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聚类分析（cluster analysis）medical aircraftClustering analysis refers to the grouping of physical or abstract objects into a class consisting of similar objects. It is an important human behavior. The goal of cluster analysis is to classify data on a similar basis. Clustering comes from many fields, including mathematics, computer science, statistics, biology and economics. In different applications, many clustering techniques have been developed. These techniques are used to describe data, measure the similarity between different data sources, and classify data sources into different clusters.CatalogconceptMainly used in businessOn BiologyGeographicallyIn the insurance businessOn Internet applicationsIn E-commerceMain stepsCluster analysis algorithm conceptMainly used in businessOn BiologyGeographicallyIn the insurance businessOn Internet applicationsIn E-commerceMain stepsClustering analysis algorithmExpand the concept of editing this paragraphThe difference between clustering and classification is that the classes required by clustering are unknown. Clustering is a process of classifying data into different classes or clusters, so objects in the same cluster have great similarity, while objects between different clusters have great dissimilarity. From a statistical point of view, clustering analysis is a way to simplify data through data modeling. Traditional statistical clustering analysis methods include system clustering method, decomposition method, adding method, dynamic clustering method, ordered sample clustering,overlapping clustering and fuzzy clustering, etc.. Cluster analysis tools, such as k- mean and k- center point, have been added to many famous statistical analysis packages, such as SPSS, SAS and so on. From the point of view of machine learning, clusters are equivalent to hidden patterns. Clustering is an unsupervised learning process for searching clusters. Unlike classification, unsupervised learning does not rely on predefined classes or class labeled training instances. Automatic marking is required by clustering learning algorithms, while instances of classification learning or data objects have class tags. Clustering is observational learning, not sample learning. From the point of view of practical application, clustering analysis is one of the main tasks of data mining. Moreover, clustering can be used as an independent tool to obtain the distribution of data, to observe the characteristics of each cluster of data, and to concentrate on the analysis of specific cluster sets. Clustering analysis can also be used as a preprocessing step for other algorithms (such as classification and qualitative inductive algorithms).Edit the main application of this paragraphCommerciallyCluster analysis is used to identify different customer groups and to characterize different customer groups through the purchase model. Cluster analysis is an effective tool for market segmentation. It can also be used to study consumer behavior, to find new potential markets, to select experimental markets, and to be used as a preprocessing of multivariate analysis.On BiologyCluster analysis is used to classify plants and plants and classify genes so as to get an understanding of the inherent structure of the populationGeographicallyClustering can help the similarity of the databases that are observed in the earthIn the insurance businessCluster analysis uses a high average consumption to identify groups of car insurance holders, and identifies a city's property groups based on type of residence, value, locationOn Internet applicationsCluster analysis is used to categorize documents online to fix informationIn E-commerceA clustering analysis is a very important aspect in the construction of Web Data Mining in electronic commerce, through clustering with similar browsing behavior of customers, and analyze the common characteristics of customers, help the users of e-commerce can better understand their customers, provide more suitable services to customers.Edit the main steps of this paragraph1. data preprocessing,2. defines a distance function for measuring similarity between data points,3. clustering or grouping, and4. evaluating output. Data preprocessing includes the selection of number, types and characteristics of the scale, it relies on the feature selection and feature extraction, feature selection important feature, feature extraction feature transformation input for a new character, they are often used to obtain an appropriate feature set to avoid the "cluster dimension disaster" data preprocessing, including outlier removal data, outlier is not dependent on the general data or model data, so the outlier clustering results often leads to a deviation, so in order to get the correct clustering, we must eliminate them. Now that is similar to the definition of a class based, so different data in the same measure of similarity feature space for clustering step is very important, because the diversity of types and characteristics of the scale, the distance measure must be cautious, it often depends on the application, for example,Usually by definition in the feature space distance metric to evaluate the differences of the different objects, many distance are applied in different fields, a simple distance measure, Euclidean distance, are often used to reflect the differences between different data, some of the similarity measure, such as PMC and SMC, to the concept of is used to characterize different data similarity in image clustering, sub image error correction can be used to measure the similarity of two patterns. The data objects are divided into differentclasses is a very important step, data based on different methods are divided into different classes, classification method and hierarchical method are two main methods of clustering analysis, classification methods start from the initial partition and optimization of a clustering criterion. Crisp Clustering, each data it belonged to a separate class; Fuzzy Clustering, each data it could be in any one class, Crisp Clustering and Fuzzy Clusterin are the two main technical classification method, classification method of clustering is divided to produce a series of nested a standard based on the similarity measure, it can or a class separability for merging and splitting is similar between the other clustering methods include density based clustering model, clustering based on Grid Based clustering. To evaluate the quality of clustering results is another important stage, clustering is a management program, there is no objective criteria to evaluate the clustering results, it is a kind of effective evaluation, the index of general geometric properties, including internal separation between class and class coupling, the quality is generally to evaluate the clustering results, effective index in the determination of the number of the class is often played an important role, the best value of effective index is expected to get from the real number, a common class number is decided to select the optimum values for a particular class of effective index, is the the validity of the standard index the real number of this index can, many existing standards for separate data set can be obtained very good results, but for the complex number According to a collection, it usually does not work, for example, for overlapping classes of collections.Edit this section clustering analysis algorithmClustering analysis is an active research field in data mining, and many clustering algorithms are proposed. Traditional clustering algorithms can be divided into five categories: partitioning method, hierarchical method, density based method, grid based method and model-based method. The 1 division method (PAM:PArtitioning method) first create the K partition, K is the number of partition to create; and then use a circular positioning technology through the object from a division to another division to help improve the quality of classification. Including the classification of typical: K-means, k-medoids, CLARA (Clustering LARge Application), CLARANS (Clustering Large Application based upon RANdomized Search). FCM 2 level (hierarchical method) method to create a hierarchical decomposition of the given data set. The method can be divided into two operations: top-down (decomposition) and bottom-up (merging). In order to make up for the shortcomings of decomposition and merging, hierarchical merging is often combined with other clustering methods, such as cyclic localization. This includes the typical methods of BIRCH (Balanced Iterative Reducing and Clustering using Hierarchies) method, it firstly set the tree structure to divide the object; then use other methods to optimize the clustering. CURE (Clustering, Using, REprisentatives) method, which uses fixed numbers to represent objects to represent the corresponding clustering, and then shrinks the clusters according to the specified amount (to the clustering center). ROCK method, it uses the connection between clusters to cluster and merge. CHEMALOEN method, it constructs dynamic model in hierarchical clustering. 