A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two‐dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real‐valued barycentric coordinates, when applied to planar domains. We show how the construction for generating real‐valued barycentric coordinates from a given weight function can be applied to generating complex‐valued coordinates, thus deriving complex expressions for the classical barycentric coordinates: Wachspress, mean value, and discrete harmonic. Furthermore, we show that a complex barycentric map admits the intuitive interpretation as a complex‐weighted combination of edge‐to‐edge similarity transformations, allowing the design of “home‐made” barycentric maps with desirable properties. Thus, using the tools of complex analysis, we provide a methodology for analyzing existing barycentric mappings, as well as designing new ones.     

Discovery of Intrinsic Primitives on Triangle Meshes

The discovery of meaningful parts of a shape is required for many geometry processing applications, such as parameterization, shape correspondence, and animation. It is natural to consider primitives such as spheres, cylinders and cones as the building blocks of shapes, and thus to discover parts by fitting such primitives to a given surface. This approach, however, will break down if primitive parts have undergone almost‐isometric deformations, as is the case, for example, for articulated human models. We suggest that parts can be discovered instead by finding intrinsic primitives, which we define as parts that posses an approximate intrinsic symmetry. We employ the recently‐developed method of computing discrete approximate Killing vector fields (AKVFs) to discover intrinsic primitives by investigating the relationship between the AKVFs of a composite object and the AKVFs of its parts. We show how to leverage this relationship with a standard clustering method to extract k intrinsic primitives and remaining asymmetric parts of a shape for a given k. We demonstrate the value of this approach for identifying the prominent symmetry generators of the parts of a given shape. Additionally, we show how our method can be modified slightly to segment an entire surface without marking asymmetric connecting regions and compare this approach to state‐of‐the‐art methods using the Princeton Segmentation Benchmark.     

基于C8051F410单片机的钨灯电源设计

针对光谱测试系统对光源稳定性越来越高的要求,介绍了一种以单片机为核心的高稳定性的钨灯电源系统.它以C8051F410单片机为核心,采用增量式PID控制算法,通过控制单片机的D/A输出来调整MOS场效应管的导通情况,从而达到稳定钨灯工作电流的目的,保证钨灯的发光稳定.通过实验验证,新设计的电源具有控制精度高、稳定性好、性能可靠等优点,可应用于光谱测试系统中.     

Solvability conditions and solutions to perfect regulation problem under measurement output feedback

The problem of perfect regulation is to design a family of control laws for a given plant such that the resulting overall closed-loop system is internally stable and its controlled output can be reduced to zero arbitrarily fast from any initial condition. Such a problem was heavily studied by many researchers in the 1970s and early 1980s. However, to the best of our knowledge, all of the earlier results deal only with the problem under full state feedback. In this paper, we solve the long-standing problem of perfect regulation via measurement output feedback for general linear time-invariant multivariable systems. In particular, we derive necessary and sufficient conditions under which the problem of perfect regulation via measurement output feedback is solvable for general systems, and, under these conditions, construct two families of feedback laws, one of full order and the other reduced order, that solve the problem.     

Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics

This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local and nonlocal quantities. UDP characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, locality preserving projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposed method is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDA when the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications     

Learning to transform time series with a few examples

We describe a semi-supervised regression algorithm that learns to transform one time series into another time series given examples of the transformation. This algorithm is applied to tracking, where a time series of observations from sensors is transformed to a time series describing the pose of a target. Instead of defining and implementing such transformations for each tracking task separately, our algorithm learns a memoryless transformation of time series from a few example input-output mappings. The algorithm searches for a smooth function that fits the training examples and, when applied to the input time series, produces a time series that evolves according to assumed dynamics. The learning procedure is fast and lends itself to a closed-form solution. It is closely related to nonlinear system identification and manifold learning techniques. We demonstrate our algorithm on the tasks of tracking RFID tags from signal strength measurements, recovering the pose of rigid objects, deformable bodies, and articulated bodies from video sequences. For these tasks, this algorithm requires significantly fewer examples compared to fully-supervised regression algorithms or semi-supervised learning algorithms that do not take the dynamics of the output time series into account.     

Network visualization by semantic substrates

Networks have remained a challenge for information visualization designers because of the complex issues of node and link layout coupled with the rich set of tasks that users present. This paper offers a strategy based on two principles: (1) layouts are based on user-defined semantic substrates, which are non-overlapping regions in which node placement is based on node attributes, (2) users interactively adjust sliders to control link visibility to limit clutter and thus ensure comprehensibility of source and destination. Scalability is further facilitated by user control of which nodes are visible. We illustrate our semantic substrates approach as implemented in NVSS 1.0 with legal precedent data for up to 1122 court cases in three regions with 7645 legal citations     

Balancing systematic and flexible exploration of social networks

Social network analysis (SNA) has emerged as a powerful method for understanding the importance of relationships in networks. However, interactive exploration of networks is currently challenging because: (1) it is difficult to find patterns and comprehend the structure of networks with many nodes and links, and (2) current systems are often a medley of statistical methods and overwhelming visual output which leaves many analysts uncertain about how to explore in an orderly manner. This results in exploration that is largely opportunistic. Our contributions are techniques to help structural analysts understand social networks more effectively. We present SocialAction, a system that uses attribute ranking and coordinated views to help users systematically examine numerous SNA measures. Users can (1) flexibly iterate through visualizations of measures to gain an overview, filter nodes, and find outliers, (2) aggregate networks using link structure, find cohesive subgroups, and focus on communities of interest, and (3) untangle networks by viewing different link types separately, or find patterns across different link types using a matrix overview. For each operation, a stable node layout is maintained in the network visualization so users can make comparisons. SocialAction offers analysts a strategy beyond opportunism, as it provides systematic, yet flexible, techniques for exploring social networks     

High-automation proofs for properties of requirements models

We describe an approach and experimental results in the application of mechanized theorem proving to software requirements analysis. Serving as the test article was the embedded controller for SAFER, a backpack propulsion system used as a rescue device by NASA astronauts. SAFER requirements were previously formalized using the prototype verification system (PVS) during a NASA pilot project in formal methods, details of which appear in a NASA guidebook. This paper focuses on the formulation and proof of properties for the SAFER requirements model. To test the prospects for deductive requirements analysis, we used the PVS theorem prover to explore the upper limits of proof automation. A set of property classes was identified, with matching proof schemes later devised. After developing several PVS proof strategies (essentially prover macros), we obtained fully automatic proofs of 42 model properties. These results demonstrate how customized prover strategies can be used to automate moderate-complexity theorem proving for state machine models.