ability to simultaneously localize a robot and accurately map its environment is considered by many to be a key prerequisite of truly autonomous robots[3,7,16]. The dominant approach to the SLAM problem was in-troduced in a seminal paper by Smith,Self,and Cheese-man[15].This paper proposed the use of the extended Kalmanﬁlter(EKF)for incrementally estimating the poste-rior distribution over robot pose along with the positions of the landmarks.In the last decade,this approach has found widespread acceptance inﬁeld robotics,as a recent tutorial paper[2]documents.Recent research has focused on scal-ing this approach to larger environments with more than aFigure1:The SLAM problem:The robot moves from pose through a sequence of controls,.As it moves,it observes nearby landmarks.At time,it observes landmark out of two landmarks,.The measurement is denoted (range and bearing).At time,it observes the other landmark, ,and at time,it observes again.The SLAM problem is concerned with estimating the locations of the landmarks and the robot’s path from the controls and the measurements.The gray shading illustrates a conditional independence relation.plementation of this idea leads to an algorithm that requires time,where is the number of particles in the particleﬁlter and is the number of landmarks.We de-velop a tree-based data structure that reduces the running time of FastSLAM to,making it signiﬁcantly faster than existing EKF-based SLAM algorithms.We also extend the FastSLAM algorithm to situations with unknown data association and unknown number of landmarks,show-ing that our approach can be extended to the full range of SLAM problems discussed in the literature. Experimental results using a physical robot and a robot simulator illustrate that the FastSLAM algorithm can han-dle orders of magnitude more landmarks than present day approaches.We alsoﬁnd that in certain situations,an in-creased number of landmarks leads to a mild reduction of the number of particles needed to generate accurate maps—whereas in others the number of particles required for accurate mapping may be prohibitively large.SLAM Problem DeﬁnitionThe SLAM problem,as deﬁned in the rich body of litera-ture on SLAM,is best described as a probabilistic Markov chain.The robot’s pose at time will be denoted.For robots operating in the plane—which is the case in all of our experiments—poses are comprised of a robot’s-coordi-nate in the plane and its heading direction.Poses evolve according to a probabilistic law,often re-ferred to as the motion model:(1) Thus,is a probabilistic function of the robot control and the previous pose.In mobile robotics,the motion model is usually a time-invariant probabilistic generalization of robot kinematics[1].The robot’s environment possesses immobile land-marks.Each landmark is characterized by its location in space,denoted for.Without loss of gen-erality,we will think of landmarks as points in the plane,so that locations are speciﬁed by two numerical values.To map its environment,the robot can sense landmarks. For example,it may be able to measure range and bearing to a landmark,relative to its local coordinate frame.The mea-surement at time will be denoted.While robots can often sense more than one landmark at a time,we follow com-monplace notation by assuming that sensor measurements correspond to exactly one landmark[2].This convention is adopted solely for mathematical convenience.It poses no restriction,as multiple landmark sightings at a single time step can be processed sequentially.Sensor measurements are governed by a probabilistic law, often referred to as the measurement model:(2) Here is the set of all landmarks,andis the index of the landmark perceived at time.For example,in Figure1,we have, and,since the robotﬁrst observes landmark, then landmark,andﬁnally landmark for a second time. Many measurement models in the literature assume that the robot can measure range and bearing to landmarks,con-founded by measurement noise.The variable is often referred to as correspondence.Most theoretical work in the literature assumes knowledge of the correspondence or,put differently,that landmarks are uniquely identiﬁable.Practi-cal implementations use maximum likelihood estimators for estimating the correspondence on-the-ﬂy,which work well if landmarks are spaced sufﬁciently far apart.In large parts of this paper we will simply assume that landmarks are iden-tiﬁable,but we will also discuss an extension that estimates the correspondences from data.We are now ready to formulate the SLAM problem.Most generally,SLAM is the problem of determining the location of all landmarks and robot poses from measurementsand controls.In probabilis-tic terms,this is expressed by the posterior, where we use the superscript to refer to a set of variables from time1to time.If the correspondences are known,the SLAM problem is simpler:(3) As discussed in the introduction,all individual landmark es-timation problems are independent if one knew the robot’s path and the correspondence variables.This condi-tional independence is the basis of the FastSLAM algorithm described in the next section.FastSLAM with Known Correspondences We begin our consideration with the important case where the correspondences are known,and so is the number of landmarks observed thus far.Factored RepresentationThe conditional independence property of the SLAM prob-lem implies that the posterior(3)can be factored as follows:(4)Put verbally,the problem can be decomposed into esti-mation problems,one problem of estimating a posterior over robot paths,and problems of estimating the locationsof the landmarks conditioned on the path estimate.This factorization is exact and always applicable in the SLAM problem,as previously argued in[12].The FastSLAM algorithm implements the path estimatorusing a modiﬁed particleﬁlter[4].As we argue further below,thisﬁlter can sample efﬁciently from this space,providing a good approximation of the poste-rior even under non-linear motion kinematics.The land-mark pose estimators are realized by Kalmanﬁlters,using separateﬁlters for different landmarks. Because the landmark estimates are conditioned on the path estimate,each particle in the particleﬁlter has its own,lo-cal landmark estimates.Thus,for particles and land-marks,there will be a total of Kalmanﬁlters,each of dimension2(for the two landmark coordinates).This repre-sentation will now be discussed in