Showing papers on "Bounding overwatch published in 1995"

Topological relations in the world of minimum bounding rectangles: a study with R-trees

Abstract: Recent developments in spatial relations have led to their use in numerous applications involving spatial databases. This paper is concerned with the retrieval of topological relations in Minimum Bounding Rectangle-based data structures. We study the topological information that Minimum Bounding Rectangles convey about the actual objects they enclose, using the concept of projections. Then we apply the results to R-trees and their variations, R+-trees and R*-trees in order to minimise disk accesses for queries involving topological relations. We also investigate queries that involve complex spatial conditions in the form of disjunctions and conjunctions and we discuss possible extensions.

Fast Learning by Bounding Likelihoods in Sigmoid Type Belief Networks

Abstract: Sigmoid type belief networks, a class of probabilistic neural networks, provide a natural framework for compactly representing probabilistic information in a variety of unsupervised and supervised learning problems. Often the parameters used in these networks need to be learned from examples. Unfortunately, estimating the parameters via exact probabilistic calculations (i.e, the EM-algorithm) is intractable even for networks with fairly small numbers of hidden units. We propose to avoid the infeasibility of the E step by bounding likelihoods instead of computing them exactly. We introduce extended and complementary representations for these networks and show that the estimation of the network parameters can be made fast (reduced to quadratic optimization) by performing the estimation in either of the alternative domains. The complementary networks can be used for continuous density estimation as well.

Global optimization of nonconvex nonlinear programs using parallel branch and bound

Abstract: A branch and bound algorithm for computing globally optimal solutions to non-convex nonlinear programs in continuous variables is presented. The algorithm is directly suitable for a wide class of problems arising in chemical engineering design. It can solve problems defined using algebraic functions and twice differentiable transcendental functions, in which finite upper and lower bounds can be placed on each variable. The algorithm uses rectangular partitions of the variable domain and a new bounding program based on convex/concave envelopes and positive definite combinations of quadratic terms. The algorithm is deterministic and obtains convergence with final regions of finite size. The partitioning strategy uses a sensitivity analysis of the bounding program to predict the best variable to split and the split location. Two versions of the algorithm are considered, the first using a local NLP algorithm (MINOS) and the second using a sequence of lower bounding programs in the search for local minima. Runtime results for both versions are presented for a set of 50 test problems. In addition, a parallel version of the branch and bound algorithm is presented and tested. Parallelism is achieved by applying a separate processor to the bounding of each region. Each processor maintains a list of regions to be analyzed, and a load balancing scheme is used to balance the quality and quantity of regions available in each processor's list.

Upper and lower bounding techniques for frequency assignment problems

Abstract: We consider two variants of the radio link frequency assignment problem These problems arise in practice when a network of radio links has to be established Each radio link has to be assigned a particular frequency The interference level between the frequencies assigned to the di erent links has to be acceptable since otherwise communication will be distorted The frequency assignments have to comply with certain regulations and physical characteristics of the transmitters Moreover the number of frequencies is to be minimized because each frequency used in the network has to be reserved at a certain cost We develop several approximation algorithms for the problems which are based on local search and we compare their performance on some practical instances Lower bounding techniques based on nonlinear programming and the chromatic number of a graph are used to estimate the quality of the approximate solutions for these instances Partially supported by the EUCLID project RTP as part of CEPA Arti cial Intelligence

Document page decomposition using bounding boxes of connected components of black pixels

Abstract: Segmentation of document images can be performed by projecting image pixels. This pixel projection approach is one of widely used top-down segmentation methods and is based on the assumption that the document image has been correctly deskewed. Unfortunately, the pixel projection approach is computationally inefficient. It is because each symbol is not treated as a computational unit. In this paper, we explain a new technique which is highly tactical in the profiling analysis. Instead of projecting image pixels, we first compute the bounding box of each connected component in a document image and then we project those bounding boxes. Using the new technique, this paper describes how to extract words, text lines, and text blocks (e.g., paragraphs). This bounding box projection approach has many advantages over the pixel projection approach. It is less computationally involved. When applied to text zones, it is also possible to infer from the projection profiles how bounding boxes (and, therefore, primitive symbols) are aligned and/or where significant horizontal and vertical gaps are present. Since the new technique manipulates only bounding boxes, it can be applied to any noncursive language documents.

Method and apparatus for rendering graphical components on a display utilizing geometric constraints

Abstract: A method and apparatus for rendering statistical graphics which utilizes geometric constraints and bounding boxes to compute coordinate transformations at the time a graphical object is rendered. The invention transforms coordinates in an intrinsic coordinate system of a drawing element into coordinates in an absolute coordinate system of a computer display device. The geometric constraints tie the drawing elements together and define linear equality constraints between the initially unknown parameters while allowing computation of rotation and reflection parameters in advance and independently of the remaining initially unknown parameters. Rendering bounding boxes are used to define linear inequality constraints that require the rendering bounding boxes to be completely confined within a display bounding box of known size. Using the linear equality constraints, the linear inequality constraints and a cost function, the values of the remaining initially unknown parameters are computable such that both the linear equality constraints and the linear inequality constraints are simultaneously satisfied.