3 density based method, according to the density to complete the object clustering. It grows continuouslyaccording to the density around the object (such as DBSCAN). The typical density based methods include: DBSCAN(Densit-based Spatial Clustering of Application with Noise): the algorithm by growing enough high density region to clustering; clustering can find arbitrary shape from spatial databases with noise in. This method defines a cluster as a set of point sets of density connectivity. OPTICS (Ordering, Points, To, Identify, the, Clustering, Structure): it does not explicitly generate a cluster, but calculates an enhanced clustering order for automatic interactive clustering analysis.. 4 grid based approach,Firstly, the object space is divided into finite elements to form a grid structure, and then the mesh structure is used to complete the clustering. STING (STatistical, INformation, Grid) is a grid based clustering method that uses the statistical information stored in the grid cell. CLIQUE (Clustering, In, QUEst) and Wave-Cluster are a combination of grid based and density based methods. 5, a model-based approach, which assumes the model of each cluster, and finds data appropriate for the corresponding model. Typical model-based methods include: statistical methods, COBWEB: is a commonly used and simple incremental concept clustering method. Its input object is represented by a symbolic quantity (property - value) pair. A hierarchical cluster is created in the form of a classification tree. CLASSIT is another version of COBWEB. It can incrementally attribute continuous attributes. For each node of each property holds the corresponding continuous normal distribution (mean and variance); and the use of an improved classification ability description method is not like COBWEB (value) and the calculation of discrete attributes but theintegral of the continuous attributes. However, CLASSIT methods also have problems similar to those of COBWEB. Therefore, they are not suitable for clustering large databases. Traditional clustering algorithms have successfully solved the clustering problem of low dimensional data. However, due to the complexity of data in practical applications, the existing algorithms often fail when dealing with many problems, especially for high-dimensional data and large data. Because traditional clustering methods cluster in high-dimensional data sets, there are two main problems. The high dimension data set the existence of a large number of irrelevant attributes makes the possibility of the existence of clusters in all the dimensions of almost zero; to sparse data distribution data of low dimensional space in high dimensional space, which is almost the same distance between the data is a common phenomenon, but the traditional clustering method is based on the distance from the cluster, so high dimensional space based on the distance not to build clusters. High dimensional clustering analysis has become an important research direction of cluster analysis. At the same time, clustering of high-dimensional data is also the difficulty of clustering. With the development of technology makes the data collection becomes more and more easily, cause the database to larger scale and more complex, such as trade transaction data, various types of Web documents, gene expression data, their dimensions (attributes) usually can reach hundreds of thousands or even higher dimensional. However, due to the "dimension effect", many clustering methods that perform well in low dimensional data space can not obtain good clustering results in high-dimensional space. Clustering analysis of high-dimensional data is a very active field in clustering analysis, and it is also a challenging task. Atpresent, cluster analysis of high-dimensional data is widely used in market analysis, information security, finance, entertainment, anti-terrorism and so on.。
项目管理中的英文缩写Project Management AcronymsProject management is a complex field that involves a wide range of processes, tools, and techniques. To streamline communication and improve efficiency, project managers often rely on a variety of acronyms. These abbreviations can help to convey information quickly and concisely, allowing team members to stay on the same page and ensure the successful completion of projects. In this essay, we will explore some of the most commonly used project management acronyms and their significance.One of the most well-known acronyms in project management is PMBOK, which stands for Project Management Body of Knowledge. The PMBOK is a comprehensive guide developed by the Project Management Institute (PMI) that outlines the standards, guidelines, and best practices for project management. It covers various aspects of project management, including project integration, scope, time, cost, quality, resource, communication, risk, procurement, and stakeholder management. Understanding and applying the principles outlined in the PMBOK can be crucial for effective project management.Another important acronym is PRINCE2, which stands for Projects in Controlled Environments. PRINCE2 is a structured project management methodology that provides a systematic approach to planning, executing, and controlling projects. It emphasizes the importance of defining clear project objectives, organizing project roles and responsibilities, and managing risks effectively. PRINCE2 is widely used in the public and private sectors, particularly in the United Kingdom, and has become a global standard for project management.The term WBS, or Work Breakdown Structure, is another essential project management acronym. The WBS is a hierarchical decomposition of the work that needs to be done to complete a project. It breaks down the project into smaller, more manageable tasks and deliverables, allowing project managers to better understand the scope of the work and allocate resources accordingly. The WBS is a crucial tool for planning, scheduling, and monitoring project progress.Another common acronym in project management is GANTT, which refers to a Gantt chart. A Gantt chart is a visual tool that displays a project's timeline, tasks, and dependencies. It helps project managers and team members to see the sequence of tasks, identify potential bottlenecks, and track the progress of the project. Gantt charts arewidely used in project management to facilitate planning, scheduling, and communication.The term CPM, or Critical Path Method, is another important project management acronym. The Critical Path Method is a technique used to identify the critical tasks that directly impact the project's completion date. By identifying the critical path, project managers can focus their attention on the tasks that are most crucial to the project's success and allocate resources accordingly. This helps to ensure that the project is completed on time and within the specified budget.Another commonly used acronym in project management is PERT, which stands for Program Evaluation and Review Technique. PERT is a statistical tool used to estimate the time and resources required to complete a project. It involves defining three time estimates (optimistic, most likely, and pessimistic) for each task, which are then used to calculate the expected duration of the project. PERT is particularly useful for large, complex projects with a high degree of uncertainty.The term EVM, or Earned Value Management, is another important project management acronym. EVM is a method of measuring and reporting the progress of a project by integrating the project's scope, schedule, and cost. It provides a way to compare the plannedprogress of a project with the actual progress, allowing project managers to identify and address any deviations from the plan. EVM is a valuable tool for project control and decision-making.Finally, the acronym ROI, or Return on Investment, is often used in project management to evaluate the financial viability of a project. ROI is a metric that measures the ratio of the net benefits of a project to the total cost of the project. It helps project managers and stakeholders to determine whether a project is worth undertaking and whether it will provide a sufficient return on the investment.In conclusion, project management is a complex field that relies on a variety of acronyms to streamline communication and improve efficiency. By understanding the meaning and significance of these acronyms, project managers and team members can work more effectively and ensure the successful completion of projects. As the field of project management continues to evolve, new acronyms may emerge, but the core principles and best practices outlined in the PMBOK, PRINCE2, and other frameworks will remain essential for effective project management.。
项目管理常用英语1. Project charter: A document that defines the project, including its objectives, scope, deliverables, and stakeholders.2. Work breakdown structure (WBS): A hierarchical decomposition of the project's scope into manageable chunks of work.3. Stakeholder: Any individual or group that is affected by or can affect the project.4. Project scope: The sum of all the project's deliverables, requirements, objectives, and work.5. Project milestone: A significant event or achievement during the project that helps track progress and provide motivation.6. Risk management: The process of identifying, assessing, and mitigating potential risks that may affect the project's success.7. Project schedule: A detailed timeline that outlines the project's activities, tasks, dependencies, and deadlines.8. Project budget: An estimate of the overall cost required to complete the project.9. Project sponsor: A person or group responsible for initiating, funding, and supporting the project.10. Project team: The group of individuals assigned to work on the project and achieve its objectives.11. Change management: The process of controlling changes to the project scope, schedule, and budget.12. Quality management: The process of ensuring that the project delivers the desired level of quality and meets the stakeholders' expectations.13. Communication plan: A document that outlines the project's communication channels, frequency, and stakeholders involved.14. Project closure: The process of formally completing and wrapping up the project, including documentation, lessons learned, and client acceptance.15. Lessons learned: A record of the project's successes, failures, and best practices that can be used to improve future projects.。