detail.Particle Filter Path EstimationFastSLAM employs a particleﬁlter for estimating the path posterior in(4),using aﬁlter that is similar (but not identical)to the Monte Carlo localization(MCL) algorithm[1].MCL is an application of particleﬁlter tothe problem of robot pose estimation(localization).At each point in time,both algorithms maintain a set of particles rep-resenting the posterior,denoted.Each particle represents a“guess”of the robot’s path:(5) We use the superscript notation to refer to the-th par-ticle in the set.The particle set is calculated incrementally,from theset at time,a robot control,and a measurement.First,each particle in is used to generate a probabilistic guess of the robot’s pose at time:(6) obtained by sampling from the probabilistic motion model. This estimate is then added to a temporary set of parti-cles,along with the path.Under the assumption that the set of particles in is distributed according to(which is an asymptotically cor-rect approximation),the new particle is distributed accord-ing to.This distribution is commonly referred to as the proposal distribution of particleﬁltering. After generating particles in this way,the new set is obtained by sampling from the temporary particle set.Each particle is drawn(with replacement)with a probability proportional to a so-called importance factor,which is calculated as follows[10]:target distribution(7) The exact calculation of(7)will be discussed further below. The resulting sample set is distributed according to an ap-proximation to the desired pose posterior,an approximation which is correct as the number of particlesgoes to inﬁnity.We also notice that only the most recent robot pose estimate is used when generating the parti-cle set.This will allows us to silently“forget”all other pose estimates,rendering the size of each particle indepen-dent of the time index.Landmark Location EstimationFastSLAM represents the conditional landmark estimatesin(4)by Kalmanﬁlters.Since this estimate is conditioned on the robot pose,the Kalmanﬁlters are attached to individual pose particles in.More speciﬁ-cally,the full posterior over paths and landmark positions in the FastSLAM algorithm is represented by the sample set(8) Here and are mean and covariance of the Gaus-sian representing the-th landmark,attached to the-th particle.In the planar robot navigation scenario,each mean is a two-element vector,and is a2by2matrix. The posterior over the-th landmark pose is easily ob-tained.Its computation depends on whether or not, that is,whether or not was observed at time.For, we obtain(9)For,we simply leave the Gaussian unchanged:(10) The FastSLAM algorithm implements the update equation (9)using the extended Kalmanﬁlter(EKF).As in existing EKF approaches to SLAM,thisﬁlter uses a linearized ver-sion of the perceptual model[2].Thus, FastSLAM’s EKF is similar to the traditional EKF for SLAM[15]in that it approximates the measurement model using a linear Gaussian function.We note that,with a lin-ear Gaussian observation model,the resulting distributionis exactly a Gaussian,even if the mo-tion model is not linear.This is a consequence of the use of sampling to approximate the distribution over the robot’s pose.One signiﬁcant difference between the FastSLAM algo-rithm’s use of Kalmanﬁlters and that of the traditional SLAM algorithm is that the updates in the FastSLAM algo-rithm involve only a Gaussian of dimension two(for the two landmark location parameters),whereas in the EKF-based SLAM approach a Gaussian of size has to be updated (with landmarks and3robot pose parameters).This cal-culation can be done in constant time in FastSLAM,whereas it requires time quadratic in in standard SLAM. Calculating the Importance WeightsLet us now return to the problem of calculating the impor-tance weights needed for particleﬁlter resampling,as deﬁned in(7):µµµµµµµµ8,Σ87,Σ76,Σ65,Σ54,Σ43,Σ32,Σ21,Σ1[m][m][m][m][m][m][m][m][m][m][m][m][m][m][m][m]Figure 2:A tree representinglandmark estimates within asingle particle.(a)(b)(c)Figure4:(a)Physical robot mapping rocks,in a testbed developed for Mars Rover research.(b)Raw range and path data.(c)Map generated using FastSLAM(dots),and locations of rocks determined manually(circles).in the map.It also has to determine if a measurement cor-responds to a new,previously unseen landmark,in whichcase the map should be augmented accordingly.In most existing SLAM solutions based on EKFs,theseproblems are solved via maximum likelihood.More specif-ically,the probability of a data association is given by(12)The step labeled“PF”uses the particleﬁlter approxima-tion to the posterior.Theﬁnal step assumesa uniform prior,which is commonly used[2].The maximum likelihood data association is simply the in-dex that maximizes(12).If the maximum value of—with careful consideration of all constantsin(12)—is below a threshold,the landmark is consideredpreviously unseen and the map is augmented accordingly.In FastSLAM,the data association is estimated on a per-particle basis:.As a result,different particles may rely on different values of.Theymight even possess different numbers of landmarks in theirrespective maps.This constitutes a primary difference toEKF approaches,which determine the data association onlyonce for each sensor measurement.It has been observedfrequently that false data association will make the conven-tional EKF approach fail catastrophically[2].FastSLAM ismore likely to recover,thanks to its ability to pursue multi-ple data associations simultaneously.Particles with wrongdata association are(in expectation)more likely to disap-pear in the resampling process than those that guess the dataassociation correctly.We believe that,under mild assumptions(e.g.,minimumspacing between landmarks and bounded sensor error),thedata association search can be implemented in time loga-rithmic in.One possibility is the use of kd-trees as anindexing scheme in the tree structures above,instead of thelandmark number,as proposed in[11].Experimental ResultsThe FastSLAM algorithm was tested extensively under vari-ous conditions.Real-world experiments were complimentedby systematic simulation experiments,to investigate thescaling abilities of the approach.Overall,the results indicatefavorably scaling to large number of landmarks and smallparticle sets.Aﬁxed number of particles(e.g.,)appears to work well across a large number of situations.Figure4a shows the physical robot