Method for creating spatially balanced bounding volume hierarchies for use in a computer generated display of a complex structure

Abstract: Disclosed is a method for processing an arbitrary collection of objects, forming a complex structure, into a hierarchy of bounding volumes, from a root volume bounding all objects, to sub-volumes bounding individual objects or assemblies thereof, for use as successive approximations to said objects in a computer generated display. The method includes the first step of creating a bounding volume for each of the objects. Selected bounding volumes are then processed through a combining algorithm determining whether or not, based upon a geometric relationship between the bounding volumes and the higher level, root volume, the selected bounding volumes can be combined. If it is determined that the bounding volumes can be combined, a new bounding volume is created with the combined volumes comprising sub-volumes thereof. This process systematically repeats and attempts to combine all sub-volumes. The combining algorithm preferably allows a combination if the volumes of the combination of the sub-volume is smaller than a fixed percentage of the parent volume. When a pair can combine, it is replaced by a box bounding volume that contains the pair as sub-volumes, and the process continues. In this way, a bounding volume hierarchy for all objects and assemblies within a complex structure is created.

The visual computation of bounding contours

Abstract: The problem of computing closed bounding contours from a visual image is addressed. The approach is motivated by the fact that many important image structures are heterogeneous and therefore cannot be segmented by traditional region-based methods based on homogeneity or smoothness constraints. Both psychophysical and computational aspects of the problem are studied. Psychophysical evidence is presented which shows that properties of bounding contour such as closure act as binding features for the segmentation of 2-D shapes, whereas texture (a region property) does not. These psychological results motivate an investigation of local and global issues in the computation of bounding contours for the purpose of figure/ground segmentation. Novel techniques for the local analysis of contour are presented which allow edges to be reliably detected and localized over a broad range of blur scale and contrast in images with shallow depth-of-field and shadows. Local estimates of contour blur are shown to be useful for computing depth segmentation from focal blur in complex images where the continuity assumptions required by existing Fourier techniques do not apply. It is hypothesized that in order to integrate contours fragmented by occlusion and insufficient contrast, the human visual system exploits a measure of geometric contour closure. The results of psychophysical experiments show that a measure for closure based on $L\sb2$ norm of contour gaps in psychophysically consistent. The existence of this measure is evidence for the computation of geometric closure by the human visual system. These psychophysical findings motivate an algorithm for computing closed bounding contours as cycles of curve tangents. Tangent cycles extracted from a variety of real images are shown to correspond to the bounding contours of 2-D image structures, many of which are heterogeneous over their interior. Thus closure computations are seen to complement region-grouping methods by extending the class of structures which may be segmented to include heterogeneous image structures.

Adaptive bounding techniques for stable neural control systems

Abstract: This paper considers the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities. The Lyapunov synthesis approach is used to develop state-feedback adaptive control schemes based on a general class of nonlinearly parametrized neural network models. The key assumptions are that the system uncertainty satisfies a "strict-feedback" condition and that the network reconstruction error and higher-order terms (with respect to the parameter estimates) satisfy certain bounding conditions. An adaptive bounding design is used to show that the overall neural control system guarantees semi-global uniform ultimate boundedness within a neighborhood of zero tracking error.

Robust, reduced-order modeling for state space systems via parameter-dependent bounding functions

Abstract: The problem of approximating a high-order system with constant real parameter uncertainty by a reduced-order model is considered. A parameter-dependent quadratic bounding function is developed that bounds the effect of uncertain real parameters on the model-reduction error. An auxiliary minimization problem is formulated that minimizes an upper bound for the model-reduction error. The principal result is a necessary condition for solving the auxiliary minimization problem which effectively provides sufficient conditions for characterizing robust reduced-order models.

Algebras of real analytic functions: Homomorphisms and bounding sets

Abstract: In this paper weare interested in subsets of a real Banach space on which different classes of functions are bounded.

Statistica: artificial neural networks for statistical data bounding

Abstract: A novel family of artificial neural networks (ANNs), Statistica, has been developed to estimate the statistical bounds of normally-distributed, multiple-time sampled data. These networks utilize bilinear error cost functions that provide rapid, uniform convergence to the desired statistical bounds. Preliminary simulations using Statistica on two- and three-dimensional datasets clearly demonstrate the bounding capabilities of this ANN. Extensions to higher dimensional datasets are currently underway. Potential applications of Statistica include establishing confidence bounds for time-series forecasts and bounding gain trajectories in adaptive control systems.