The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.

. This paper presents a symbolic model checking algorithm for continuous-time Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a time-bounded until-operator and a novel operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady state-operator) and a Volterra integral equation system for timebounded until. We propose a symbolic approximate method for solving the integrals using MTDDs (multi-terminal decision diagrams), a generalisation of MTBDDs. These new structures are suitable for numerical integration using quadrature formulas based on equally-spaced abscissas, like trapezoidal, Simpson and Romberg integration schemes. 1 Introduction The mechanised verification of a given (usually) finite-state model against a property expressed in some temporal logic is known as model checking. For probabilistic...

Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an object-centered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and self-occlusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe...

Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of self-intersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model-based constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple two-dimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3-D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness. © 2000 Academic Press 1.

Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a time-bounded until operator to express probabilistic timing properties over paths as well as an operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady-state operator) and a Volterra integral equation system (for time-bounded until). We then show that the problem of model-checking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all formulas in the logic.

We develop a framework for 3–D shape and motion recovery of articulated deformable objects. We propose a formalism that incorporates the use of implicit surfaces into earlier robotics approaches that were designed to handle articulated structures. We demonstrate its effectiveness for human body modeling from video sequences. Our method is both robust and generic. It could easily be applied to other shape and motion recovery problems. 1.

Our HiBall Tracking System generates over 2000 head-pose estimates per second with less than one millisecond of latency, and less than 0.5 millimeters and 0.02 degrees of position and orientation noise, everywhere in a 4.5 by 8.5 meter room. The system is remarkably responsive and robust, enabling VR applications and experiments that previously would have been difficult or even impossible. Previously we published descriptions of only the Kalman filter-based software approach that we call Single-Constraint-at-a-Time tracking. In this paper we describe the complete tracking system, including the novel optical, mechanical, electrical, and algorithmic aspects that enable the unparalleled performance. 1.1 Keywords virtual environments, tracking, calibration, autocalibration, delay, latency, sensor fusion, Kalman filter, optical sensor 2. INTRODUCTION In 1991 the University of North Carolina demonstrated a working scalable optoelectronic head-tracking system in the Tomorrow'...

Loop blocking (tiling) is a well-known compiler optimization that helps improve cache performance by dividing the loop iteration space into smaller blocks (tiles); reuse of array elements within each tile is maximized by ensuring that the working set for the tile fits into the data cache. Padding is a data alignment technique that involves the insertion of dummy elements into a data structure for improving cache performance. In this work, we present DAT, a technique that augments loop tiling with data alignment, achieving improved efficiency (by ensuring that the cache is never under-utilized) as well as improved flexibility (by eliminating self-interference cache conflicts independent of the tile size). This results in a more stable and better cache performance than existing approaches, in addition to maximizing cache utilization, eliminating self-interference, and minimizing cross-interference conflicts. Further, while all previous efforts are targetted at programs characterized by the reuse of a single array, we also address the issue of minimizing conflict misses when several tiled arrays are involved. To validate our technique, we ran extensive experiments using both simulations as well as actual measurements on SUN Sparc5 and Sparc10 workstations. The results on benchmarks exhibiting varying memory access patterns demonstrate the effectiveness of our technique through consistently high hit ratios and improved performance across varying problem sizes.

In automated negotiation systems consisting of self-interested agents, contracts have traditionally been binding. Leveled commitment contracts—i.e. contracts where each party can decommit by paying a predetermined penalty were recently shown to improve Pareto efficiency even if agents rationally decommit in Nash equilibrium using inflated thresholds on how good their outside offers must be before they decommit. This paper operationalizes the four leveled commitment contracting protocols by presenting algorithms for using them. Algorithms are presented for computing the Nash equilibrium decommitting thresholds and decommitting probabilities given the contract price and the penalties. Existence and uniqueness of the equilibrium are analyzed. Algorithms are also presented for optimizing the contract itself (price and penalties). Existence and uniqueness of the optimum are analyzed. Using the algorithms we offer a contract optimization service on the web as part of ('Mediator, our next generation electronic commerce server. Finally, the algorithms are generalized to contracts involving more than two agents.

Line drawings provide an effective means of communication about the geometry of 3-D objects. An understanding of how to duplicate the way humans interpret line drawings is extremely important in enabling man-machine communication with respect to images, diagrams, and spatial constructs. In particular, such an understanding could be used to provide the human with the capability to create a line-drawing sketch of a polyhedral object that the machine can automatically convert into the intended 3-D model. A recently published paper (Marill 1991) presented a simple optimization procedure supposedly able to duplicate human judgment in recovering the 3-D "wire frame" geometry of objects depicted in line drawings. Marill provided some impressive examples, but no theoretical justification for his approach. In this paper we introduce our own work by first critically examining Marill's algorithm. We provide an explanation for why Marill's algorithm was able to perform as well as it did on the exa...