testbed,which consistsof a small arena set up under NASA funding for Mars Roverresearch.A Pioneer robot equipped with a SICK laser rangeﬁnder was driven along an approximate straight line,gener-ating the raw data shown in Figure4b.The resulting mapgenerated with samples is depicted in Figure4c,with manually determined landmark locations marked bycircles.The robot’s estimates are indicated by x’s,illustrat-ing the high accuracy of the resulting maps.FastSLAM re-sulted in an average residual map error of8.3centimeters,when compared to the manually generated map.Unfortunately,the physical testbed does not allow for sys-tematic experiments regarding the scaling properties of theapproach.In extensive simulations,the number of land-marks was increased up to a total of50,000,which Fast-SLAM successfully mapped with as few as100particles.Here,the number of parameters in FastSLAM is approx-imately0.3%of that in the conventional EKF.Maps with50,000landmarks are entirely out of range for conventionalSLAM techniques,due to their enormous computationalcomplexity.Figure5shows example maps with smallernumbers of landmarks,for different maximum sensor rangesas indicated.The ellipses in Figure5visualize the residualuncertainty when integrated over all particles and Gaussians.In a set of experiments speciﬁcally aimed to elucidate thescaling properties of the approach,we evaluated the map androbot pose errors as a function of the number of landmarks,and the number of particles,respectively.The resultsare graphically depicted in Figure6.Figure6a illustratesthat an increase in the number of landmarks mildly re-duces the error in the map and the robot pose.This is be-cause the larger the number of landmarks,the smaller therobot pose error at any point in time.Increasing the numberof particles also bears a positive effect on the map andpose errors,as illustrated in Figure6b.In both diagrams,thebars correspond to95%conﬁdence intervals.Figure5:Maps and estimated robot path,generated using sensors with(a)large and(b)small perceptualﬁelds.The correct landmark locations are shown as dots,and the estimates as ellipses,whose sizes correspond to the residual uncertainty.ConclusionWe presented the FastSLAM algorithm,an efﬁcient new so-lution to the concurrent mapping and localization problem. This algorithm utilizes a Rao-Blackwellized representation of the posterior,integrating particleﬁlter and Kalmanﬁlter representations.Similar to Murphy’s work[12],FastSLAM is based on an inherent conditional independence property of the SLAM problem.However,Murphy’s approach main-tains maps using grid positions with discrete values,and therefore scales poorly with the size of the map.His ap-proach also did not deal with the data association problem, which does not arise in the grid-based setting.In FastSLAM,landmark estimates are efﬁciently repre-sented using tree structures.Updating the posterior requires time,where is the number of particles and the number of landmarks.This is in contrast to the complexity of the common Kalman-ﬁlter based ap-proach to SLAM.Experimental results illustrate that Fast-SLAM can build maps with orders of magnitude more land-marks than previous methods.They also demonstrate that under certain conditions,a small number of particles works well regardless of the number of landmarks. Acknowledgments We thank Kevin Murphy and Nando de Freitas for insightful discussions on this topic.This research was sponsored by DARPA’s MARS Program(Contract number N66001-01-C-6018)and the National Science Foundation(CA-REER grant number IIS-9876136and regular grant number IIS-9877033).We thank the Hertz Foundation for their support of Michael Montemerlo’s graduate research.Daphne Koller was supported by the Ofﬁce of Naval Research,Young Investigator (PECASE)grant N00014-99-1-0464.This work was done while Sebastian Thrun was visiting Stanford University.References[1] F.Dellaert,D.Fox,W.Burgard,and S.Thrun.Monte Carlolocalization for mobile robots.ICRA-99.[2]G.Dissanayake,P.Newman,S.Clark,H.F.Durrant-Whyte,and M.Csorba.An experimental and theoretical investigation into simultaneous localisation and map building(SLAM).Lecture Notes in Control and Information Sciences:Exper-imental Robotics VI,Springer,2000.[3]G.Dissanayake,P.Newman,S.Clark,H.F.Durrant-Whyte,and M.Csorba.A solution to the simultaneous localisation and map building(SLAM)problem.IEEE Transactions of Robotics and Automation,2001.[4] A.Doucet,J.F.G.de Freitas,and N.J.Gordon,editors.Se-quential Monte Carlo Methods In Practice.Springer,2001.(a)(b)Figure6:Accuracy of the FastSLAM algorithm as a function of (a)the number of landmarks,and(b)the number of particles .Large number of landmarks reduce the robot localization error, with little effect on the map error.Good results can be achieved with as few as100particles.[5]A Doucet,N.de Freitas,K.Murphy,and S.Russell.Rao-Blackwellised particleﬁltering for dynamic Bayesian net-works.UAI-2000.[6]J.Guivant and E.Nebot.Optimization of the simultaneouslocalization and map building algorithm for real time imple-mentation.IEEE Transaction of Robotic and Automation, May2001.[7] D.Kortenkamp,R.P.Bonasso,and R.Murphy,editors.AI-based Mobile Robots:Case studies of successful robot sys-tems,MIT Press,1998.[8]J.J.Leonard and H.J.S.Feder.A computationally efﬁcientmethod for large-scale concurrent mapping and localization.ISRR-99.[9] F.Lu and ios.Globally consistent range scan alignmentfor environment mapping.Autonomous Robots,4,1997. [10]N.Metropolis, A.W.Rosenbluth,M.N.Rosenbluth, A.H.Teller,and E.Teller.Equations of state calculations by fast computing machine.Journal of Chemical Physics,21,1953.[11] A.W.Moore.Very fast EM-based mixture model clusteringusing multiresolution kd-trees.NIPS-98.[12]K.Murphy.Bayesian map learning in dynamic environments.NIPS-99.[13]K.Murphy and S.Russell.Rao-blackwellized particleﬁl-tering for dynamic bayesian networks.In Sequential Monte Carlo Methods in Practice,Springer,2001.[14]P.Newman.On the Structure and Solution of the Simulta-neous Localisation and Map Building Problem.PhD thesis, Univ.of Sydney,2000.[15]R.Smith,M.Self,and P.Cheeseman.Estimating uncertainspatial relationships in robotics.In Autonomous Robot Vehni-cles,Springer,1990.[16] C.Thorpe and H.Durrant-Whyte.Field robots.ISRR-2001.[17]S.Thrun,D.Fox,and W.Burgard.A probabilistic approachto concurrent mapping and localization for mobile robots.Machine Learning,31,1998.。

