We describe a semi-automated approach for designing morphological operators to detect image structures. We automatically combine morphological primitives from a pool to generate an enumerable family of complex morphological operators spanning a receiver operating curve (ROC). Domain knowledge can be encoded by biasing the pool with primitives; the system subsequently automatically selects and combines operators based on the joint statistics of training data. The major advantages are that the designer can focus on constructing simple operators, yet is able to rapidly combine them to yield more powerful, system-specific solutions, whose operating point can easily be changed. We illustrate the approach using birth and death processes and associated operators. Examples of video text detection are presented.

We p r e s e n t DEADLINER, a search engine that catalogs conference and workshop announcements, and ultimately will monitor and extract a wide range of academic convocation material from the web.The system currently extracts speakers, locations, dates, paper submission (and other) deadlines, topics, program committees, abstracts, and aÆliations.A user or user agent can perform detailed searches on these elds.DEADLINER was constructed using a methodology for rapid implementation of specialized search engines.This methodology avoids complex hand-tuned text extraction solutions, or natural language processing, by B a yesian integration of simple extractors that exploit loose formatting and keyw ord con ventions.The Bayesian framework further produces a search engine where each user can control the false alarm rate on a eld in an intuitive y et rigorous fashion.

We analyze the persistence of information on the web, looking at the percentage of invalid URLs contained in academic articles within the CiteSeer (ResearchIndex) database.The number of URLs contained in the papers has increased from an average of 0.06 in 1993 to 1.6 in 1999.We found that a significant percentage of URLs are now invalid, ranging from 23% for 1999 articles, to 53% for 1994.We also found that for almost all of the invalid URLs, it was possible to locate the information (or highly related information) in an alternate location, primarily with the use of search engines.However, the ability to relocate missing information varied according to search experience and effort expended.Citation practices suggest that more information may be lost in the future unless these practices are improved.We discuss persistent URL standards and their usage, and give recommendations for citing URLs in research articles as well as for finding the new location of invalid URLs.

Background modeling is a common component in video surveillance systems and is used to quickly identify regions of interest. To increase the robustness of background subtraction techniques, researchers have developed techniques to update the background model and also developed probabilistic/statistical approaches for thresholding the difference. This paper presents an error analysis of this type of background modeling and pixel labeling, providing both theoretical analysis and experimental validation. Evaluation is centered around the tradeoff of probability of false alarm and probability of miss detection, and this paper shows how to efficiently compute these probabilities front simpler values that are more easily measured. It includes an analysis for both static and dynamic background modeling. The paper also examines the assumptions of Gaussian and mixture of Gaussian models for a pixel.

In this paper we formulate a homotopy approach for solving for the weights of a network by smoothly transforming a linear single layer network into a nonlinear perceptron network. While other researchers have reported potentially useful numerical results based on heuristics related to this approach, the work presented here provides the first rigorous exposition of the deformation process. Results include a complete description of how the weights relate to the data space, a proof of the global convergence and validity of the method, and a rigorous formulation of the generalized orthogonality theorem to provide a geometric perspective of the solution process. This geometric interpretation clarifies conditions resulting in the appearance of local minima and infinite weights in network optimization procedures, and the similarities of and differences between optimizing the weights in a nonlinear network and optimizing the weights in a linear network. The results provide a strong theoretical foundation for quantifying performance bounds on finite neural networks and for constructing globally convergent optimization approaches on finite data sets.

In this paper the geometric formulation of the single layer perceptron weight optimization problem previously described by Coetzee et al. (1993, 1996) is combined with results from other researchers on nonconvex set projections to describe sufficient conditions for uniqueness of weight solutions. It is shown that the perceptron data surface is pseudoconvex and has infinite folding, allowing for the specification of a region of desired vectors having unique projections purely in terms of the local curvature of the data surface. No information is therefore required regarding the global curvature or size of the data surface. These results in principle allow for a posteriori evaluation of whether a weight solution is unique or globally optimal, and for a priori scaling of desired vector values to ensure uniqueness, through analysis of the input data. The practical applicability of these results from a numerical perspective is evaluated on some carefully chosen examples.

Homotopy methods have achieved significant success in solving systems of nonlinear equations for which the number of solutions are known and the homotopy paths are bounded. We present a two-stage homotopy process which does not require a-priori knowledge of the number of solutions to a system of nonlinear equations. This approach makes use of compact manifolds to find solutions sequentially along disconnected homotopy paths. The procedure is tested on two standard optimization and neural network benchmark problems.

In this paper the topological and geometric properties of the weight solutions for multilayer perceptron (MLP) networks under the MSE error criterion are characterized. The characterization is obtained by analyzing a homotopy from linear to nonlinear networks in which the hidden node function is slowly transformed from a linear to the final sigmoidal nonlinearity. Two different geometric perspectives for this optimization process are developed. The generic topology of the nonlinear MLP weight solutions is described and related to the geometric interpretations, error surfaces, and homotopy paths, both analytically and using carefully constructed examples. These results illustrate that although the natural homotopy provides a practically valuable heuristic for training, it suffers from a number of theoretical and practical difficulties. The linear system is a bifurcation point of the homotopy equations, and solution paths are therefore generically discontinuous. Bifurcations and infinite solutions further occur for data sets that are not of measure zero. These results weaken the guarantees on global convergence and exhaustive behavior normally associated with homotopy methods. However, the analyses presented provide a clear understanding of the relationship between linear and nonlinear perceptron networks, and thus a firm foundation for development of more powerful training methods. The geometric perspectives and generic topological results describing the nature of the solutions are further generally applicable to network analysis and algorithm evaluation.