This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations. The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state with operations in the tropical algebra. The abstract model is a finite-state transition system: we show that the abstract states can be generated by operations on the tropical algebra, and that the generation of transitions can be established by tropical multiplications of matrices. The complexity of the algorithms based on tropical algebra is discussed and their performance is tested on a numerical benchmark against an existing alternative abstraction approach.
The computation of image and of inverse image of a DBM is described in @cite_7 . These computations are used to perform forward and backward reachability analysis, respectively. The worst-case complexity of both procedures is @math , where @math is the number of variables in @math excluding @math . A more detailed explanation about image and inverse image computation of a DBM is in Section 3.3.
@cite_7
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Many database management systems support whole-image matching. However, users may only remember certain subregions of the images. In this paper, we develop Padding and Reduction Algorithms to support subimage queries of arbitrary size based on local color information. The idea is to estimate the best- case lower bound to the dissimilarity measure between the query and the image. By making use of multiresolution representation, this lower bound becomes tighter as the scale becomes finer. Because image contents are usually pre- extracted and stored, a key issue is how to determine the number of levels used in the representation. We address this issue analytically by estimating the CPU and I O costs, and experimentally by comparing the performance and accuracy of the outcomes of various filtering schemes. Our findings suggest that a 3-level hierarchy is preferred. We also study three strategies for searching multiple resolutions. Our studies indicate that the hybrid strategy with horizontal filtering on the coarse level and vertical filtering on remaining levels is the best choice when using Padding and Reduction Algorithms in the preferred 3-level multiresolution representation. The best 10 desired images can be retrieved efficiently and effectively from a collection of a thousand images in about 3.5 seconds.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.