Markov Chain

Proof: We ﬁrst observe that by Lemma 1.1, P(Xm+n = j |Xm = i, Xm−1 = im−1 , . . . , X0 = i0 ) = P(Xm+n = j |Xm = i). We will argue by induction on n. The assertion is trivial for n = 1. Suppose that it is true for n. Then P(Xm+n+1 = j |Xm = i) = =
for all n and any i0 , . . ., in−1 , i, j ∈ S. Note that the transition probability matrix P is necessarily a stochastic matrix, and Pij is the transition probability from i to j . Since the transition probability does not depend on the time step n, such Markov chains are said to be time homogeneous. It follows immediately from deﬁnition that the distribution of a Markov chain X is completely determined by its initial distribution, i.e., the distribution of X0 , and the transition probability matrix P. Indeed, P( X 0 = i 0 , X 1 = i 1 , · · · , X n = i n ) = P( X 0 = i 0 ) P( X 1 = i 1 | X 0 = i 0 ) · · · P(Xn = in |Xn−1 = in−1 , · · · , X1 = i1 , X0 = i0 )

奈奎斯特采样定理英文表达

奈奎斯特采样定理英文表达
English: The Nyquist sampling theorem, also known as the Nyquist-Shannon sampling theorem, states that in order to accurately reconstruct a signal, it must be sampled at a rate of at least twice the highest frequency present in that signal. This means that in order to avoid aliasing, where high frequencies are misinterpreted as lower frequencies, the sampling rate must be sufficiently high. Essentially, the theorem provides a guideline for how to accurately sample and reconstruct a signal without losing information or introducing distortions.
中文翻译:奈奎斯特采样定理，也称为奈奎斯特-香农采样定理，指出为了准确重建信号，采样率必须至少是信号中存在的最高频率的两倍。

这意味着为了避免混叠，即高频被错误地解释为低频，采样率必须足够高。

基本上，这个定理提供了一个指导原则，如何能够准确地采样和重建信号，而不会丢失信息或引入失真。

马尔可夫决策过程中的策略迭代算法收敛性证明(六)