基于谱聚类的三维⽹格分割算法（SpectralClustering） 谱聚类（Spectral Clustering）是⼀种⼴泛使⽤的数据聚类算法，[Liu et al. 2004]基于谱聚类算法⾸次提出了⼀种三维⽹格分割⽅法。
该⽅法⾸先构建⼀个相似矩阵⽤于记录⽹格上相邻⾯⽚之间的差异性，然后计算相似矩阵的前k个特征向量，这些特征向量将⽹格⾯⽚映射到k维谱空间的单位球上，最后使⽤K-means⽅法对谱空间中的数据点进⾏聚类。
具体算法过程如下：⼀．相似矩阵 ⽹格分割以⾯⽚为基本单元，为了能使算法沿着⼏何模型的凹形区域进⾏分割，⽹格相邻⾯⽚之间的距离采⽤[Katz et al. 2003]中提到的⽅法，具体形式在“”中有所解释，距离由测地距离Geod_Dist和⾓度距离Ang_Dist两部分组成，如下所⽰： 上式中有两个重要的参数δ和η，参数δ通常取值范围为[0.01, 0.05]，其⽤于控制测地距离和⾓度距离之间的权重⽐例，参数η通常取值范围为[0.1, 0.2]，其使得分割边界更倾向于凹形区域。
计算完相邻⾯⽚之间的距离后，相似矩阵中对应位置的值由距离的⾼斯函数得到：其中：⼆．⽹格谱聚类 谱聚类⽅法在本质上都是类似的，都是利⽤相似矩阵的特征向量将原始空间中的数据映射到谱空间，并在谱空间中进⾏聚类。
⽹格上的谱聚类⽅法如下： 1 由上述定义计算相似矩阵W； 2 计算归⼀化矩阵N：N = D-1/2WD-1/2； 3 计算矩阵N的前k个最⼤特征向量e1, e2, … , e k，以这k个特征向量为列组成矩阵U = [e1, e2, … , e k]； 4 将矩阵U的每⼀⾏单位化后得到矩阵Ȗ； 5 提取出k个初始聚类中⼼⽤于K-means聚类，该过程先计算矩阵Q = ȖȖT，然后查找矩阵Q中的最⼩元素Q rs，那么r和s点就是两个距离最远的点，然后继续查找后续点； 6 以Ȗ的⾏向量为数据样本进⾏K-means聚类。
实施方案英文怎么说Implementing Plan。
An effective implementation plan is crucial for the success of any project or initiative. It outlines the steps, resources, and timeline needed to achieve the desired goals and objectives. In this document, we will discuss the key components of an implementation plan and provide guidelines for creating a comprehensive and actionable plan.1. Define the Objectives。
The first step in creating an implementation plan is to clearly define the objectives of the project. This includes identifying the desired outcomes, measurable goals, and specific targets to be achieved. By clearly articulatingthe objectives, all stakeholders can align their efforts towards a common purpose.2. Identify the Scope。
Once the objectives are established, it is important to identify the scope of the project. This involves definingthe boundaries of the project, including the deliverables, resources, and constraints. A clear understanding of the project scope will help in managing expectations and avoiding scope creep.3. Develop a Work Breakdown Structure (WBS)。
PMI Lexicon of ProjectManagement TermsThe PMI Lexicon of Project Management Terms offers you a standardized set of frequently used project, program and portfolio management terms with clear and concise definitions. Included are 145 terms that have a unique use in the profession and high relevance to its vocabulary. While our Combined Standards Glossary© contained all of the definitions from PMI's global standards, in some instances the definitions differed from standard to standard. The lexicon is the first step toward a consistent…Acceptance CriteriaA set of conditions that is required to be met before deliverables are accepted.ActivityA distinct, scheduled portion of work performed during the course of a project.Actual CostThe realized cost incurred for the work performed on an activity during a specific time period.Analogous EstimatingA technique for estimating the duration or cost of an activity or a project, using historical data from a similar activity or project.Apportioned EffortAn activity where effort is allotted proportionately across certain discrete efforts and not divisible into discrete efforts. (Note: Apportioned effort is one of three earned value management [EVM] types of activities used to measure work performance.)AssumptionA factor in the planning process that is considered to be true, real, or certain, without proof or demonstration.Backward PassA critical path method technique for calculating the late start and late finish dates by working backward through the schedule model from the project end date.BaselineThe approved version of a work product that can be changed only through formal change control procedures and is used as a basis for comparison.Bottom-up EstimatingA method of estimating project duration or cost by aggregating the estimates of the lower-level components of the work breakdown structure (WBS).Budget at CompletionThe sum of all budgets established for the work to be performed.Change ControlA process whereby modifications to documents, deliverables, or baselines associated with the project are identified, documented, approved, or rejected.Change Control BoardA formally chartered group responsible for reviewing, evaluating, approving, delaying, or rejecting changes to the project and for recording and communicating such decisions.Change Control SystemA set of procedures that describes how modifications to the project deliverables and documentation are managed and controlled.Change RequestA formal proposal to modify any document, deliverable, or baseline.Code of AccountsA numbering system used to uniquely identify each component of the work breakdown structure.Communication Management PlanA component of the project, program, or portfolio management plan that describes how, when, and by whom information will be administered and disseminated.ConstraintA limiting factor that affects the execution of a project, program, portfolio, or process.Control AccountA management control point where scope, budget, actual cost, andschedule are integrated and compared to earned value for performance measurement.Corrective ActionAn intentional activity that realigns the performance of the project work with the project management plan.Cost Management PlanA component of a project or program management plan that describes how costs will be planned, structured, and controlled.Cost Performance IndexA measure of the cost efficiency of budgeted resources expressed as the ratio of earned value to actual cost.Cost VarianceThe amount of budget deficit or surplus at a given point in time, expressed as the difference between the earned value and the actual cost.CrashingA technique used to shorten the schedule duration for the least incremental cost by adding resources.Critical Chain MethodA schedule method that allows the project team to place buffers on any project schedule path to account for limited resources andproject uncertainties.Critical PathThe sequence of activities that represents the longest path through a project, which determines the shortest possible duration.Critical Path ActivityAny activity on the critical path in a project schedule.Critical Path MethodA method used to estimate the minimum project duration and determine the amount of scheduling flexibility on the logical network paths within the schedule model.Data DateA point in time when the status of the project is recorded.Decision Tree AnalysisA diagramming and calculation technique for evaluating the implications of a chain of multiple options in the presence of uncertainty.DecompositionA technique used for dividing and sub-dividing the project scope and project deliverables into smaller, more manageable parts.Defect RepairAn intentional activity to modify a nonconforming product or product component.DeliverableAny unique and verifiable product, result, or capability to perform a service that is required to be produced to complete a process, phase, or project.Discrete EffortAn activity that can be planned and measured and that yields a specific output. (Note: Discrete effort is one of three earned value management [EVM] types of activities used to measure work performance.)Early Finish DateIn the critical path method, the earliest possible point in time when the uncompleted portions of a schedule activity can finish based on the schedule network logic, the data date, and any schedule constraints.Early Start DateIn the critical path method, the earliest possible point in time when the uncompleted portions of a schedule activity can start based on the schedule network logic, the data date, and any schedule constraints.Earned ValueThe measure of work performed expressed in terms of the budget authorized for that work.Earned Value ManagementA methodology that combines scope, schedule, and resource measurements to assess project performance and progress.EffortThe number of labor units required to complete a schedule activity or work breakdown structure component, often expressed in hours, days, or weeks.Enterprise Environmental FactorsConditions, not under the immediate control of the team, that influence, constrain, or direct the project, program, or portfolio.Estimate at CompletionThe expected total cost of completing all work expressed as the sum of the actual cost to date and the estimate to complete.Estimate to CompleteThe expected cost to finish all the remaining project work.Fast TrackingA schedule compression technique in which activities or phases normally done in sequence are performed in parallel for at least a portion of their duration.Finish-to-FinishA logical relationship in which a successor activity cannot finish until a predecessor activity has finished.Finish-to-StartA logical relationship in which a successor