Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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TL;DR: This work proposes a fast splitting approach to the classical variational formulation of the image partitioning problem, which is frequently referred to as the Potts or piecewise constant Mumford--Shah model, and produces results of a quality comparable with that of graph cuts and the convex relaxation strategies.
Abstract: We propose a fast splitting approach to the classical variational formulation of the image partitioning problem, which is frequently referred to as the Potts or piecewise constant Mumford--Shah model. For vector-valued images, our approach is significantly faster than the methods based on graph cuts and convex relaxations of the Potts model which are presently the state-of-the-art. The computational costs of our algorithm only grow linearly with the dimension of the data space which contrasts the exponential growth of the state-of-the-art methods. This allows us to process images with high-dimensional codomains such as multispectral images. Our approach produces results of a quality comparable with that of graph cuts and the convex relaxation strategies, and we do not need an a priori discretization of the label space. Furthermore, the number of partitions has almost no influence on the computational costs, which makes our algorithm also suitable for the reconstruction of piecewise constant (color or vect...
84 citations
TL;DR: In this paper, a piecewise continuous Ljapunov function is used for stability in systems of ordinary differential equations with impulse effect. But the approach presented is based on the specially introduced piecewise continuously LjAPunov functions.
84 citations
TL;DR: For the hyperelastic-viscoplastic large deformation problems considered here with varying levels of randomness in the input and boundary conditions, the NISG method provides highly accurate estimates of the statistical quantities of interest within a fraction of the time required using existing Monte Carlo methods.
84 citations
TL;DR: In this paper, the authors proposed the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure, using wavelets to estimate the number and locations of changepoints consistently as well as identifying whether they originate in the common or idiosyncratic components.
84 citations
TL;DR: In this article, the initial-boundary value problem for linearized gravitational theory in harmonic coordinates is investigated, and the results are used to formulate computational algorithms for Cauchy evolution in 3D bounded domains.
Abstract: We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a set of six wave equations. The results are used to formulate computational algorithms for Cauchy evolution in a 3-dimensional bounded domain. Numerical codes based upon these algorithms are shown to satisfy tests of robust stability for random constraint violating initial data and random boundary data; and shown to give excellent performance for the evolution of typical physical data. The results are obtained for plane boundaries as well as piecewise cubic spherical boundaries cut out of a Cartesian grid.
84 citations