马尔可夫决策过程（Markov Decision Process, MDP）是一个被广泛应用于强化学习领域的数学模型。

在MDP中，智能体通过与环境的交互来学习最优的决策策略。

策略迭代算法是一种常用的强化学习方法，用于寻找MDP中的最优策略。

本文将对策略迭代算法的收敛性进行证明。

首先，我们来回顾一下MDP的基本定义。

MDP是由一个状态空间S、一个动作空间A、一个状态转移概率函数P和一个奖励函数R组成的四元组(S, A, P, R)。

在每个时间步t，智能体处于状态s，并选择动作a，之后根据状态转移概率函数P 转移到下一个状态s'，并获得奖励R(s, a, s')。

智能体的目标是找到一个最优的策略π，使得长期累积奖励最大化。

策略迭代算法是一种基于价值迭代的方法，它通过不断更新价值函数来寻找最优策略。

算法分为两个步骤：策略评估和策略改进。

在策略评估中，我们根据当前策略π计算状态的价值函数Vπ，然后在策略改进中寻找一个更好的策略π'。

重复这两个步骤直到策略收敛为止。

接下来，我们将证明策略迭代算法的收敛性。

首先，我们定义价值函数的贝尔曼期望方程：Vπ(s) = Eπ [Rt+1 + γVπ(St+1) | St = s]其中γ是折扣因子，表示未来奖励的重要性。

我们可以用动态规划的方法来求解这个方程，得到当前策略下的状态价值函数。

在策略改进步骤中，我们将根据当前的状态价值函数来更新策略。

如果存在一个状态s和动作a，使得执行a后可以获得更高的长期累积奖励，那么我们将更新策略，使得在状态s下选择动作a。

这样不断改进策略直到收敛。

现在我们来证明策略迭代算法的收敛性。

首先，我们注意到在策略评估步骤中，我们使用了动态规划的方法来求解状态价值函数。

由于MDP满足马尔可夫性质，我们知道状态价值函数是收敛的。

因此，策略评估步骤是收敛的。

在策略改进步骤中，我们不断更新策略直到找到最优策略。

由于每次策略改进都可以获得更高的长期累积奖励，我们知道策略迭代算法是收敛的。

马尔可夫链蒙特卡洛采样方法中的马尔可夫链收敛速度分析

马尔可夫链蒙特卡洛采样（Markov Chain Monte Carlo, MCMC）方法是一种统计学习中常用的技术，它通过模拟马尔可夫链的转移过程来实现对复杂概率分布的采样。

在实际应用中，对MCMC算法的收敛速度进行分析是非常重要的，因为它决定了算法的效率和稳定性。

本文将从理论和实践两个方面来探讨马尔可夫链收敛速度的分析方法。

首先，我们来看一下MCMC方法的基本原理。

MCMC方法是一种基于马尔可夫链的随机采样方法，其核心思想是通过构建一个马尔可夫链，使得该链的平稳分布恰好是我们希望采样的目标分布。

在MCMC方法中，我们首先选择一个合适的转移核函数，然后通过不断地迭代，从而逼近目标分布。

然而，MCMC方法存在一个关键问题，即如何确定马尔可夫链的收敛速度。

下面我们将从数学角度和实践角度来分析这个问题。

从数学角度来看，马尔可夫链的收敛速度可以通过研究其遍历时间（mixing time）来进行分析。

遍历时间是指从任意一个起始状态出发，使得马尔可夫链能够达到平稳分布的时间。

对于遍历时间的分析往往需要考虑马尔可夫链的不可约性、周期性和正常态等性质。

通常情况下，我们可以通过研究马尔可夫链的谱（spectral）性质来估计其遍历时间。

谱方法是一种常用的分析马尔可夫链收敛速度的数学工具，它通过研究马尔可夫链转移矩阵的特征值和特征向量来估计遍历时间。

谱方法的优点是能够提供较为准确的收敛速度估计，但是在实际计算中可能会面临复杂的数值计算和数学推导。

除了数学方法之外，我们还可以从实践角度来分析马尔可夫链的收敛速度。

在实际应用中，通常采用一些统计学的方法来评估MCMC算法的收敛速度。

例如，我们可以通过观察马尔可夫链的轨迹、自相关函数和收敛诊断统计量来评估其收敛性。

自相关函数是一种用于检验时间序列相关性的统计工具，我们可以通过计算马尔可夫链的自相关函数来评估其收敛速度。

此外，收敛诊断统计量是一些用于检验马尔可夫链收敛性的统计量，例如Gelman-Rubin统计量和Raftery-Lewis统计量等。

卡尔曼滤波 python

卡尔曼滤波 python卡尔曼滤波（Kalman Filter，KF）是一种经典的、非常有效的随机信号处理方法，它是1960年由美国科学家Rudolf Kalman发明的，主要用于模型化动态系统，根据系统的观测值和估计值，通过不断地迭代来求出系统的状态。

它可以应用于各种形式的系统，如多元线性系统、非线性系统、时变系统等。

卡尔曼滤波也可以用于处理不确定信息，即使模型不精确，也能得出相对准确的结果。

卡尔曼滤波python实现主要依赖于NumPy和SciPy等第三方库，它可以实现卡尔曼滤波的各种功能，比如计算卡尔曼增益、更新卡尔曼滤波状态、检测噪声、确定参数等。

在python中，通常使用KalmanFilter类来实现卡尔曼滤波，该类提供了一系列方法，可以完成卡尔曼滤波过程。

首先，需要定义卡尔曼滤波参数，比如状态空间矩阵、观测空间矩阵和状态转移函数等。

然后，可以使用KalmanFilter类的predict()方法来预测状态，此时可以使用高斯噪声来表示不确定性。

此外，KalmanFilter类还提供了update()方法，用于更新模型的状态，根据新的观测数据更新模型的状态。

使用KalmanFilter类还可以用来确定卡尔曼滤波的参数，比如模型系数、噪声方差等，以最大化滤波器的性能。

最后，使用KalmanFilter类还可以实现自适应滤波，即根据系统的变化而自动调整滤波器的参数，以便更好地拟合系统的变化。

在python中，可以使用pykalman库来实现自适应滤波，pykalman库提供了一系列API，可以实现自适应滤波的各种功能。

总之，卡尔曼滤波python实现是一种非常有效的处理随机信号的方法，它可以应用于多种系统，用于处理不确定信息，以及实现自适应滤波。

在python中，可以使用KalmanFilter类和pykalman库来实现卡尔曼滤波，它们都提供了大量的API，可以完成各种功能。

马尔可夫决策过程中的策略迭代算法复杂度分析(七)

