The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX cross-references are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The

We have created a system for capturing both the three-dimensional geometry and color and shading information for human facial expressions. We use this data to reconstruct photorealistic, 3D animations of the captured expressions. The system uses a large set of sampling points on the face to accurately track the three dimensional deformations of the face. Simultaneously with the tracking of the geometric data, we capture multiple high resolution, registered video images of the face. These images are used to create a texture map sequence for a three dimensional polygonal face model which can then be rendered on standard 3D graphics hardware. The resulting facial animation is surprisingly life-like and looks very much like the original live performance. Separating the capture of the geometry from the texture images eliminates much of the variance in the image data due to motion, which increases compression ratios. Although the primary emphasis of our work is not compression we have investigated the use of a novel method to compress the geometric data based on principal components analysis. The texture sequence is compressed using an MPEG4 video codec. Animations reconstructed from 512x512 pixel textures look good at data rates as low as 240 Kbits per second.

We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edge-wise partial correlation coefficients. This representation holds for a large class of Gaussian graphical models which we call walk-summable. We give a precise characterization of this class of models, and relate it to other classes including diagonally dominant, attractive, nonfrustrated, and pairwise-normalizable. We provide a walk-sum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. The walk-sum perspective leads to a better understanding of Gaussian belief propagation and to stronger results for its convergence in loopy graphs.

the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra actuators; the expectation derived from a good model can minimize sensing requirements. Despite this, most robot systems attempt to dominate or nullify task mechanics, rather than exploit them. There has been little e ort to understand the manipulation capabilities of even the simplest robots under more complete mechanics models. This thesis addresses that knowledge de cit by studying graspless or nonprehensile manipulation. Nonprehensile manipulation exploits task mechanics to achieve a goal state without grasping, allowing simple mechanisms to accomplish complex tasks. With nonprehensile manipulation, a robot can manipulate objects too large or heavy to be grasped and lifted, and a low-degree-of-freedom robot can control more degrees-of-freedom of an object by allowing relative motion between the object and the manipulator. Two key problems are determining controllability of and motion planning for

Abstract. We give an algorithm for learning a permutation on-line. The algorithm maintains its uncertainty about the target permutation as a doubly stochastic matrix. This matrix is updated by multiplying the current matrix entries by exponential factors. These factors destroy the doubly stochastic property of the matrix and an iterative procedure is needed to re-normalize the rows and columns. Even though the result of the normalization procedure does not have a closed form, we can still bound the additional loss of our algorithm over the loss of the best permutation chosen in hindsight. 1

We are concerned with finding a few eigenvalues of the large sparse nonsymmetric generalized eigenvalue problem Ax = Bx that arises in stability studies of incompressible fluid flow. The matrices have a block structure that is typical of mixed finite-element discretizations for such problems. We examine the use of shift-invert and Cayley transformations in conjunction with the implicitly restarted Arnoldi method along with using a semi-inner product induced by B and purification techniques. Numerical results are presented for some model problems arising from the ENTWIFE finite-element package. Our conclusion is that, with careful implementation, implicitly restarted Arnoldi methods are reliable for linear stability analysis. AMS classification: Primary 65F15; Secondary 65F50 Key Words: eigenvalues, sparse nonsymmetric matrices, Arnoldi's method. 1 Introduction Mixed finite-element discretizations of time-dependent equations modelling incompressible fluid flow problems ty...

The word idempotency signifies the study of semirings in which the addition operation is idempotent: a+ a = a. The best-known example is the max-plus

Stochastic subgradient methods are widely used, well analyzed, and constitute effective tools for optimization and online learning. Stochastic gradient methods ’ popularity and appeal are largely due to their simplicity, as they largely follow predetermined procedural schemes. However, most common subgradient approaches are oblivious to the characteristics of the data being observed. We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. The adaptation, in essence, allows us to find needles in haystacks in the form of very predictive but rarely seenfeatures. Ourparadigmstemsfromrecentadvancesinstochasticoptimizationandonlinelearning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. In a companion paper, we validate experimentally our theoretical analysis and show that the adaptive subgradient approach outperforms state-of-the-art, but non-adaptive, subgradient algorithms. 1

Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schur-concavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schur-concave functions, which are the class of functions consistent with the so-called Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schur-concave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.

Programming by demonstration is a promising approach to automatic robot programming, however methods are required to remove suboptimal actions that can be demonstrated by end users. In this paper we use the partial knowledge of Configuration Space (C-space) derived in previous work to remove suboptimal actions from a demonstration. Our idea is to use demonstrated paths to predict what regions in C-space are obstacle free. Suboptimal actions in a demonstration are then avoided by planning alternative actions that pass through the obstacle free regions. Experimental results show the validity of the approach. A demonstrated path containing significant sub-optimality was converted by the approach into a short, efficient path suitable for execution by the robot.