Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

A method for objective edge detection evaluation and detector parameter selection

Abstract: Subjective evaluation by human observers is usually used to analyze and select an edge detector parametric setup when real-world images are considered. We propose a statistical objective performance analysis and detector parameter selection, using detection results produced by different detector parameters. Using the correspondence between the different detection results, an estimated best edge map, utilized as an estimated ground truth (EGT), is obtained. This is done using both a receiver operating characteristics (ROC) analysis and a Chi-square test, and considers the trade off between information and noisiness in the detection results. The best edge detector parameter set (PS) is then selected by the same statistical approach, using the EGT. Results are demonstrated for several edge detection techniques, and compared to published subjective evaluation results. The method developed here suggests a general tool to assist in practical implementations of parametric edge detectors where an automatic process is required.

Parametric motion graphs

Abstract: In this paper, we present an example-based motion synthesis technique that generates continuous streams of high-fidelity, controllable motion for interactive applications, such as video games. Our method uses a new data structure called a parametric motion graph to describe valid ways of generating linear blend transitions between motion clips dynamically generated through parametric synthesis in realtime. Our system specifically uses blending-based parametric synthesis to accurately generate any motion clip from an entire space of motions by blending together examples from that space. The key to our technique is using sampling methods to identify and represent good transitions between these spaces of motion parameterized by a continuously valued parameter. This approach allows parametric motion graphs to be constructed with little user effort. Because parametric motion graphs organize all motions of a particular type, such as reaching to different locations on a shelf, using a single, parameterized graph node, they are highly structured, facilitating fast decision-making for interactive character control. We have successfully created interactive characters that perform sequences of requested actions, such as cartwheeling or punching.

Robustness analysis of nonlinear feedback systems: an input-output approach

Abstract: This paper presents an approach to robustness analysis for nonlinear feedback systems. We pursue a notion of model uncertainty based on the closeness of input-output trajectories which is not tied to a particular uncertainty representation, such as additive, parametric, structured, etc. The basic viewpoint is to regard systems as operators on signal spaces. We present two versions of a global theory where stability is captured by induced norms or by gain functions. We also develop local approaches (over bounded signal sets) and give a treatment for systems with potential for finite-time escape. We compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations, e.g., small-time delays. We also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations. The paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection.

Parametric Model Order Reduction by Matrix Interpolation

Abstract: In this paper, a new framework for model order reduction of LTI parametric systems is introduced. After generating and reducing several local original models in the parameter space, a parametric reduced-order model is calculated by interpolating the system matrices of the local reduced models. The main task is to find compatible system representations with optimal interpolation properties. Two approaches for this purpose are presented together with several numerical simulations.