activity cannot start until a predecessor activity has finished.Forward PassA critical path method technique for calculating the early start and early finish dates by working forward through the schedule model from the project start date or a given point in time.Free FloatThe amount of time that a schedule activity can be delayed without delaying the early start date of any successor or violating a schedule constraint.Gantt ChartA bar chart of schedule information where activities are listed on the vertical axis, dates are shown on the horizontal axis, andactivity durations are shown as horizontal bars placed according to start and finish dates.Human Resource PlanA component of the project or program management plan that describes how the roles and responsibilities, reporting relationships, and staff management will be addressed and structured.LagThe amount of time whereby a successor activity is required to be delayed with respect to a predecessor activity.Late Finish DateIn the critical path method, the latest possible point in time when the uncompleted portions of a schedule activity can finish based on the schedule network logic, the project completion date, and any schedule constraints.Late Start DateIn the critical path method, the latest possible point in time when the uncompleted portions of a schedule activity can start based on the schedule network logic, the project completion date, and any schedule constraints.LeadThe amount of time whereby a successor activity can be advanced with respect to a predecessor activity.Lessons LearnedThe knowledge gained during a project which shows how project events were addressed or should be addressed in the future for the purpose of improving future performanceLevel of EffortAn activity that does not produce definitive end products and is measured by the passage of time. (Note: Level of effort is one of three earned value management [EVM] types of activities used to measure work performance.)Logical RelationshipA dependency between two activities, or between an activity and a milestone.MilestoneA significant point or event in a project, program, or portfolio.Most Likely DurationAn estimate of the most probable activity duration that takes into account all of the known variables that could affect performance.OpportunityA risk that would have a positive effect on one or more project objectives.Optimistic DurationAn estimate of the shortest activity duration that takes into account all of the known variables that could affect performance.Organizational Breakdown StructureA hierarchical representation of the project organization, which illustrates the relationship between project activities and the organizational units that will perform those activities.Organizational Process AssetsPlans, processes, policies, procedures and knowledge bases specific to and used by the performing organization.Organizational Project Management MaturityThe level of an organization's ability to deliver the desired strategic outcomes in a predictable, controllable, and reliable manner.Parametric EstimatingAn estimating technique in which an algorithm is used to calculate cost or duration based on historical data and project parameters.Path ConvergenceA relationship in which a schedule activity has more than one predecessor.Path DivergenceA relationship in which a schedule activity has more than one successor.Percent CompleteAn estimate expressed as a percent of the amount of work that has been completed on an activity or a work breakdown structure component.Performing OrganizationAn enterprise whose personnel are the most directly involved in doing the work of the project or program.Pessimistic DurationAn estimate of the longest activity duration, which takes into account all of the known variables that could affect performance.Phase GateA review at the end of a phase in which a decision is made to continue to the next phase, to continue with modification, or to end a project or program.Planned ValueThe authorized budget assigned to scheduled work.PortfolioProjects, programs, subportfolios, and operations managed as a group to achieve strategic objectives.Portfolio BalancingThe process of optimizing the mix of portfolio components to further the strategic objectives of the organization.Portfolio ManagementThe centralized management of one or more portfolios to achieve strategic objectives.Precedence Diagramming MethodA technique used for constructing a schedule model in whichactivities are represented by nodes and are graphically linked by one or more logical relationships to show the sequence in which the activities are to be performed.Predecessor ActivityAn activity that logically comes before a dependent activity in a schedule.Preventive ActionAn intentional activity that ensures the future performance of the project work is aligned with the project management plan.Probability and Impact MatrixA grid for mapping the probability of each risk occurrence and its impact on project objectives if that risk occurs.Procurement Management PlanA component of the project or program management plan that describes how a team will acquire goods and services from outside of the performing organization.Product Life CycleThe series of phases that represent the evolution of a product, from concept through delivery, growth, maturity, and to retirement.ProgramA group of related projects, subprograms and program activities that are managed in a coordinated way to obtain benefits not available from managing them individually.Program ManagementThe application of knowledge, skills, tools, and techniques to a program to meet the program requirements and to obtain benefits and control not available by managing projects individually.Program Management OfficeA management structure that standardizes the program-related governance processes and facilitates the sharing of resources, methodologies, tools, and techniques.Progressive ElaborationThe iterative process of increasing the level of detail in a project management plan as greater amounts of information and more accurate estimates become available.ProjectA temporary endeavor undertaken to create a unique product, service, or result.Project CalendarA calendar that identifies working days and shifts that are available for scheduled activities.Project CharterA document issued by the project initiator or sponsor that formally authorizes the existence of a project and provides the project manager with the authority to apply organizational resources to project activities.Project Life CycleThe series of phases that a project passes through from itsinitiation to its closure.Project ManagementThe application of knowledge, skills, tools, and techniques to project activities to meet the project requirements.Project Management OfficeA management structure that standardizes the project-related governance processes and facilitates the sharing of resources, methodologies, tools, and techniques.Project Management PlanThe document that describes how the project will be executed, monitored, and controlled.Project ManagerThe person assigned by the performing organization to lead the team that is responsible for achieving the project objectives.Project PhaseA collection of logically related project activities that culminates in the completion of one or more deliverables.Project ScheduleAn output of a schedule model that presents linked activities with planned dates, durations, milestones, and resources.Project Schedule Network DiagramA graphical representation of the logical relationships among the project schedule activities.Project ScopeThe work performed to deliver a product, service, or result with the specified features and functions.Project Scope StatementThe description of the project scope, major deliverables, assumptions, and constraints.Quality Management PlanA component of the project or program management plan that describes how an organization's quality policies will be implemented.RequirementA condition or capability that is required to be present in a product, service, or result to satisfy a contract or other formally imposed specification.Requirements Management PlanA component of the project or program management plan that describes how requirements will be analyzed, documented and managed.Requirements Traceability MatrixA grid that links product requirements from their origin to the deliverables that satisfy them.Resource Breakdown StructureA hierarchical representation of resources by category and type.Resource CalendarA calendar that identifies the working days and shifts upon which each specific resource is available.Resource LevelingA technique in which start and finish dates are adjusted based on resource constraints with the goal of balancing demand for resources with the available supply.Responsibility Assignment MatrixA grid that shows the project resources assigned to each work package.RiskAn uncertain event or condition that, if it occurs, has a positive or negative effect on one or more project objectives.Risk AcceptanceA risk response strategy whereby the project team decides to acknowledge the risk and not take any action unless the risk occurs.Risk AvoidanceA risk response strategy whereby the project team acts to eliminate the threat or protect the project from its impact.Risk Breakdown StructureA hierarchical representation of risks that is organized according to risk categories.Risk CategoryA group of potential causes of