马尔可夫决策过程（Markov Decision Process，简称MDP）是一种用于描述随机决策过程的数学框架。

在MDP中，智能体通过一系列决策来实现某种目标，每个决策都会对环境产生影响，并且这种影响是随机的。

马尔可夫决策过程中的策略迭代算法是一种常用的解决方案，它通过不断迭代优化策略来寻求最优解。

本文将对马尔可夫决策过程中的策略迭代算法的复杂度进行分析。

首先，我们来回顾一下马尔可夫决策过程中的一些基本概念。

在MDP中，我们通常会定义状态空间、动作空间、奖励函数、状态转移函数等。

智能体在不同的状态下可以采取不同的动作，并且每个动作都会对环境产生影响，从而导致状态的转移。

此外，环境会根据智能体采取的动作给予奖励，智能体的目标就是通过选择合适的动作来最大化长期奖励的累积。

策略迭代算法是一种常用的求解MDP最优策略的方法。

该算法包括策略评估和策略改进两个步骤。

在策略评估阶段，我们会对当前策略进行评估，计算每个状态的值函数。

具体来说，我们可以通过求解Bellman方程或者进行蒙特卡洛模拟来估计值函数。

在策略改进阶段，我们会根据已经计算出的值函数来更新策略，使得策略朝着更优的方向前进。

接下来，我们来分析策略迭代算法的复杂度。

在策略评估阶段，通常需要解线性方程组或进行蒙特卡洛模拟。

如果状态空间和动作空间较大，那么线性方程组的求解会变得非常耗时，而蒙特卡洛模拟的计算量也会随之增加。

因此，在大规模问题下，策略评估的复杂度会随着状态空间和动作空间的增加而指数级增长。

在策略改进阶段，通常需要对值函数进行迭代优化，直到值函数收敛。

这一过程的复杂度取决于值函数的收敛速度，如果值函数收敛速度较慢，那么策略改进的复杂度也会相应增加。

综合来看，策略迭代算法的复杂度主要取决于两个方面：一是策略评估阶段的复杂度，二是策略改进阶段的复杂度。

在大规模问题下，这两个阶段的复杂度都会变得非常高，甚至难以处理。

因此，针对大规模MDP问题，需要采用一些高效的近似算法来求解最优策略，比如基于近似值函数的策略迭代算法或者基于采样的增强学习算法。

马尔可夫链蒙特卡洛方法中的重要性采样技巧(八)

马尔可夫链蒙特卡洛方法中的重要性采样技巧马尔可夫链蒙特卡洛（MCMC）方法是一种用于估计复杂概率分布的统计方法，它通过使用马尔可夫链来生成样本，从而近似计算目标分布的期望值。

然而，对于高维、多峰或者具有长尾分布的目标分布，传统的MCMC方法效率较低，收敛速度较慢。

为了提高MCMC方法的效率，重要性采样技巧被引入其中。

重要性采样是一种用于计算期望值的统计方法，它利用一个已知的较简单的分布（称为重要性分布）来生成样本，然后使用这些样本来近似计算目标分布的期望值。

在MCMC方法中，重要性采样技巧可以被用来改进采样过程，提高采样效率。

下面将从几个方面来探讨马尔可夫链蒙特卡洛方法中的重要性采样技巧的重要性。

1. 重要性分布的选择在重要性采样技巧中，重要性分布的选择对于采样的效率起着至关重要的作用。

一般来说，重要性分布应当被选择为与目标分布尽可能接近的分布，以确保生成的样本能够较好地代表目标分布。

在MCMC方法中，重要性分布的选择通常可以通过先验知识或者经验来确定，也可以通过试验和比较不同的重要性分布来找到最优的选择。

2. 重要性权重的计算在重要性采样技巧中，生成的样本需要对应的重要性权重，这些权重用于调整每个样本的贡献，以便更好地近似目标分布的期望值。

在MCMC方法中，重要性权重的计算通常可以通过目标分布和重要性分布的密度比来得到。

然而，在实际应用中，密度比通常难以精确计算，因此需要通过一些近似方法（如比例估计、核密度估计等）来计算重要性权重，以保证采样的效率和准确性。

3. 重要性采样与MCMC的结合重要性采样技巧可以与MCMC方法结合，以改进MCMC方法的效率和收敛速度。

一种常见的方法是在MCMC采样过程中使用重要性采样来生成样本，然后根据重要性权重来调整每个样本的贡献，以提高采样的效率。

另一种方法是利用重要性采样来初始化MCMC采样过程，以提高初始样本的代表性，从而加速MCMC方法的收敛。

4. 重要性采样技巧在实际应用中的挑战尽管重要性采样技巧在理论上具有很好的性质，但在实际应用中也面临着一些挑战。

马尔可夫决策过程中的策略迭代算法收敛性证明(Ⅱ)

