10647129
A new zero-crossing-based discontinuity detector
General zero-crossing-based discontinuity detectors in two dimensions, which include Marr-Hildreth (1980), residual, difference of Gaussians, and other detectors as special cases, are discussed. Mathematical justification for this class of detectors is presented. An optimal detector that maximizes the signal-to-noise ratio is derived. Preliminary experimental results for real images are reported.
38528864
Coping With Discontinuities In Computer Vision: Their Detection, Classification, And Measurement
206418940
Residual Analysis for Feature Detection
It is shown that in a very simple form residual analysis achieves results that are at least as good as if not better than those obtained by other techniques. There are many ways for extensions of the method. For example, moving average filters of regularization can be used to obtain the residual images. Also, the strength of the correlation, measured by D/sub rr/(O), can be used to eliminate noise, weak edges, etc. A more ambitious extension is by considering smoothing filters that leave invariant the function representing the reflectance from smooth surfaces. >
206832588
Optimization problems from feature testing of communication protocols
In feature testing of communication protocols, we want to construct a minimal number of tests with a desirable fault coverage. We model the protocols by extended finite state machines and reduce the test generation process to optimization problems on graphs. We study efficient algorithms and their complexity. We report experimental results on real systems, including Personal HandyPhone System, a 5ESS based ISDN wireless system, and 5ESS Intelligent Network Application Protocol.
45853491
Testing Finite-State Machines: State Identification and Verification
We study the complexity of two fundamental problems in the testing of finite-state machines. 1) Distinguishing sequences (state identification). We show that it is PSPACE-complete to determine whether a finite-state machine has a preset distinguishing sequence. There are machines that have distinguishing sequences, but only of exponential length. We give a polynomial time algorithm that determines whether a finite-state machine has an adaptive distinguishing sequence. (The previous classical algorithms take exponential time.) Furthermore, if there is an adaptive distinguishing sequence, then we give an efficient algorithm that constructs such a sequence of length at most n(n/spl minus/1)/2 (which is the best possible), where n is the number of states. 2) Unique input output sequences (state verification). It is PSPACE-complete to determine whether a state of a machine has a unique input output sequence. There are machines whose states have unique input output sequences but only of exponential length. >
11856887
Approximation of linear functionals on a banach space with a Gaussian measure
Abstract We study approximation of linear functionals on separable Banach spaces equipped with a Gaussian measure. We study optimal information and optimal algorithms in average case, probabilistic, and asymptotic settings, for a general error criterion. We prove that adaptive information is not more powerful than nonadaptive information and that μ-spline algorithms, which are linear, are optimal in all three settings. Some of these results hold for approximation of linear operators. We specialize our results to the space of functions with continuous r th derivatives, equipped with a Wiener measure. In particular, we show that the natural splines of degree 2 r + I yield the optimal algorithms. We apply the general results to the problem of integration.
12888903
Steiner Problems on Directed Acyclic Graphs
Two variations of the minimum-cost Steiner problem on a directed acyclic graph with non-negative weights edges are studied.
13517188
Computational geometry
Computational geometry [Edelsbrunner 1987; Preparata and Shamos 1985] evolves from the classical discipline of design and analysis of algorithms. It is concerned with the computational complexity of geometric problems that arise in various disciplines such as pattern recognition, computer graphics, computer vision, robotics, VLSI layout, operations research, statistics, and so on. In contrast with the classical approach to proving mathematical theorems about geometry-related problems, this discipline emphasizes the computational aspect of these problems and attempts to exploit the underlying geometric properties possible, for example, the metric space, to derive efficient algorithmic solutions. An objective of this discipline in the theoretical context is to study the intrinsic difficulty of geometric computation under a certain computation model and to devise provably efficient algorithms for the problems at hand. The measure of intrinsic difficulty of a geometric problem or efficiency of an algorithm is in terms of time and space complexities when the problem size tends to `. This is the so-called asymptotic computational complexity. Traditionally there are two types of complexity analysis of the asymptotic behavior of an algorithm: worst-case analysis and average-case analysis. In the former, the behavior of the algorithm with respect to the worst possible case of the input instance is considered, whereas in the latter, the expected behavior is considered when the input is randomly drawn from a given distribution. Recently the notion of randomized algorithms has emerged as an important area of study within algorithm design and analysis. Similar to average-case analysis, the analysis of randomized algorithms is also probabilistic with the exception that in the latter the input instance is fixed whereas the steps taken by the algorithm are random and governed by the outcomes of some probabilistic event, for example, the toss of a coin. Due to its applications to various science and engineering related disciplines, researchers in computational geometry have begun to address the efficacy of the algorithms; the issues concerning robustness and numerical stability [Fortune 1993] and the actual running times of their implementations have now become centers of attention as well. We concentrate here on the theoretical development of this field in the context of sequential computation. We adopt the real RAM (random-access machine) model of computation in which all arithmetic operations, comparisons, kth-root, exponential, or logarithmic functions take unit time. For more details refer to [Preparata and Shamos 1985]. Those who are interested in the implementations or would like more information about available software may consult the Proceedings of the Annual ACM Symposium on Computational Geometry, which has a video session, or the WWW page on Geometry in Action
17000976
A Faster One-Dimensional Topological Compaction Algorithm
We consider the problem of one-dimensional topological compaction with jog insertions. Combining both geometric and graph theoretic approaches we present a faster and simpler algorithm, improving over previous results. The compaction algorithm takes as input a sketch consisting of a set F of features and a set W of wires, and minimizes the horizontal width of the sketch while maintaining its routability. The algorithm consists of the following steps: constructing a horizontal constraint graph, computing all possible jog positions, computing the critical path, relocating the features and reconstructing a new sketch homotopic to the input sketch suitable for detailed routing. The algorithm runs in O(|F| · |W|) worst-case time and space, which is asymptotically optimal in the worst case. Experimental results are also presented.
15096399
A Faster One-Dimensional Topological Compaction Algorithm with Jog Insertion
Abstract. We consider the problem of one-dimensional topological compaction with jog insertions. By combining both geometric and graph-theoretic approaches we present a faster and simpler algorithm to improve over previous results. The compaction algorithm takes as input a sketch consisting of a set F of features and a set W of wires, and minimizes the horizontal width of the sketch while maintaining its routability. The algorithm consists of the following steps: constructing a horizontal constraint graph, computing all possible jog positions, computing the critical path, relocating the features, and reconstructing a new sketch homotopic to the input sketch, which is suitable for detailed routing. The algorithm runs in O(|F| ⋅ |W|) worst-case time and space, which is asymptotically optimal in the worst case. Experimental results are also presented.
15924002
On the Effectiveness of Relevance Profiling
Relevance profiling is a general process for withindocument retrieval. Given a query, a profile of retrieval status values is computed by sliding a fixed sized window across a document. In this paper, we report a series of bench experiments on relevance profiling, using an existing electronic book, and its associated book index. The book index is the source of queries and relevance judgements for the experiments. Three weighting functions based on a language modelling approach are investigated, and we demonstrate that the well-known query generation model outperforms one based on the Kullback-Leibler divergence, and one based on simple term frequency. The relevance profiling process proved highly effective in retrieving relevant pages within the electronic book, and exhibits stable performance over a range of sliding window sizes. The experimental study provides evidence for the effectiveness of relevance profiling for within-document retrieval, with the caveat that the experiment was conducted with a particular electronic book.