risk.Risk Management PlanA component of the project, program, or portfolio management plan that describes how risk management activities will be structured and performed.Risk MitigationA risk response strategy whereby the project team acts to reduce the probability of occurrence or impact of a risk.Risk RegisterA document in which the results of risk analysis and risk response planning are recorded.Risk TransferenceA risk response strategy whereby the project team shifts the impact of a threat to a third party, together with ownership of the response.Rolling Wave PlanningAn iterative planning technique in which the work to be accomplished in the near term is planned in detail, while the work in the future is planned at a higher level.Schedule BaselineThe approved version of a schedule model that can be changed only through formal change control procedures and is used as a basis for comparison to actual results.Schedule CompressionA technique used to shorten the schedule duration without reducing the project scope.Schedule Management PlanA component of the project or program management plan that establishes the activities for developing, monitoring, and controlling the project or program.Schedule ModelA representation of the plan for executing the project's activities including durations, dependencies and other planning information, used to produce a project schedule along with other scheduling artifacts.Schedule Model AnalysisA process used to investigate or analyze the output of the schedule model in order to optimize the scheduleSchedule Performance IndexA measure of schedule efficiency expressed as the ratio of earned value to planned value.Schedule VarianceA measure of schedule performance expressed as the difference between the earned value and the planned value.Scope BaselineThe approved version of a scope statement, work breakdown structure (WBS), and its associated WBS dictionary, which can be changed only through formal change control procedures and is used as a basis for comparison.Scope CreepThe uncontrolled expansion to product or project scope without adjustments to time, cost, and resources.Scope Management PlanA component of the project or program management plan that describes how the scope will be defined, developed, monitored, controlled, and verified.S-Curve AnalysisAn earned value management technique used to indicate performance trends by using a graph that displays cumulative costs over aspecific time period.Secondary RiskA risk that arises as a direct result of implementing a risk response.SponsorA person or group who provides resources and support for the project, program, or portfolio, and is accountable for enabling success.Staffing Management PlanA component of the human resource plan that describes when and how team members will be acquired and how long they will be needed.StakeholderAn individual, group, or organization who may affect, be affected by, or perceive itself to be affected by a decision, activity, or outcome of a project, program, or portfolio.Start-to-FinishA logical relationship in which a successor activity cannot finish until a predecessor activity has started.Start-to-StartA logical relationship in which a successor activity cannot start until a predecessor activity has started.Successor ActivityA dependent activity that logically comes after another activity in a schedule.Summary ActivityA group of related schedule activities aggregated and displayed as a single activity.ThreatA risk that would have a negative effect on one or more project objectives.Three-Point EstimateA technique used to estimate cost or duration by applying an average of optimistic, pessimistic, and most likely estimates when there is uncertainty with the individual activity estimates.To-Complete Performance IndexA measure of the cost performance that is required to be achieved with the remaining resources in order to meet a specified management goal, expressed as the ratio of the cost to finish the outstanding work to the remaining budget.Total FloatThe amount of time that a schedule activity can be delayed or extended from its early start date without delaying the projectfinish date or violating a schedule constraint.Trigger ConditionAn event or situation that indicates that a risk is about to occur.Variance AnalysisA technique for determining the cause and degree of difference between the baseline and actual performance.Variance at CompletionA projection of the amount of budget deficit or surplus, expressed as the difference between the budget at completion and the estimate at completion.WBS DictionaryA document that provides detailed deliverable, activity, and scheduling information about each component in the work breakdown structure.What-If Scenario AnalysisThe process of evaluating scenarios in order to predict their effect on project objectives.Work Breakdown StructureA hierarchical decomposition of the total scope of work to be carried out by the project team to accomplish the project objectives and create the required deliverables.Work PackageThe work defined at the lowest level of the work breakdown structure for which cost and duration can be estimated and managed.WorkaroundA response to a threat that has occurred, for which a prior response had not been planned or was not effective.。
Project management is a complex field that involves a multitude of terms and phrases. To facilitate effective communication and understanding among professionals in this field, here is a comprehensive list of project management English vocabulary, categorized into various sections:I. Basic Project Management Terms1. Project - A temporary endeavor with a defined beginning and end, undertaken to create a unique product, service, or result.2. Project Management - The application of knowledge, skills, tools, and techniques to project activities to meet the project requirements.3. Project Life Cycle - The sequence of phases that a project goes through from start to finish.4. Project Phase - A distinct section of the project life cycle with specific objectives and deliverables.5. Project Phase Exit or Termination Point - The point at which aproject phase is completed and the project moves to the next phase or is terminated.6. Project Management Office (PMO) - A group or department within an organization that oversees the management of the organization's projects.7. Project Portfolio - A collection of projects, programs, and other work that an organization has under way.8. Project Scope - The specific set of deliverables, tasks, andactivities that the project team is required to complete.II. Project Planning and Scheduling1. Work Breakdown Structure (WBS) - A deliverable-oriented hierarchical decomposition of the work to be executed by the project team.2. Schedule - A document that lists the activities of the project, their durations, and the sequence in which they are to be performed.3. Critical Path Method (CPM) - A technique used to determine thecritical activities and the critical path of a project.4. Program Evaluation and Review Technique (PERT) - A project management technique for scheduling and coordinating tasks.5. Milestone - A significant event or point in a project that indicates that the project has reached a critical stage or is on schedule.6. Resource Allocation - The process of assigning resources to project activities to ensure the project's objectives are met.7. Risk Management - The process of identifying, analyzing, and responding to project risks.III. Project Execution and Control1. Change Management - The process of managing changes to the project scope, schedule, or resources.2. Quality Management - The process of ensuring that the project deliverables meet the specified requirements.3. Communication Management - The process of planning, collecting, disseminating, and managing project information.4. Stakeholder Management - The process of engaging with stakeholders to ensure their expectations and concerns are addressed.5. Risk Response - The actions taken to reduce the likelihood or impact of a risk.6. Quality Assurance - The process of monitoring and evaluating project activities to ensure that the project is being executed according to the project management plan.7. Quality Control - The process of monitoring the results of project activities to ensure that the deliverables meet the specified requirements.IV. Project Closure1. Project Closure - The formal acceptance of the completed project deliverables and the conclusion of all project activities.2. Lessons Learned - The knowledge gained from a project that can be applied to future projects.3. Project Handover - The transfer of the completed project deliverables to the client or end-user.4. Post-Project Evaluation - The review of the project's performance and outcomes to identify successes, failures, and areas for improvement.V. Project Management Tools and Techniques1. Gantt Chart - A bar chart that illustrates a project schedule.2. PERT Chart - A network diagram that represents the project activities and their dependencies.3. Risk Register - A document that lists identified risks, their potential impact, and the risk response strategies.4. Quality Assurance Plan - A document that outlines the quality management activities for the project.5. Communication Plan - A document that defines the communication requirements for the project.By familiarizing yourself with these project management English vocabulary terms, you will be better equipped to communicate effectively with colleagues, clients, and stakeholders, and to successfully manage projects in the global marketplace.。