马尔可夫决策过程（MDP）是一种用来描述具有随机性和不确定性的决策问题的数学模型。

在MDP中，一个决策代理通过选择不同的行动来影响环境的状态，并根据环境的奖励和转移概率来学习最优的决策策略。

在MDP中，最优策略是指能够使代理获得最大累积奖励的决策策略。

策略迭代是一种常用的解决MDP最优策略的算法。

策略迭代算法通过不断地更新代理的策略，直到策略收敛为止。

在本文中，我们将讨论策略迭代算法的收敛性证明。

首先，我们来回顾一下MDP的基本定义。

一个MDP可以用一个四元组(S, A, T, R)来表示，其中S是状态空间，A是行动空间，T是状态转移概率函数，R是奖励函数。

在MDP中，代理根据当前状态选择行动，环境根据行动和转移概率函数确定下一个状态，并给出相应的奖励。

代理的目标是找到一个最优策略π*，使得在该策略下能够获得最大的期望累积奖励。

策略迭代算法包括策略评估和策略改进两个步骤。

在策略评估中，代理根据当前策略π来计算每个状态的值函数。

值函数表示在当前策略下，从某个状态开始遵循该策略所能获得的期望累积奖励。

在策略改进中，代理根据值函数来更新策略，使得策略朝着最优的方向改进。

策略迭代算法的收敛性证明通常基于策略迭代定理。

策略迭代定理指出，在策略迭代算法中，只要策略评估和策略改进两个步骤能够无限循环执行下去，并且每个状态的值函数都能够收敛，那么最终算法将收敛到最优策略。

这意味着，策略迭代算法在一定条件下是收敛的。

接下来，我们来讨论策略迭代算法的收敛性证明。

首先，我们需要证明在策略迭代算法中，策略评估和策略改进两个步骤能够无限循环执行下去。

这通常可以通过引入一个收敛条件来证明。

例如，我们可以引入一个阈值ε，当值函数的变化小于ε时，我们认为值函数已经收敛。

在策略评估中，我们可以通过不断更新值函数来逼近真实值函数，直到值函数收敛。

在策略改进中，我们可以通过贪婪地选择行动来更新策略，使得值函数朝着最优的方向改进。

这样，策略评估和策略改进两个步骤就能够无限循环执行下去。

马尔可夫链蒙特卡洛采样中的收敛诊断技巧(Ⅲ)

马尔可夫链蒙特卡洛(Markov chain Monte Carlo, MCMC)采样是一种常见的概率统计方法，用于对复杂的概率分布进行近似抽样。

在实际应用中，MCMC方法的效率和可靠性往往受到收敛性的影响。

因此，对MCMC采样中的收敛诊断技巧进行研究和应用具有重要意义。

## 理论基础MCMC方法的核心思想是通过构建一个马尔可夫链，使其平稳分布为所需的目标分布，从而实现对目标分布的抽样。

而MCMC采样的关键在于要确保所构建的马尔可夫链在有限步之后能够收敛到平稳分布。

因此，收敛诊断技巧是保证MCMC采样有效性的关键。

## 基本收敛诊断方法### 自相关函数自相关函数是一种常见的收敛诊断方法，用于衡量马尔可夫链中采样值之间的相关性。

如果链已经收敛，那么采样值之间的相关性应该趋于稳定。

通过计算不同滞后阶数下的自相关系数，可以判断马尔可夫链的收敛情况。

### Gelman-Rubin 统计量Gelman-Rubin 统计量是另一种常用的收敛诊断方法，它通过对多个并行运行的马尔可夫链进行比较，来判断链是否已经收敛。

该统计量基于链内变异和链间变异的比较，当链足够长并且已经收敛时，Gelman-Rubin 统计量将趋于1。

## 进阶收敛诊断技巧### 收敛诊断图除了基本的收敛诊断方法外，研究人员还开发了一些进阶的技巧。

比如，通过绘制马尔可夫链的收敛诊断图，可以直观地观察链的收敛情况。

这些图形通常包括时间序列图、密度图、自相关图等，可以帮助分析人员更直观地判断链是否已经收敛。

### 混合马尔可夫链混合马尔可夫链是一种将几个不同的马尔可夫链组合在一起的方法，用于解决传统MCMC方法收敛速度慢的问题。

通过引入混合策略，混合马尔可夫链可以在一定程度上提高采样的效率和收敛速度。

## 实际应用与挑战MCMC方法在统计学、机器学习、贝叶斯推断等领域都有广泛的应用，但在实际应用中也面临一些挑战。

比如，对于高维问题，马尔可夫链的收敛速度往往较慢，需要更多的收敛诊断技巧来确保采样的有效性。

马尔科夫随机场在计算机视觉中的性能优化技巧(Ⅲ)

