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.

A novel scheme for the detection of object boundaries is presented. The technique is based on active contours evolving in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of several objects and both interior and exterior boundaries. The proposed approach is based on the relation between active contours and the computation of geodesics or minimal distance curves. The minimal distance curve lays in a Riemannian space whose metric is defined by the image content. This geodesic approach for object segmentation allows to connect classical "snakes" based on energy minimization and geometric active contours based on the theory of curve evolution. Previous models of geometric active contours are improved, allowing stable boundary detection when their gradients suffer from large variations, including gaps. Formal results concerning existence, uniqueness, stability, and correctness of the evolution are presented as well. The scheme was implemented using an efficient algorithm for curve evolution. Experimental results of applying the scheme to real images including objects with holes and medical data imagery demonstrate its power. The results may be extended to 3D object segmentation as well.

We present an approach to modeling with truly mutable yet completely controllable free-form surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patch-based approaches. Triangulated point sets are used to approximate these smooth variational surfaces, bridging the gap between patch-based and particle-based representations. Automatic refinement, mesh smoothing, and re-triangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around in the surface that oriented particles enjoy. The resulting surface triangulations are constructed and maintained in real time. 1 Introduction ...

This article analyzes the behavior of local propagation rules in graphical models with a loop.

A new regression technique based on Vapnik's concept of support vectors is introduced. We compare support vector regression (SVR) with a committee regression technique (bagging) based on regression trees and ridge regression done in feature space. On the basis of these experiments, it is expected that SVR will have advantages in high dimensionality space because SVR optimization does not depend on the dimensionality of the input space. 1. Introduction In the following, lower case bold characters represent vectors and upper case bold characters represent matrices. Superscript "t" represents the transpose of a vector. y represents either a vector (in bold) or a single observance of the dependent variable in the presence of noise. y (p) indicates a predicted value due to the input vector xx (p) not seen in the training set. Suppose we have an unknown function G(xx) (the "truth") which is a function of a vector xx (termed input space). The vector xx t = [x 1 , x 2 , ..., x d ] has ...

Absfruet-A new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used “smoothness constraint” ’yl”. regularization. The interpretation of the smoothness constraint is utilized as a “fractal prior ” to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatially-varying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of ill-posed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.

This article develops a dynamic generalization of the nonuniform rational B-spline (NURBS) model. NURBS have become a de facto standard in commercial modeling systems because of their power to represent free-form shapes as well as common analytic shapes. To date, however, they have been viewed as purely geometric primitives that require the user to manually adjust multiple control points and associated weights in order to design shapes. Dynamic NURBS, or D-NURBS, are physics-based models that incorporate mass distributions, inertial deformation energies, and other physical quantities into the popular NURBS geometric substrate. Using D-NURBS, a modeler can interactively sculpt curves and surfaces and design complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and weights, but also through direct physical manipulation, by applying simulated forces and local and global shape constraints. D-NURBS move and deform in a physically intuitive manner in response to the user's direct manipulations. Their dynamic behavior results from the numerical integration of a set of nonlinear differential equations that automatically evolve the control points and weights in response to the applied forces and constraints. To derive these equations, we employ Lagrangian mechanics and finite-element-like discretization. Our approach supports the trimming of D-NURBS surfaces using D-NURBS curves. We demonstrate D-NURBS models and constraints in applications including the rounding of solids, optimal surface fitting to unstructured data, surface design from cross-sections, and free-form deformation. We also introduce a new technique for 2D shape metamorphosis using constrained D-NURBS surfaces.

We present a method for the efficient re-rendering of a scene under a directional illuminant at an arbitrary orientation. We take advantage of the linearity of the rendering operator with respect to illumination for a fixed scene and camera geometry. Re-rendering is accomplished via linear combination of a set of pre-rendered "basis" images. The theory of steerable functions provides the machinery to derive an appropriate set of basis images. We demonstrate the technique on both simple and complex scenes illuminated by an approximation to natural skylight. We show re-rendering simulations under conditions of varying sun position and cloudiness.

Stone is widespread in its use as a building material and artistic medium. One of its most remarkable qualities is that it changes appearance as it interacts with the environment. These changes are mainly confined to the surface but involve complex volumetric effects such as erosion and mineral dissolution. This paper presents an approach for the modeling and rendering of changes in the shape and appearance of stone. To represent stone, we introduce a slab data structure, which is a surface-aligned volume confined to a narrow region around the boundary of the stone. Our weathering model employs a simulation of the flow of moisture and the transport, dissolution, and recrystallization of minerals within the porous stone volume. In addition, this model governs the erosion of material from the surface. To render the optical effects of translucency and coloration due to the composition of minerals near the surface, we simulate the scattering of light inside the stone using a general subsurface Monte Carlo ray tracer. These techniques can capture many aspects of the time-dependent appearance of stone. We demonstrate the approach with models of granite and marble statues, as well as a sandstone column.

This paper introduces a novel interface for digitallyaugmented cooperative play. We present the concept of the "athletic-tangible interface," a new class of interaction which uses tangible objects and full-body motion in physical spaces with digital augmentation. We detail the implementation of PingPongPlus, a "reactive ping-pong table", which features a novel sound-based ball tracking technology. The game is augmented and transformed with dynamic graphics and sound, determined by the position of impact, and the rhythm and style of play. A variety of different modes of play and initial experiences with PingPongPlus are also described. Keywords tangible interface, enhanced reality, augmented reality, interactive surface, athletic interaction, kinesthetic interaction, computer-supported cooperative play. INTRODUCTION When an expert plays ping-pong, a well-used paddle becomes transparent, and allows a player to concentrate on the task -- playing ping-pong. The good fit of grasp is vit...