日本综合超市的管理模式分析与启示--以永旺综合超市为例郑斌斌【摘要】Based on the investigation done in AEON in Japan,from the perspective of the Duality Princi-ple,the paper discovers that its management model is the integration of store decentralization and the gen-eral skills of talents.The system of personnel management consists of the emphasis of the on-spot experi-ence,the rotating system and the system of functional qualifications.This kind of management model can promote the development of the general skills of talents,improve the resilience of stores to the business en-vironment,and hence provides a reference to the management of Chinese general supermarkets.%以双对原理为视角，通过对日本永旺综合超市的实地调查，可以看出其管理模式为门店分权管理与人才综合技能互为补充，人事管理制度则由注重现场经验的积累、轮岗和职能资格制度等组成。
这种管理模式促进了人才综合技能的发展，提高了门店对商圈环境变化的应对能力，为中国综合超市管理提供借鉴。
【期刊名称】《河北北方学院学报（社会科学版）》【年(卷),期】2016(032)006【总页数】6页(P69-73,113)【关键词】双对原理;日本综合超市;永旺超市:管理模式【作者】郑斌斌【作者单位】莆田学院商学院，福建莆田 351100【正文语种】中文【中图分类】F272.3网络出版时间：2016-11-28 10:32:18综合超市(general merchandising store，GMS)是零售业的主力业态。
Hierarchical Mesh Decomposition using Fuzzy Clustering and CutsSagi Katz and Ayellet TalDepartment of Electrical EngineeringTechnion–Israel Institute of Technologysagikatz@techunix.technion.ac.il and ayellet@ee.technion.ac.ilAbstractCutting up a complex object into simpler sub-objects is a funda-mental problem in various disciplines.In image processing,imagesare segmented while in computational geometry,solid polyhedraare decomposed.In recent years,in computer graphics,polygonalmeshes are decomposed into sub-meshes.In this paper we proposea novel hierarchical mesh decomposition algorithm.Our algorithmcomputes a decomposition into the meaningful components of agiven mesh,which generally refers to segmentation at regions ofdeep concavities.The algorithm also avoids over-segmentation andjaggy boundaries between the components.Finally,we demonstratethe utility of the algorithm in control-skeleton extraction.Keywords:Mesh decomposition,mesh segmentation,control-skeleton extraction1IntroductionA hard problem might become easier if only the objects at handcould be cut up into smaller and easier to handle sub-objects.Incomputational geometry,solid convex decomposition has been ex-haustively investigated[Chazelle and Palios1994].Similarly,inimage processing,image segmentation has been considered a fun-damental problem,which is a necessary pre-processing step formany higher-level computer vision algorithms[Sharon et al.2000;Shi and Malik2000].The last few years have witnessed a growinginterest in mesh decomposition for computer graphics applications[Chazelle et al.1997;Gregory et al.1999;Mangan and Whitaker1999;Li et al.2001;Shlafman et al.2002].Mesh decomposition benefits many applications.In metamor-phosis[Gregory et al.1999;Zockler et al.2000;Shlafman et al.2002],mesh decomposition is used for establishing a correspon-pression[Karni and Gotsman2000]and simplifica-tion[Garland et al.2001;Zuckerberger et al.2002]use decom-position for improving their compression rate.In3D shape re-trieval,a decomposition graph serves as a non-rigid invariant signa-ture[Zuckerberger et al.2002].In collision detection,decomposi-tion facilitates the computation of bounding-volume hierarchies[Liet al.2001].In texture mapping,parameterization is applied to eachcomponent[Levy et al.2002].Other potential applications includemodification and modeling by parts.(a)object(b)skeleton(c)deformed skeleton(d)deformed objectFigure2:Deformation of a dino-petbeen on generating either meaningful components or components which comply with certain geometric properties.The boundaries between the components,however,were a by-product of the pro-cess.As a result,the boundaries were often too jagged[Chazelle et al.1997;Mangan and Whitaker1999;Shlafman et al.2002]or too straight[Li et al.2001]in a way that did not alwaysfit the model.The current algorithm aims at avoiding jagginess,by specif-ically handling the boundaries.Finally,the algorithm avoids over-segmentation and decomposes the objects into meaningful components.A meaningful component refers to a component which can be perceptually distinguished from the remaining object.The boundaries between the meaningful com-ponents pass at regions of deep concavities[Biederman1987],as illustrated in Figure1,where the dino-pet is decomposed into its organs.(Each component is colored differently.)To demonstrate the usefulness of the algorithm,we show that decomposition gives rise to an automatic,general(i.e.,meshes need neither be closed nor-manifolds),fast,and simple algorithm for extracting control-skeletons[Gagvani et al.1998;Teichmann andTeller1998;Bloomenthal and Lim1999;Wade and Parent2002]. Since skeleton extraction is done automatically,skeletal animations can be created by novice users(Figure2).The rest of this paper is structured as follows.Section2describes the problem and outlines our hierarchical decomposition algorithm. Section3discusses the details of the algorithm for the binary case, whereas Section4describes the extension to the-way case.Sec-tion5shows some results.Section6presents the control-skeleton extraction application.Finally,Section7concludes and discusses future directions.2OverviewThis section begins with a few notations and then provides an out-line of our algorithm.Let be an orientable mesh.It need neither be triangulated nor closed or a-manifold.(Non-manifold meshes might yield less expected results.)Definition2.1k-way Decomposition:is a k-way decomposition of(i),,(ii),is connected,(iii),and are face-wise disjoint and(iv).Definition2.2Binary Decomposition:is a binary decom-position of if it is a way decomposition with.Definition2.3Patch:Given,a k-way decomposi-tion of,each is called a patch of.The algorithm proceeds from coarse tofine.Each node in thehierarchy tree is associated with a mesh of a particular patch andthe root is associated with the whole input object.At each node,thealgorithm determines a suitable number of patches,and computes a-way decomposition of this node.If the input object consists of multiple connected components,the algorithm is applied to eachcomponent separately.The examples in this paper contain a singleconnected component,which is the more challenging case.A key idea of our algorithm is tofirstfind the meaningful compo-nents,while keeping the boundaries between the components fuzzy.Then,the algorithm focuses on the small fuzzy areas andfinds theexact boundaries which go along the features of the object.Tofind fuzzy components,we relax the condition that every faceshould belong to exactly one patch,and allow fuzzy membership.In essence,this is equivalent to assigning each face a probability ofbelonging to each patch.The algorithm consists of four stages:1.Assigning distances to all pairs of faces in the mesh.2.After computing an initial decomposition,assigning each facea probability of belonging to each patch.puting a fuzzy decomposition by refining the probabilityvalues using an iterative clustering scheme.4.Constructing the exact boundaries between the components,thus transforming the fuzzy decomposition into thefinal one.For instance,we wish to partition the objects in Figure3into twocomponents.After computing distances,each polygon is assigneda probability of belonging to the patches.In Figure3(a),a greenpolygon has a high probability of belonging to the back(or upper)patch.Conversely,a blue polygon has a high probability of belong-ing to the front(or lower)patch.The fuzzy decomposition is shownin Figure3(b),where the fuzzy region is drawn in red.Figure3(c)illustrates thefinal binary decomposition,after the exact boundariesare found.3Algorithm–the binary caseThis section describes each stage of the algorithm for the binarycase(i.e.,each node in the hierarchy is decomposed into two sub-meshes).An extension to the way case is presented in the next section.3.1Computing distancesThe probability that a face belongs to a certain patch depends on its distance from other faces in this patch.The underlying assumption(a)probabilities(b)fuzzy decomposition(c)decompositionFigure3:Binary decompositionis that distant faces,both in terms of their geodesic distance and of their angular distance,are less likely to belong to the same patch than faces which are close together.Given and,two adjacent faces and,the angle between their normals,we define their angular distance to bebe the average angular distance between these faces.Consider the dual graph of the mesh,where every face ofthe mesh is a vertex in this graph and two vertices are joined by anarc if and only if their corresponding faces are adjacent.The weightof the arc connecting the dual vertices of and is then definedas follows:(1)Thefirst term is affected by the geodesic distance whereas the sec-ond term is affected by the angular distance.Note that the latter is zero when the faces are coplanar.The denominator reduces effects that may appear for similar objects having different sampling rates. Given any pair of faces on the mesh and,their distanceis defined to be the shortest path between their dual vertices on the dual graph.The distances between all pairs of faces are calculated once,in a pre-processing step,using an all-pair shortest paths algorithm[Cormen et al.2001],where the distance between faces which belong to different connected components