马尔科夫随机场（Markov Random Field，MRF）是一种概率图模型，常用于对图像、语音、自然语言等数据进行建模和分析。

在计算机视觉领域，马尔科夫随机场被广泛应用于图像分割、目标识别、图像去噪等任务中。

然而，由于马尔科夫随机场的复杂性和计算量大，其在实际应用中存在一些性能上的挑战。

本文将介绍一些马尔科夫随机场在计算机视觉中的性能优化技巧，帮助读者更好地理解和应用这一强大的模型。

1. 参数学习马尔科夫随机场的性能优化技巧之一是参数学习。

马尔科夫随机场的性能取决于其参数的选择，因此对参数进行有效的学习是至关重要的。

传统的参数学习方法包括最大似然估计和贝叶斯方法。

最大似然估计通过最大化数据的似然函数来估计参数，而贝叶斯方法则通过引入先验分布来对参数进行估计。

此外，还有一些基于梯度下降的优化算法，如随机梯度下降和拟牛顿方法，可以用于参数学习。

这些方法可以帮助优化马尔科夫随机场的性能，提高其在计算机视觉任务中的表现。

2. 近似推断马尔科夫随机场的另一个性能优化技巧是近似推断。

由于马尔科夫随机场的复杂性，精确推断通常是不可行的，因此需要使用一些近似推断的方法。

常用的近似推断方法包括变分推断和近似推断传播。

变分推断通过寻找一个近似分布来近似真实后验分布，从而简化推断过程。

近似推断传播则通过将问题分解为多个子问题，然后通过迭代的方式来逼近真实后验分布。

这些近似推断方法可以有效地减少计算量，提高马尔科夫随机场的性能。

3. 结构化预测马尔科夫随机场的第三个性能优化技巧是结构化预测。

在一些计算机视觉任务中，需要对多个相关的变量进行联合预测，这就需要考虑这些变量之间的依赖关系。

马尔科夫随机场可以很好地处理这种结构化预测问题，通过考虑全局一致性来提高预测的准确性。

为了进一步优化性能，可以使用一些高效的结构化预测算法，如线性松弛和置信传播算法。

这些算法可以帮助提高马尔科夫随机场在结构化预测任务中的性能。

4. 图割方法最后，马尔科夫随机场的性能优化技巧还包括图割方法。

一种邻帧匹配与卡尔曼滤波相结合的多目标跟踪算法

一种邻帧匹配与卡尔曼滤波相结合的多目标跟踪算法梅立雪;汪兆栋;张浦哲【摘要】传统目标跟踪算法很难在户外视频中进行行人实时跟踪及人流量统计,针对该问题,提出一种联合邻帧匹配与卡尔曼滤波器的多目标跟踪算法.该算法首先以方向梯度直方图(HOG)为特征的自适应推进(Adaboost)分类器进行行人人头检测,进而采用卡尔曼滤波进行行人轨迹预测,并应用邻帧匹配算法对该目标运动轨迹进行校正.在邻帧匹配法中,新颖地将跟踪过程中的目标匹配问题转化为基于匈牙利算法的指派问题.因邻帧匹配法能更好地区分不同待匹配目标的特征,较传统跟踪算法,能更好地避免误匹配、漏匹配等问题,提高了目标跟踪的准确率,实验证明,该监控系统准确率高,且能满足扶梯监控系统应用场景下的鲁棒性、实时性要求.【期刊名称】《科学技术与工程》【年(卷),期】2019(019)015【总页数】7页(P204-210)【关键词】方向梯度直方图;运动目标跟踪;邻帧匹配;卡尔曼滤波【作者】梅立雪;汪兆栋;张浦哲【作者单位】景德镇学院机械与电子工程系,景德镇333000;景德镇学院机械与电子工程系,景德镇333000;景德镇学院机械与电子工程系,景德镇333000【正文语种】中文【中图分类】TP391.41目标跟踪是对视频中的感兴趣目标区域进行实现跟踪的过程，是智能视频监控领域的基本任务之一，很多现实应用都要以此为基础；如：客流量统计、异常行为识别、拥堵检测等。

对监控场景中的感兴趣区域进行检测跟踪通常有两类方法，第一种是先检测出该目标所在的区域，再在相邻帧中对这些感兴趣区域进行配对，进而确定目标在每帧图像中的位置及运动轨迹；第二种是直接对视频中每帧图像的感兴趣目标进行识别与标定，进而对每个目标进行实时跟踪及预测其运动轨迹。

目前常见的目标跟踪算法有均值漂移法、曲线演化法、活动轮廓模型、粒子滤波、卡尔曼滤波以及基于预测与估计的跟踪方法等。

均值漂移(meanshift)是利用概率密度函数的局部极值来预测下一帧图像中感兴趣区域中心点位置的目标跟踪方法[1]。

基于高斯平滑的自适应角点检测

基于高斯平滑的自适应角点检测
肖茜;鲁宏伟
【期刊名称】《计算机辅助设计与图形学学报》
【年(卷),期】2003(015)011
【摘要】文中算法首先在曲线尺度空间中通过高斯平滑以消除噪声;然后再基于自适应弯曲度计算和角点筛选准则确定角点.该算法不需要预先输入参数,具有较好的抗干扰性,实现简单有效.
【总页数】4页(P1358-1361)
【作者】肖茜;鲁宏伟
【作者单位】华中科技大学计算机科学与技术学院,湖北,430074;华中科技大学计算机科学与技术学院,湖北,430074
【正文语种】中文
【中图分类】TP391
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