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: Fast-Match is a fast algorithm for approximate template matching under 2D affine transformations that minimizes the Sum-of-Absolute-Differences (SAD) error measure and it is proved that they can be sampled using a density that depends on the smoothness of the image.
Abstract: Fast-Match is a fast algorithm for approximate template matching under 2D affine transformations that minimizes the Sum-of-Absolute-Differences (SAD) error measure. There is a huge number of transformations to consider but we prove that they can be sampled using a density that depends on the smoothness of the image. For each potential transformation, we approximate the SAD error using a sublinear algorithm that randomly examines only a small number of pixels. We further accelerate the algorithm using a branch-and-bound-like scheme. As images are known to be piecewise smooth, the result is a practical affine template matching algorithm with approximation guarantees, that takes a few seconds to run on a standard machine. We perform several experiments on three different datasets, and report very good results.
90 citations
TL;DR: In this paper, it was shown that an exponential tridiagonal difference scheme, when applied with a uniform mesh of size h to: euXx + b(x)ux = f(x), for O O, b and f smooth, e in (0, 1], and u(O) and u (I) given, is uniformly second-order accurate (i.e., the maximum of the errors at the grid points is bounded by Ch 2 with the constant C independent of h and e).
Abstract: It will be proven that an exponential tridiagonal difference scheme, when applied with a uniform mesh of size h to: euXx + b(x)ux = f(x) for O O, b and f smooth, e in (0, 1], and u(O) and u(I) given, is uniformly second-order accurate (i.e., the maximum of the errors at the grid points is bounded by Ch2 with the constant C independent of h and e). This scheme was derived by El-Mistikawy and Werle by a C' patching of a pair of piecewise constant coefficient approximate differential equations across a common grid point. The behavior of the approximate solution in between the grid points will be analyzed, and some numerical results will also be given.
90 citations
TL;DR: A novel level set method for complex image segmentation, where the local statistical analysis and global similarity measurement are both incorporated into the construction of energy functional to avoid the time-consuming re-initialization step.
90 citations
TL;DR: In this article, the authors deal with two key problems for delta (or singular) shock solutions to systems of conservation laws: their entropy admissibility conditions (which is connected to the notorious uniqueness problem) and their interaction.
Abstract: This paper deals with two key problems for delta (or singular) shock solutions to systems of conservation laws: that of their entropy admissibility conditions (which is connected to the notorious uniqueness problem) and that of their interaction. We choose to represent systems of conservation laws by nets of functions which are piecewise constant (or constant with respect only to the space variable), here called shadow waves. All the calculations can then be done on each element of such nets using only the usual Rankine–Hugoniot conditions. A 3 × 3 pressureless gas dynamics model is the main example in the paper.
90 citations
TL;DR: This paper addresses the problem of delay-dependent robust and reliable static output feedback (SOF) control for a class of uncertain discrete-time Takagi–Sugeno fuzzy-affine systems with time-varying delay and actuator faults in a singular system framework.
Abstract: This paper addresses the problem of delay-dependent robust and reliable $\mathscr {H}_{\infty }$ static output feedback (SOF) control for a class of uncertain discrete-time Takagi–Sugeno fuzzy-affine (FA) systems with time-varying delay and actuator faults in a singular system framework. The Markov chain is employed to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular FA system. By constructing a piecewise-Markovian Lyapunov–Krasovskii functional, a new $\mathscr {H}_{\infty }$ performance analysis criterion is then presented, where a novel summation inequality and S-procedure are succeedingly employed. Subsequently, thanks to the special structure of the singular system formulation, the piecewise-affine SOF controller design is proposed via a convex program. Lastly, illustrative examples are given to show the efficacy and less conservatism of the presented approach.
89 citations