isdefined to be.3.2Initialization and assigning probabilitiesDuring an initialization phase,faces which are considered the rep-resentatives of the initial patches,are chosen.In the binary case,the initial pair of representatives and(representing patches and,respectively)is chosen such that the distance be-tween them is the largest possible.Our goal is to assign each face its probability of belonging to patch.Let and.We define(and equivalently)as follows:It can be easily verified that if a face is closer to patch than to,the probability of belonging to is larger than the probabil-ity of belonging to,and vice-versa.Moreover,a face which is equally distant from and from is as likely to belong to one as to the other.Finally,,,and for all other faces.3.3Generating a fuzzy decompositionOne way to obtain a decomposition is to apply a-means cluster-ing scheme[Duda and Hart1973]as done in[Shlafman et al.2002]. Our goal,however,is to construct a fuzzy decomposition,thus we use fuzzy clustering.Let be a face representing a patch and let be a face.The goal of our algorithm is to cluster the faces into patches by minimizing the following function(3)During an initialization phase,a subset of representatives, is chosen,as described above.Then,the algorithm iterates on the following steps.pute the probabilities of faces to belong to each patch,asdescribed in Equation2.2.Re-compute the set of representatives,minimizing thefunction in Equation3.3.If is different from,set and go back to1.Choosing the set of new representatives(i.e.,Step2)is done by using the following formulas:Next,if the probability of a face of belonging to a patch exceeds a certain value,it is assigned to the patch.There are,however,faces which are almost as likely to belong to one patch as to the other. In this case,the faces are considered fuzzy.In the binary case, the mesh is decomposed into three patches,and,where contains all the faces which are(almost)as likely to belong to as to.This is done by partitioning the faces as follows and is illustrated in Figure3(b)where is the red region.A practical problem which arises in this step is the dependence of the probability values on the specific representative of the patch. One way to overcome this problem is to re-define and using the average distances:and.Empirically,this definition improves the results and expedites convergence.(a)first level(b)second level(c)third levelFigure4:Hierarchical binary decompositions of a dove3.4Generating thefinal decompositionIn the previous stage the meaningful components were found butnot the exact boundary between them.The goal of the current stageis to construct this boundary within region.Once the boundary isdetermined,the faces of are assigned to either patch or patch.We formulate our problem as a graph partitioning problem.Con-sider the dual graph of the mesh and the set of the dualvertices of patches and,and respectively.Our goalis to partition into two subsets of vertices and,suchthat the disassociation between and is minimized.We areessentially looking for a constrained minimum cut in,requiringthat:is minimal.We denote the dual graph of by and the setof all vertices in whose corresponding faces in share an edgewith faces in by(resp.,).We now construct an undi-rectedflow network graph adding two new verticesand,as follows(Figure5).(4)Figure5:Theflow network graph,where is the red regionNext,the capacities of the arcs need to be defined.There aremany ways to define capacities within this framework.The keyprinciple is that the minimum cut tends to pass through arcs withsmall capacities.We experimented with various capacity functions,some which take only dihedral angles into account and others whichalso take arc length into account.We found the following functionto produce good results.For two vertices and,let bethe angle between the normals of their dual faces.The capacityis defined as follows(where the average factor handlesprecision problems):ifelse(5)A boundary between the components can now be found by ap-plying a maximumflow(minimum cut)algorithm from to(e.g.,[Cormen et al.2001][Goldberg and Tarjan1988]).By thedefinition of,the cut tends to pass through edges havinghighly concave dihedral angles.3.5Stopping conditionsEach node in the hierarchy is recursively decomposed until at leastone of the following conditions is met:(a)the distance between therepresentatives is smaller than a given threshold;(b)the differencebetween the maximal dihedral angle and the minimal dihedral angleis smaller than a threshold,so that patches having a fairly constantcurvature will not be decomposed;(c)the ratio between the averagedistance in the patch and that of the overall object does not exceeda threshold.Since the average distance captures both the size(i.e.,the geodesic distance)and the angular information,further decom-position is unnecessary when both are small relative to the originalobject.Figure4demonstrates results of a hierarchical binary decompo-sition.Note how the different organs are progressively extracted.4Algorithm–the k-way caseA way decomposition is a generalization of the binary case.There are,however,three issues which require explanation.Thefirst issue is the determination of the number of patches a node inthe hierarchy should be decomposed into.The second issue is theassignment of probabilities.The third issue is the extraction of thefuzzy area.We discuss these issues below.Unlike the binary case,in the way case,the representativesare chosen iteratively.Thefirst representative is assigned to be theface having the minimum sum of distances from all other faces.This is done in order to represent the main“body”of the object.Then,representatives are added,each in turn,so as to maximizetheir minimum distance from previously assigned representatives.The remaining question is how many representatives to add.Welook at the following function which is the minimum distance ofthe representative from previously assigned representatives:Obviously,this function decreases as we add more representatives.Empirical experiments show that after assigning representatives to(a)object (b)function(c)first derivative ofFigure 6:Determining the number of patchesall the major parts of an object,adding one more representative will cause a large decrease of .This observation aids in determining the number of components .We choose to be the value that maximizes the first derivative of .See Figure 6.The second issue is the assignment of probabilities.For a repre-sentative,the probability of belonging to its own patch is defined tobe .Otherwise,for a face ,the probabilityof belonging to patch is defined as:(a)first level(b)second level(c)third levelFigure8:Hierarchical k-way decompositions of a cheetah and an inner part of a human earcosts where is the size of the fuzzy region.5ResultsIn order to handle large models,we utilize the consistency in theway similar objects are decomposed.The procedure for decompos-ing large models consists of four stages.First,the model is sim-plified[Garland and Heckbert1997].Second,a decomposition iscomputed for the simplified model using our algorithm.Third,theboundaries found for the simplified model are used to define thefuzzy regions in the original model,by“projecting”the faces ad-jacent to the boundaries to the original model.This projection isperformed by assigning each face in the original model to the patchcontaining the closest face in the simplified model,where voxeliza-tion is used to further accelerate this step.Fourth,the minimum cutsare computed on these fuzzy regions(in the original model),whichare very small.In order to avoid erroneous projections,this pro-cess is performed progressively,using simplified models at varioussimplification levels.Figure9shows several objects at different levels of hierarchy asdecomposed by our algorithm,where for Figures9(e)-(f),a sim-plification was applied,as described above.The running times forthe objects described in this paper,on a,MHz,MbRAM PC,vary between second for the mechanical part andseconds for the dino-pet(faces,levels of hierarchy).Therunning times of decomposing Venus and the skeleton hand(Fig-ure9(e)-(f)),using simplification as described above,are sec-onds and seconds respectively(including loading,simplifica-tion and storing).Figure10demonstrates results of three algorithms:[Li et al.2001],[Shlafman et al.2002]and the algorithm described here.First,notice the boundaries between the back legs and the body.Only in Figure10(c),the“natural”ones were extracted.Second,the boundaries in Figure10(a)tend to be very straight due to spacesweeping utilized in the algorithm,whereas in Figure10(b)theboundaries are jaggy.In Figure10(c),the boundaries pass alongthe object’s features.Finally,since our algorithm is hierarchical,only the major organs were found,but not the smaller ones suchas thefingers and the toes.The latter would be extracted at afinerlevel of the hierarchy,as shown in Figure7.An alternative approach to ours is to use graph partitioning meth-ods on the whole model,rather than on constrained regions.Possi-ble cuts are minimal cuts.Their drawback is that they tend tofavor(a)alien–3999faces(b)camel–2674faces6patches14patches(c)mechanical part–1270faces(d)heart–1619faces7patches4patches(e)Venus–67,170faces(f)skeleton hand–654,666faces3patches6patchesFigure9:Decompositions of various objects(a)[Li et al](b)[Shlafman et al](c)Our algorithmFigure10:Comparison to[Li et