Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.

Modeling and parameter identification of systems with multisegment piecewise-linear characteristics

Abstract: This paper deals with the modeling and parameter identification of nonlinear systems having multi-segment piecewise-linear characteristics. The decomposition of the corresponding mapping provides a new form of multi-segment nonlinearity representation, leading to an output equation where all the parameters to be estimated are separated. Hence, an iterative method with internal variable estimation can be applied for parameter identification using input/output data records. The only required a-priori knowledge of the nonlinear characteristic represents the limits for the domain partition. The proposed model of given static nonlinearity is also incorporated into the Hammerstein model. Examples of parameter identification for static and dynamic systems with multi-segment piecewise-linear characteristics are presented.

Bayesian image reconstruction in SPECT using higher order mechanical models as priors

Abstract: While the ML-EM algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem. Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, the authors propose an extension to a piecewise linear model-the weak plate-which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for the authors' application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, the authors model the prior as a Gibbs distribution and use a GEM formulation for the optimization. They compare quantitative performance of the ML-EM algorithm, a GEM algorithm with a prior favoring piecewise constant regions, and a GEM algorithm with their weak plate prior. Pointwise and regional bias and variance of ensemble image reconstructions are used as indications of image quality. The authors' results show that the weak plate and membrane priors exhibit improved bias and variance relative to ML-EM techniques.

Interactive 3D distance field computation using linear factorization

Abstract: We present an interactive algorithm to compute discretized 3D Euclidean distance fields. Given a set of piecewise linear geometric primitives, our algorithm computes the distance field for each slice of a uniform spatial grid. We express the non-linear distance function of each primitive as a dot product of linear factors. The linear terms are efficiently computed using texture mapping hardware. We also improve the performance by using culling techniques that reduce the number of distance function evaluations using bounds on Voronoi regions of the primitives. Our algorithm involves no preprocessing and is able to handle complex deforming models at interactive rates. We have implemented our algorithm on a PC with NVIDIA GeForce 7800 GPU and applied it to models composed of thousands of triangles. We demonstrate its application to medial axis approximation and proximity computations between rigid and deformable models. In practice, our algorithm is more accurate and almost one order of magnitude faster as compared to previous distance computation algorithms that use graphics hardware.

A New Piecewise Linear Hyperchaotic Circuit

Abstract: When the polarity information in diffusionless Lorenz equations is preserved or removed, a new piecewise linear hyperchaotic system results with only signum and absolute-value nonlinearities. Dynamical equations have seven terms without any quadratic or higher order polynomials and, to our knowledge, are the simplest hyperchaotic system. Therefore, a relatively simple hyperchaotic circuit using diodes is constructed. The circuit re- quires no multipliers or inductors, as are present in other hyper- chaotic circuits, and it has not been previously reported.