al]and[Shlafman et al]small sets of isolated nodes since the weight of the cut increaseswith the number of edges[Wu and Leahy1993].Another option is to use normalized cuts[Shi and Malik2000],which is an NP-complete problem.We implemented an extensionof[Shi and Malik2000]to meshes,where the weight is defined totake into account both the geodesic distance and the angular dis-tance.The results varied.For some objects,good decompositionswere produced while for other objects,the meaningful componentswere not found or the boundaries between them were jagged orstep-wise.This can be explained by the fact that the cut approx-imation might cause artifacts.In addition,balancing the size of theparts need not alwaysfit the model.6Control Skeleton ExtractionControl skeletons are beneficial for various applications,includ-ing matching,retrieval,metamorphosis and computer animation.Previous algorithms are based on medial surface extraction[Gag-vani et al.1998;Teichmann and Teller1998;Bloomenthal and Lim1999;Wade and Parent2002],level set diagrams[Lazarus and Ver-roust1999]or Reeb Graphs[Shinagawa et al.1991].Mesh decom-position gives rise to a novel control-skeleton extraction algorithm,where the joints are calculated directly from the hierarchical struc-ture of the decomposition.The algorithm is general(i.e.,the modelsneed not be closed or2-manifolds),fully automatic,simple and fast.It is thus beneficial for applications requiring automation as well asfor novice users of applications where user-intervention is accept-able or desirable.Figure11demonstrates the use of skeletons foranimating otherwise static objects.The algorithm starts by decomposing the given model.It is es-sential that features which depend on the position of another featurebecome its descendants in the hierarchy.For instance,the elbowjoint of a humanoid object should be a descendant of the shoulderjoint,so that a shoulder motion will cause an elbow motion.A sim-ple way to achieve this is to guarantee that the decomposition ofevery node in the hierarchy consists of a central patch connected toall other patches.To force this star-shaped decomposition structure,the decompo-sition algorithm is slightly modified.We consider the central patchto be the one which contains thefirst assigned representative.Afterdecomposing a given patch,the algorithm verifies that the decom-position is star-shaped.If not,a patch which is not adjacent to thecentral patch is merged with a neighboring patch with which it hasthe smallest average angle between their normals along the cut.Once the hierarchical k-way decomposition is computed,the de-composition tree is traversed and a tree of joints is generated.Ateach level of the hierarchy,joints between the central patch and itsadjacent patches are created.Each joint is positioned at the centerof mass of the boundary between the patches.Each node in the treeof joints is associated with a list of faces.Initially,the root nodeis associated with the whole model.As the tree is traversed fromcoarse tofine,the relevant faces are transfered from a parent nodeto its children.In order to animate articulated objects,it is necessary to bindthe joints and pose of the object.Each vertex of the mesh is as-signed a weight indicating the extent to which it belongs to joint.The simplest approach is to let be the percentage of facesthat belong to joint and adjacent to vertex.This guaranteesthat an internal vertex is bound only to the patch it resides on,thateach vertex corresponds to at least one joint and that.More advanced methods take also the cut’s angles into account.Fi-nally,to pose the object,a skeleton-subspace deformation methodis used[Lewis et al.2000].Objects are deformed by adjusting the joints’angles of theirskeletons.To compute the modified vertex position we use the fol-lowing equation[Weber2000]:whereis the number of joints,is the original vector position of rel-ative to the coordinate system of joint,and is the transforma-tion matrix of joint.Thus,a vertex which belongs to a single jointhas a constant position relative to this joint,while a vertex whichbelongs to more than one joint is positioned between the locationsit would have,had it belonged entirely to each of the joints.7ConclusionWe have presented an algorithm for hierarchically decomposingmeshes.The algorithm avoids jaggy boundaries as well as over-segmentation.The key idea of the algorithm is tofirstfind themeaningful components of the mesh and only then focus on gen-erating the exact boundaries between the components.Tofind thecomponents,both geodesic distances and convexity are considered.Computing the boundaries is done by formulating the problem as aconstrained networkflow problem.We demonstrated the applica-bility of the algorithm for control skeleton extraction.Several enhancements can be added to our algorithm.For in-stance,different distance functions and different capacity functionscan be experimented with.Furthermore,non-geometric features,such as color and texture,can be embedded in the algorithm.Webelieve that the spectrum of applications which will benefit frommesh decomposition will further grow in the future.We are cur-rently looking at compression and texture mapping.AcknowledgmentsThis research was supported in part by the Israeli Ministry of Sci-ence,Culture&Sports,Grant01-01-01509.We are grateful toDaniel Aliaga,Tom Funkhouser,Idan Hadari,Itai David and theanonymous referees for their help.We thank Huang Zhiyong,Marcelo Kallmann and Ronen Basri for letting us use their images.ReferencesB IEDERMAN,I.1987.Recognition-by-components:A theory of humanimage understanding.Psychological Review94,115–147.B LOOMENTHAL,J.,AND L IM,C.1999.Skeletal methods of shape ma-nipulation.In International Conference on Shape Modeling and Appli-cations,44–49.C HAZELLE,B.,AND P ALIOS,L.1992.Decomposing the boundary of anonconvex polyhedron.In SWAT,364–375.C HAZELLE,B.,AND P ALIOS,L.1994.Decomposition algorithms ingeometry.In Algebraic Geometry and its Applications,Springer-Verlag,C.C.Bajaj,Ed.,Ed.,419–447.(a)object (b)skeleton (c)deformed skeleton (d)deformed objectFigure 11:Deformations of various objectsC HAZELLE ,B.,D OBKIN ,D.,S HOURHURA ,N.,AND T AL ,A.1997.Strategies for polyhedral surface decomposition:An experimental putational Geometry:Theory and Applications 7,4-5,327–342.C ORMEN ,T.,L EISERSON ,C.,R IVEST ,R.,ANDS TEIN ,C.2001.Intro-duction to Algorithms .McGraw-Hill.D UDA ,R.,AND H ART ,P.1973.Pattern Classification and Scene Analysis .New-York,Wiley.G AGVANI ,N.,K ENCHAMMANA -H OSEKOTE ,D.,AND S ILVER ,D.1998.V olume animation using the skeleton tree.In IEEE Symposium on Vol-ume Visualization ,47–53.G ARLAND ,M.,AND H ECKBERT ,P.1997.Surface simplification using quadric error metrics.In Proceedings of SIGGRAPH 1997,209–216.G ARLAND ,M.,W ILLMOTT ,A.,AND H ECKBERT ,P.2001.Hierarchical face clustering on polygonal surfaces.In Proceedings of ACM Sympo-sium on Interactive 3D Graphics ,49–58.G OLDBERG ,A.,AND T ARJAN ,R.1988.A new approach to the maximum flow problem.Journal of the ACM 35,4,921–940.G REGORY ,A.,S TATE ,A.,L IN ,M.,M ANOCHA ,D.,AND L IVINGSTON ,M.1999.Interactive surface decomposition for polyhedral morphing.The Visual Computer 15,453–470.K ARNI ,Z.,AND G OTSMAN ,C.2000.Spectral compression of mesh geometry.In Proceedings of SIGGRAPH 2000,ACM SIGGRAPH,279–286.L AZARUS ,F.,AND V ERROUST ,A.1999.Level set diagrams of polyhedral objects.In ACM Symposium on Solid Modeling and Applications ,130–140.L EVY ,B.,P ETITJEAN ,S.,R AY ,N.,AND M AILLOT ,J.2002.Least squares conformal maps for automatic texture atlas generation.In Pro-ceedings of SIGGRAPH 2002,ACM SIGGRAPH,362–371.L EWIS ,J.,C ORDNER ,M.,ANDF ONG ,N.2000.Pose space deformations:A unified approach to shape.In Proceedings of SIGGRAPH 2000,ACM SIGGRAPH,165–172.L I ,X.,T OON ,T.,T AN ,T.,AND H UANG ,Z.2001.Decomposing polygon meshes for interactive applications.In Proceedings of the 2001sympo-sium on Interactive 3D graphics ,35–42.M ANGAN ,A.,AND W HITAKER ,R.1999.Partitioning 3D surface meshes using watershed segmentation.IEEE Transactions on Visualization and Computer Graphics 5,4,308–321.S HARON ,E.,B RANDT ,A.,AND B ASRI ,R.2000.Fast multiscale image segmentation.In Proceedings IEEE Conference on Computer Vision and Pattern Recognition ,70–77.S HI ,J.,AND M ALIK ,J.2000.Normalized cuts and image segmentation.IEEE Transactions on Pattern Analysis and Machine Intelligence 22,8,888–905.S HINAGAWA ,Y.,K UNII ,T.,AND K ERGOSIEN ,Y.1991.Surface coding based on morse theory.IEEE Computer Graphics and Applications 11,5,66–78.S HLAFMAN ,S.,T AL ,A.,AND K ATZ ,S.2002.Metamorphosis of poly-hedral surfaces using decomposition.In Eurographics 2002,219–228.T EICHMANN ,M.,AND T ELLER ,S.1998.Assisted articulation of closed polygonal models.In Conference abstracts and applications:SIG-GRAPH ,ACM SIGGRAPH,14–21.W ADE ,L.,AND P ARENT ,R.2002.Automated generation of control skele-tons for use in animation.The Visual Computer 18,2,97–110.W EBER ,J.2000.Run–Time Skin Deformation .Intel Architecture Labs,.W U ,Z.,AND L EAHY ,R.1993.An optinal graph theoretic approach to data clustering:Theory and its application to image segmentation.PAMI 11,1101–1113.Z OCKLER ,M.,S TALLING ,D.,AND H EGE ,H.-C.2000.Fast and intuitive generation of geometric shape transitions.The Visual Computer 16,5,241–253.Z UCKERBERGER ,E.,T AL ,A.,AND S HLAFMAN ,S.2002.Polyhedral surface decomposition with puters &Graphics 26,5,733–743.。
